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Les diagrammes suivants illustrent la m^thode. 1 2 3 1 2 3 4 5 6 1 V EXAMINATION PAPEES ni ARITHMETIC, u filler * (Ro'n. ({Ebtttaibnal Sitxm. EXAMINATION PAPERS IN ARITHMETIC DESIGNED FOB USB IN HIGH AND PUBLIC SOHOOLB, AND ESPEOIALLT ADAPTED FOB THE PBEPABA- TION OF CANDIDATES FOB THE VABIOUS EXAMINATIONS IN ONTABIO. BY /..e^ J? AY MoLELLAN, M.A., LL.D., Inspector of High Sohool$, ▲ MS THOMAS KIBKLXnD, M.A., BcUnee Mattw, Normal School, Toronto, TORONTO : ADAM MILLER ft CO., 11 WELLINGTON STREET -WEST. 1877. QA 'if M32. Entered accordiag to the Act of the Parliament of Canada, in the year one thomand eif ht hundred and seventy-seven, by Adam Millbr k €&» in the Office of the Minister of Agriculture. {if PREFACE. This work has been prepared at the request of many Teachers and Inspectors, to meet an acknowledged want in connection with the High and Pubhc Schools of this country. It contains all the papers that have been set at the Provincial Examinations since 1871, together with a large number of additional questions, original and selected, some of which have been specially prepared by Mathematical teachers of unquestionable ability. The questions have been arranged in sets, similar in character and about equal in difficulty to those usually given at the various examinations instituted by the Educational Department of Ontario. This arrangement, it is believed, will be found of great advantage, as affording the best means of inteUigent training and the best preparation for the examinations referred to. To be successful at these examinations, students must be trained to a complete independence of the mechanical rules and routine of the ordinary text- books. This independence, with the self-reliance result- ing from it, is to be secured, not by solving questions set under given rules and formulas, but by constant practice in properly prepared sets of problems, in which neither rule nor answer is at hand to furnish clews and crutcb's to the halt and blind. For such practice, abundant materials wiU be found in the following collection c- problems, which is sufficiently large and varied to enable all classes of students to make the necessaiy prepara- tion for the searching examinations that now form so prominent a feature in the educational system of } 1 I. II !r if Mi : t * ; ! i PBEFAOE. Ontario. The work can be used with great ctdvantage by all pupils that have mastered the fundamental rules ; for such should at once begin to solve pboblems, and write out solutions with a proper regard to neatness and method. In maintaining the superiority of the "Unitary Method," it is not intended to assert that nUet should be entirely ignored. On the contrary, rules have their proper place ; but the pupil should be the master of the rule, not the rule the master of the pupil. To secure intellectual training^ independent methods must be fol- lowed ; but for the sake of practical facility in reaching results, rules may be framed as logical inferences from independent investigation. Take for example question 7, page 17 ; the independent solution leads to an easy practical rule for solving all such questions, e,g. : 255 ^ •06 = 6100, then add two % for the price of the cot- ton ; and (as a similar investigation will show) mbtract three % for the price of the city property — and so a general rule can easily be stated. Of course the results are more easily reached by the rule in this case ; but there is little or no intellectual discipline in the applica- tion of the ruUi though there is in the investigation which leads to it. The Unitary Method, the general theory of Arithmetic, and the utility and true function of TuUa as formulating the results of independent reasoning, will be found fully treated in the Canadian Edition of Hamblin Smith's Arithmetic. The Publishers will be glad to receive information as to any errors which may have crept into the work, and to consider any suggestions which may lead to an improvement of a future edition. ToBONTo, April, 1877. CONTENTS. Chapter I. The Unitary Method — Solutions showing its application to a variety of Problems 1-84 Chapter IE. Elementary Bules, Measures and Multiples, Vulgar and Decimal Fractions 86-62 Chapter III. Examination Papers for entrance into High Schools and Collegiate Institutes 68-111 Chapter IV. I Examination Papers for Candidates for Third Class Certificates 112-141 Chapter V. [Examination Papers for Candidates for the In- termediate Examination and Second Class Certificates 142-224 Chapter VI. Examination Papers for Candidates for First Class Certificates and University Honors... 225-290 fl -■ '. r < } I t I 8 Q C t: 1] u 8( CI aj THE UNITARY SYSTEM. The Unitary System may be described in general terms as the method of solving arith tical problems without reference to formal rules. It :■ . so named from tlie fact that in solving questions by independent analy- sis, we usually reason from the given elements to unity, and from unity to the required result. The unit, how- ever, is not necessarily one of the given elements ; to secure clearness in reasoning, or facility in solution, the required result itself, or any element of the question logically connected with that result, may be taken as the unit of reference. In attaining the two important objects of instruction in arithmetic — valuable intellect- ual disciphne and practical mastery of the subject — the superiority of the Unitary Method over the cumbrous and mechanical processes of the ordinary text-books, will hardly be questioned. These methods are of a purely routine and arbitrary character, t<=^nding to induce a " numb rigidity " of intellect, as well as a hazy and all but worthless knowledge of the subject. On the other hand, the Unitary Method, demanding as it does the closest attention and severest exercise of the reason- ing faculty, familiarizes the mind with the forms oi strict logical inference, and tends to secure that power of continuity of thought which is the very essence of intellectual energy. It is maintained by the greatest scholars and the most successful educators — mathemati- cal and non-mathematical — that arithmetic thus taught affords a logical exercise of the highest value. The stu- dent is compelled to set clearly before himself the pre- THE XmiTABT 8TSTBM. »!' 1)1 r i , 1 mises from which he reasons, and to comprehend so thoroughly the necessary connection of the successive steps in the investigation, that he can hardly fail to acquire logical habits of thought and an acute perception of the essence and form of sound reasoning. The great mass of students will never attain, in even a limited extent, these invaluable results, unless the logical sub- jects of the school curriculum are logically taught. They have no time to study treatises on formal logic ; but so far as truly practical results are concerned, equal benefit may be derived by constant exercise in the com- mon logic of arithmetic — a subject which all must study, and which, taught on the Unitary Method, has been not inaptly designated a veritable Course of Logic for the People. The method will be found equaUy effective in giving a thorough mastery of the subject. In the attempt to produce inteUigent, practical arithmeticians, the old mechanical method has been tried and found wanting. Under its influence students become slaves of rule and formula — ^not capable of interpreting the formula^ and entirely in the dark as to the reasons of the rule. The slave of rules can never have an intelligent command of the subject, and can never be truly practical. He only is truly practical whose knowledge is founded on reason- ing which he fully comprehends, and who has been so thoroughly exercised in logical analysis that he is inde- pendent of arbitrary rules, and obeys nd laws but the necessary laws of strict logical method. Bule-taught ** practical " arithmeticians are usually found to be any- thing but intelligently practical in the solution of prac- tical questions, unless they are charitably told what rule to apply. They apply the rule to the problems is^^ven THE UNITABY SYSTEM. 8 under it ; they work mechanically ; they walk by a blind faith in the infaUibility of the rule-maker ; they arc mere machines except as to accuracy, in which the machine has the advantage ; they become, perhaps, expert in the making of figures, which, whatever its value as an exercise of the muscles of the fingers, is absolutely worthless as an exercise of mind. Hence i< is that students of this class are utterly bewildered a1 an examination demanding an intelligent knowledge oi the subject, and a moderate power of independent thought ; while those trained to habits of strict analysis — taught to reason with mathematical consistency from the known to the unknown — come up to such examina- tions with a consciousness of power, and a calm self- rehance which are essential to the highest success. The following soluitions vidll serve to illustrate the simphcity and power of the Unitary Method, as well as its value as a logical exercise. It is believed that those who thoroughly master this chapter, and apply its principles to the solution of the Examination Papers in which they are more especially interested, will have but Httle difficulty in passing any examination for which they thus faithfully prepare themselves. The solutions, it wiU be seen, are written out with consider- able minuteness, all the successive steps in the reason- ing being, in general, given. This is, without doubt, the true course to follow, until familiarity with the method, and considerable power of analysis have been acquired; afterwards, several steps may be combined, and the solution much simplified. Decimal fractions have been but Uttle used, not because they are to be dis- carded, but because analysis by vulgar fractions is more readily understood. Of coarse, the pupil is in due time THE UMITABT SYSTEM. ii; ' to be taught, for example, that ^\j of a quantity may he obtained by multiplying it by '06 ; after proper instruc- tion and reasonable practice he will be able to use either vulgar or decimal fractions, as either affords the easier solution of any proposed problem. Various other solutions of these problems may bo given ; the unit may be varied, or may be obtained in different ways, or by a shorter process ; these yariations will afford excellent practice for the student, as well as for the teacher who wishes to make himself completely master of the Unitary Method. For example : K $16 will buy 20 lbs. of tea, what quantity will $40 buy? If $16 will buy 20 lbs. .-. $1^ buys 1 lb. And$|^( = $l)willbuylilbs. .-. $40 will buy 1 J x 40. (Since f^ is } more ih&n |^.) If $16 buys 20 lbs. .-. $40 will buy 20 x 2}, since 40 is 2^ times 16. And 30 on with any of the following solutions. If $16 buys 20 lbs. .-. 1 buys 4f " And 40 will buy f^x 40. M V. A THE UNITARY METHOD. I. — PBOPORTION, SIMPLE AND OOHPOUND. 1. If 15 barrels of flour cost $111, what will 86 barrels cost ? 15 cost 111. ••• 1 " w- and 85 " i^^^=$259. 2. If 25 lbs. of tea cost $16, how many lbs. con be bought for $56 ? $16 wiU buy 25. .-. 1 " H. and 56 " ff x 66=87^ lbs. 8. If 56 men do a work in 21 days, how long will 24 men require to do it ? Time for 56 men is 21. " 1 man " 21 x 56. and " 24 men " ^i^ =49 days. 4. If the 4 lb. loaf costs 11 cents when flour is $6 a bbl., find its cost when flour is $7^ a bbl. $6 price demands 11 cents a loaf. .-. 1 « V " and 7^ " V x7^=18f cents. \ 5. A bankrupt owes $8000 ; his assets are $1740. What sum wiU a creditor receive whose claim is $850 ? On $8000 $1740 is received. and " 850 ^^x360=$208. I I If H I ■ : In li' f: \ 6 THE UNITABT METHOD. 1 / 6. The expense of carpeting a room was $100 ; if the breadth of the room had been 4 ft. greater, the ex- pense would have been $120. Find the breadth. $20 pays for 4 ffc. of breadth. 1 (( 4 (« ..X -^jf and 100 «« ^x 100=20 ft. 7. A man has $2340 per annum, after paying an income tax of 2^ cents in the dollar ; find his gross income $0.97^ is left of $1 income (i.e. after tax is paid). .-. 1 " ^\ and 2840 " ^^ x 2340=^ x 2340=$2400. 8. What quantity of carpet 27 in. wide will cover a room 18 ft 6 in. long by 12 feet 4 in. wide ? Koom contains 18^ xl2i=^^^ sq. ft. Since the carpet is 2^ ft. wide, we get 2^ f q. ft. carpet in 1 ft. length. . ..1 ^ —-ff It f^^^juLM. « ♦xtijiisiomfb. \f 9. If ^ of a ton of coal cost $4.26, what will 1^ - tons cost ? ^ cost $4}. .-.1 (( and li^ TS (( in ¥x SS 33 — TT'^aT- / 10. K 20 men can dig 60 yds. of earth in 4 days, how many yards can 30 men dig in 9 days ? 20 men in 4 days dig 60. 1 « 4 " f^. It f« «0X4* THE UNITABT METHOD. 80 80 (( or one cent each. 18. Flour is sold for $6 a bbl., at a loss of 17% ; find what selling price would give 16%. Sold at 17% loss, i.e., 100 sold for 88. To gain 16% 100 should sell for 116 ; heno€ $88 must bring 116. 6 " 1^6x6=8||. J 14. If 8% more be gained by selling a horse for 38 than by selling him for $824, find his original price. 888—824=9 increase. 8% gain from increase of 9. .'.1 " " 8. and 100 " ** 800, which was .-. the price. m. — PBOPORTIONil. PAETS, PARTNERSHIP, OHAm BULB, EXCHANGE, ALLIGATION. "^ 1. Divide $600 among A, B and in the ratio of 3, 4, 6. V THB UNITABT METHOD. 11 of « « 8+ 4 4-5-12, therefore $12, A gets 8, £ 4, 600, " ^x600 " tVx600 -160, ' 200, C 6. ^xOOO 260. 2. A bankrupt owes three creditors $620, $470 and $380 respectively ; his assets amount to $688. Find each man's share. 620+470 + 880-1470. A debt of $1470 is discharged with $688. (( 888 9 T¥7TT — S' 1 and 620 «• |x 620=248. ; "^70 «• 1x470=188. 880 «« 1x880=162. 8. Divide $980 among A, B, C, and D, so that A's share may be to B's as 2:8, B's to C's as 4:6, and O's toD'sas8:6. Take As share as the unit; A's is to B's as 2:8, i. e. B's=| A's; B's is to C's as 4:6, i.e. C's=| B's; O's is to D's as 8:6, t. e. D's=| O's. A's is 1, B's " f O's " I B's=|x f=Y. D's" 4 C's=4x V=V• .^ill^/the shares==l+|+V + y=7i times A's share. 74 times A's=980. A's=980-7i=124, B's=| x 124=186. 0's=| X 186=232.60, D's=^ x 282.60=887.60. 4. A and B join in business ; A puts in $700 for 12 months, and B $600 for 18 months. Divide a profit of $1306 equitably between them. 700 for 12 months=8400 for one month. ^00 " ^8 " =9000 '< 12 THE UNITABY METHOD. !>SI !i li'^ 1 m \ N / Tlie profits must therefore be divided in the ratio of 84:90=14:15. 14 + 15=29. Of 29, A gets 14, • " 1 « If and " 1805 " ^| x 1806 or, A's=680, B's=675. B 15. 27- n ^i X 1806. 5. Two merchants, A and B, engaged in business, with capitals in the ratio of 6 to 7 ; at the end of 5 months they withdrew ^ and ^ of their capitals re- spectively. Divide fairly between them the year's profits of $8092. Take A's capital as the unit. B'8=^ A's. Then A has 1 for 5 months +f for 7 months=10-| for one month. B has I for 6 months + (|— J of ^) for 7 months=15^ for one month. Which numbers give the ratio in which the profits are to be divided. 103:16^=818:465. 818+455=778. Of 773 A gets 818, B gets 456. (« 1 (( 318 .-. "8092 " ff|x8092, or, A's=1272, B's=1820. 6. In a certain constituency the total number of votes was 1800 ; in an election of a member for the Legislature the votes polled by the candidates were in the ratio of 8 to 6, and the winning candidate had a majority of 869. How many voters did not go to the poU? The winning man had a majority of 8 in 18 votes polled. ti « 400 Iff X 8092. and <( (( 1 {(13 (I 869 (( V X 869=1599— total poUed, THE UNITARY BfETHOD* 18 .-. 1800- 169fl—201 not polled. 7. A and B are partners in trade ; A contributes 40% of the joint capital for 10^ months, and B receives I of the gain. Find^'s period of investment. 40%=§ ; ^ for 10^ month8= V for 1 month. Profit of f arises from y for 1 month. .*. " * " i and " f "7 " which is the product of B's stock by time of investment ; but B's stock is I of whole capital, .'. 7-T-f =llf B's time. , b. If 4 lbs. of tea be worth 40 lbs. of sugar, and 8 lbs. of sugar be worth 1^^ lbs. of coffee, and 8 lbs. oi coffee be worth 12 lbs. of biscuits, how many lbs. oi biscuits are worth 168 lbs. of tea ? 1 lb. tea = 10 lb. sugar. 1 lb. sug. = ^\ lb. coffee. 1 lb. coffee = 4 lb. biscuits. 1 lb. tea = 10 X y^ x 4. and 168 lb. i< 10x^x4x168=1260. 9. The exchange between London and Frankfort is 11 florins 62 ki-eutzers for the & sterling ; the exchange between Paris and Frankfort is 20 francs for 9 florins 20 kreutzers. What is the exchange between London and Paris, taking a florin as equal to 60 kreutzers. 9^ florins=20 francs, .". 1 florin=^^=y francs. Also, llff florins=£l, .-.1 florin=£l-r-llf§=je-^. Hence £y\^=y francs. .-. £1= V X VbP =25^ francs. 10. Calculate the ratio between the values of gold and silver, it being given that 2 lbs. of standard gold are coined into 89 guineas, and 1 lb. of standard silver is coined into 66 shillings, and that ^ of standard gold u TBB UNITABT METHOD. I < and ^ of standard silver are alloy. Here 11 lbs. pure gold=12 lbs. standard, and 87 lbs. pore silver=40 lbs. standard ; we have, therefore, 1 lb. pure gold:ss4^ st. gold. 1 lb. St. " =i»|^ shiUings. 1 shilling =^ lb. st. silver. 1 lb. st. silver :=f ^ lb. pure silver. .-. 1 lb. pure gold.-=|^ X ^^^ X A X |J=14|fU lbs. pure silver. 11. A merchant in Montreal owes another in Lisbon 1628| nulrees, and he resolves to remit through Lon- don, Amsterdam and Paris ; exchange between Montreal and London is at 9^% ; between London and Amster- dam, £1 sterling for £1^ Flemish ; between Amsterdam and Paris, £1 Flemish for 18 francs ; and between Paris and Lisbon, 8 francs per 460 rees. If the ex- penses of this circuitous course be 2^ per cent., what will it cost the Montreal merchant to settle his Lisbon account ? (1000 rees=l milree.) Since stg. exchange is 9^, .*. £9= $40 (1.096). Also, 8 francs=460 rees=-/;Aftr= A lailrees. we have, there- tore, 1 Milree = '^ francs. 1 Franc = ^ Flem. £, 1 Flem.j^. = ll Eng. ^. 1 Eng. £. = 40 X 1.096 dollars debt. $1 debt = *A1==$M actually paid (since ex- pense = 2i^, or.97i debt, is paid with 100). vl628f Miboes = V x iVx^x*o?^^;»<* x i_3|87 x *§ = 2190. 12. How much sugar worth 6 cts., 7 ots., 12 cts., and 18 ots. per lb. will form a mixture worth 10 ots. per lb. ? THB UNITABY METHOD. 16 By selling at the average prioe (10) we have 6 ots. gain on 1 lb. (^ 6 .'. 1 ot. gain on \ lb. 8 cts. gain on llh. (3^ 7 .'. 1 ct. gain on ^ lb. 2 ots. loss on 1 lb. @ 12 ;. 1 ct. has on ^ lb. 8 cts. loss on 1 lb. (^ 18 .*. 1 ct. Iohi^ on \ lb. A.nd with every cent gain we must take a cent loss^ hence we have *@ 7 i@ 18; We may also combine gains and losses thus : i@18 *@ 7 i@ 12 '8 @ 6. 6 @ 18. 2 @ 7. ^8 @ 12. 13. How much sugar worth 10 ots., 18 ots., 15 ots., 17 cts., and 18 cts., will make a mixture worth 16 cts. ? 6 cts. gain on 1 tb. (^ 10, .*. 1 ct. gain on ^ lb. ct gain on 1 lb. @ 18, .'. 1 ct. gain on ^ lb. gain on 1 lb. (^ 15, .*. 1 ct. gain on 1 tb. loss on 1 lb. (^17, .'. 1 ct. loss on 1 lb. loss on 1 lb. (^ 18, .'. 1 ct. loss on ^ lb. Each cent gain must be balanced by a cent loss^ and hence one of the losses (it is immaterial which) must be taken tunce. 8 1 1 2 ({ «( (< .*. we have ^ @ lOx 1 at 10; i @ 18 2 " 18. 1 @16 or 6 " 15. 1@ 17 6 " 17. 1 @ la 6 " 18. Any gain may be combined with any loss ; e. g. -i 16 THE UNITABY METHOD. i @ 10) 1 ; i @ 18) 1 ; 1 @ 15. i @ 18j "~ 8 1 @ 17] 8 1 @ 17. .*. we have 1 @ 10. 1 @ 13. 1 @ 15. 4 @ 17. 8 @ 18. They may, of course, be combined in various other ways, giving, for example : 1 @ 10 2 @ 18 1 @ 15 7 @ 17 8 @ 18 8 @ 10 8 @ 18 8 @ 15 10 @ 17 10 @ 18 2 @ 10 1 @ 18 8 @ 16 4@ 17 7 @ 18 1 @ 10 8 @ 18 2 @ 15 9 @ 17 4 @ 18 From an examination of the above analysis, may be deduced a very simple and convenient practical rule, which will be given in the Canadian Edition of Hamblin Smith's Arithmetic. rv. — COMMISSION, INSURANCE, ETC., STOCKS. Y 1. An agent received $40.62^ for selling a house / \ worth $1625 ; find his rate per cent, of commission. / $1625 gives |40.62i. (( 40-e2 t 1625 • And 100 " ^^*'x 100=2i. 2. A broker received $46.50 for buying stock on a commission of f per cent.; how much stock did he buy*? Com. of f received on 100. 1 " 100^1=160. And 46.50 " 160x46^=7440. 8. A merchant in Toronto sends a commission mer- chant in Montreal $8120, instructing him to purchase ^oods, reserving his commission at 4 per cent.; find his sommission. THE UMITABY METHOD. 17 4 JL -Lx 8120=120. On $104 he gets $4 commission. And" 8120 " ^ \/ 4. For what amount must property worth $7600 be A insured, at 6 per cent., so that in case of loss both the ' premium and the value of the goods may be recovered ? To realize 95 we must insure 100 ( «^^^5^'") «( 1 t( 100 30 " 7600 " f^x 7600=8000. 5. A man allows his agent 5 fo for collecting his rents ; he spends 14f , paying on this $16 more than was received for the entire risk ; find the amount of the risk. 1 J ^^^ •*• saves ^i^. The 2nd year his gross income is 25^0 (=^) more than 1st year=^. His personal expenses=§+12^yo of f =f. His income tax=2yo oi ^ = -^oi ^ —A* . • . his total outlay =i + ^ =M' «« saving=^~|^ =^. .•.difference between the two savings=J^— t^=^=» |200, and 1 =$1200 » original income. THE UNITABY METHOD. 21 16. How much currency is required to purchase U. S. 6^° bonds, interest payable in gold, to yield an income of $796 in currency, gold being at a premium of 6%, and the broker's commission being ^% on the par value of the bonds ? ^ 100 gold=106 currency. • 1 tl log.. 6 .83 and 6 " =fg^ x 5=4^ income ^ in currency. {% income from JOO bonds. .-. 1 " 100--fJ=l00x|§. and 796 " 100 -r- ^ x 796=16000 in bonds, on which ^o has to be paid. 100 gives ^. 1 " J -100. 16000 " ^x 15000=871. .•.whole amount required=16037.50 V. — MISCELLANEOUS PBOBLEMS. 1. A can do a piece of work in 8 days, B in 4 days, and C in 8 days ; in what time will all working together doit? A does ^ of the work in 1 day, B ^, and C i. ,\All do ^+i+i in 1 day, 8 + 6 + 3. 94 1 (C m TT day, / ■h and 1 in ^xU=zl-^. 2. A man engages to do a piece of work in !^0 days I for $80 ; after doing J of it in 16^ days, he finds he cannot complete it in the time, 8.nd he gets the assist- ance of another workman, and they together finish it in the allotted time. How long would the second man take to do the whole work, and how ought the $80 to be divided between them ? 22 THE UNITABY METH' ']!> i f t A does f of the work in lo^ days, andl " L»ix8=28. 3 i was done in 15^ days. ^ has to be done in the re- maining 4f days. * In 1 day A does ^. .-. 4f " ^x4f=^; hence , i— W=A=A> wliat B ' / SIMPLE RULES. I. 1. Explain why in the addition of numbers the oper- ation is begun at the unit's place. Is this necessary ? 2. What is the difference between the aggregate of 1050, 826, 1769, 150801, and a million ? Show that the same difference is obtained by taking one of the numbers from a million, another from the remainder^ and so on for the rest of the numbers. 8. How may the accuracy of the process of subtrac- tion be verified ? Give an example. Substraot 819 from 918, explaining the process. 4. A merchant exchanges a stock of goods worth $6725, and a house worth $8120, with a farmer for a farm valued at $5900, — the farmer paying the balance in money. "What sum must the merchant receive ? 5. Upon what principle is the ordinary method of multiplication based ? Is there any advantage in be- gin uiug with the right-hand figure ,^1) of the multipli- oaud, (2) of the multiplier? 6. Exemplify the truth that two or more factors will give the same product in whatever order they are multiplied 7. A speculator bought 150 head of cattle, and 47 mules. He made a profit of $18 a head on the former, ■Sf 86 EXAMINATION PAPBBS IN and $17 each on the latter; what was gained by the speculation ? 8. What is the object of division ? In what cases may it be considered as a shortened form of subtraction? Kjf-' 9. If the quotient be 6000 when the divisor is 2001 and the remainder 100, what is the dividend 9 10. Divide 10149 by 7 and the quotient by 6 ; thence deduce the true remainder, and show that it is the same as affcer the division of 10149 by 85* n. ^ ^ |i '. ¥ 1. What number is that to which if 88 and 5 times 88 be added, and the sum so found be increased by 7 times itself, « he total sum is 2400 ? a. A lorM- "R $9780 ; B repays A by giving him bank stc&Ii to tlie amount of $1946, a farm worth 4 times as i n?h as tlio bank stock minvs $999, and the balance in casu , how rir»??h cash did B pay A ? 8. How much time, in the course of 88 years, will a person who rises at 6 o'clock a. m., gain over another who rises at 8 o'clock, supposing both to go to bed at 10 p. m., and the year to be 866^ days ? 4. If the quotient of a divison question be -j^ of the divisor, and the divisor be 88 times greater than the remainder, find the dividend when the remainder is 212. 6. In 1876 a call of £22 per share was made on the convertible five per cent, stock issued at £90, and the sum realized was £94754 ; find the number of shares issued. 6. Find the circumference of a wheel which revolves 1460 times in a mile. 7. When A dies at the age of 67, B is 81 years old ; >■ • SIMPLE BULES. 87 B dies at the age of 59, when is 26 ; at O's death, -when he is 70, D is 48 and dies 26 years after C ; tiud atie interval between A's birth and D's death. 8. A dealer in horses gave $9900 for a certain number, and sold a part of them for $8825 at $85 each, and by so doing lost $5 a head ; for how much per head must he sell the remainder so as to gain $1140 on the whole ? ^9. A receives on 225 shares of mining stock an ''annual dividend of $96 a share; and £ receives the same total annual dividend on 270 shares of oil stock ; find the annual dividend on one share of B's stock. — 10. A drover bought a number of cattle for $17100 and sold a certain number of them for $12474, at $126 a head, gaining on those he sold $2574 ; how many did he buy at £b:st, and how much did he gain on each sold? m. 1. How may the accuracy of the process of subtrac- tion be verified ? Give an example. Show that the difference of 254 and 125 is the same as the difference when these numbers are each increased by 128. 2. In the multiplication of numbers, how do you prove the correctness of the operation by casting out the nines ? Explain and give reasons for the rule, and show the errors to which it is liable. 8. The product of two numbers is 760,069,888, one them being 26078 ; show that then- sum divided by 1584 is 86. 4. If division by a composite number be performed by successively dividing by its prime or composite fac- tors, show how the complete remainder may be found. >i V ! KXAMtNATtON PAPEBS IN Ex., 1487281 divided by 106. ^6. Find that number which, when divided by 90009 gives 746115 for a quotient, with 83837 for a remain- der? ^^. If 7 yards of cloth cost $84, how many pounds of butter at 40 cents a pound must I pay for 4 yards of the same cloth ? '^ 7. A ship sailed 66 hours at the rate of 11 miles per ' nour, when she encountered a storm of 16 hours' dura- tion, which drove her back at the rate of 14 miles per hour. How far from port was she at the expiration of the 72 hours ? ^Ks. A is worth 1266 dollars, B is worth 4 times as much as A, and 188 dollars, and C is worth three times as much as A and B lacking 2848 dollars. How mucii are B and G worth respectively ? and how much ai-e they all worth ? 9. Explain how any number may be multiplied by 11 by addition, and divided by 9 by subtraction. Ex., 46789x11 and 46789-7-9. i^ 10. What number divided by 628 will give 86 for quotient and leave 44 as a remainder ? COMPOUND HULR8. IV. — 1. The weekly amount of wages at a factory where an equal number of men, women, and boys was employ- ed was £82 168. ; the men received 45. 6d. per day, the women 2«., and the boys 1». 2d, : how many were there of each ? 2. The fore-wheel of a carriage is 8 ft. in circumfer- ence, and in a distance of 18 miles makes 2840 revolu- / en OOMPOOND BULBS. 89 tions more than tbe hind wheel ; find the circumference of the hind-wheel. 8. The length of a wall, according to the French metric system, is 9 metres 4 decimetres 8 centimetres; find its length in English yards, the length of the metre being 89.871 inches. 4. A rod of brickwork, viz., a sqtiare pole or 272 J square feet, has a standard thickness of a brick and a half : if a piece of work be 48 feet long, 22 feet high and 8^ bricks thick, to how many rods of standard thickness is it equivalent? '^6 Divide $2640.76 among 4 men, 6 women, and 8 ^^^^ >•, children, giving to each child double a woman's share, and each woman triple a man's share. S 7'7 t^l > //S *^7\ ^ 6. Express 8547962 sq. feet in acres, roods, and poles. ■4- 7. Multiply the difference between 25 lbs. 2 oz. 8 y • dwts. 18 grs., and 27 lbs. 6 oz. by 191J. 8. If 44J guineas weigh a lb. Troy when 82 half- pennies weigh a lb. Avoirdupois, what is the difference ill grains between the weights of a guinea and a half- penny, a lb. Avoirdupois containing 7000 grains ? 3fr 9. A person pays $62 50 income tax, which is at the rate of 2^ cents on the dollar ; find his gross income. 10. Divide 448 m. 8 rds. 24 p. of land among A, B, C, and D, so that A shall have ^ of the whole +4 ac. 8 rds. 6 p. ; 6 J of the whole; G ^ of what remains ; and D. the rest. Y V. 1. In a multiplying train of wheels a driver of three inches radius acts on a i-inch pinion keyed to a 8-inoh mm 40 BXAlIINAnON PAFEBS IN ! H |i wheel; the second wheel will therefore moTO times as fast as the :&rst. Supposing there to be 6 such wheels and pinions following a driver which makes 40 revolu- tions a minnte, find how many revolutions the last will make in an hour. 2. On a certain parallel the earth measures 12,815 miles round. Find the length of a minute of longitude on that parallel. 8. A grain merchant bought 40640 lbs. of wheat at $1.20 a bushel, and shipped it to Toronto at an ex- pense of three cents a bushel. Before he sold it there was a loss in handling, etc., of -^i^ of the original weight ; his profit on the transaction was $69.85. At what price did he sell the wheat ? 4. Find the difference in the price of a field of 28 acres at £58 17«. 4^. per acre, and at 6«. 8f^. per pole. 5. Show that the process by which Long Division is performed is the converse of that by which Long Multi- pUcation is performed. 6. The returns of a gold mine are 241 tons of ore, yielding 2 oz. 1 dwt. 15 grs. of fine gold per ton, and 193 tons yielding 1 oz. 12 dwts. 9 grs. per ton. Find the value in dollars and cents of the whole yield; at £8 lis. lO^d. per oz., reckoning the £1 at $4.80. 7. Explain the rsason for what is called " carrying one " in subtraction. Show by an example that there is no difference in principle between " Simple " and " Compound ' ' Subtraction. 8. A sidereal day is 28 h. 56 m. 4 sec. mean solar time. How many sidereal days are there in the sidereal year of 865J solar days ? 9. The profits of a tradesman are $186.16 per week. Of this sum he pays 5 persons at the rate of $5.04 each, COMPOUND BULEB. 41 8 others at the rato of $4.20 each ; his expenses for rent, etc., are $1785.64 per year. Find his net annual income. 10. How many guineas, sovereigns, half crowns, shillings and sixpences (find of each an equal number), are there in S600 15«. VI. -11. A rod 640 inches long, has a pieco of 8 inches cut o£F from it, then another piece of the same length cut off the remainder, then another piece of same length, tlicn another, and so on : how often may this be done, and what is the length of the piece remaining at last ? ;?f^ 2. The sum of $142,862 was paid for a quantity of land at $99 an acre : find the number of acres. 8. If it be supposed that as many persons die in 88 years as are equal to the entire population, it is required to find how many persons, on an average, die annually out of every million. jJ/4. Ten bricklayers and 5 carpenters were employed m building a house, each of the former receiving $12*96 a week, and each of the latter $18'92 a week ; what was the amount of wages in 16 weeks ? 6. A silversmith purchases a large dish weighing 8 oz., and forms it into 2 dozen dessert spoons, and one dozen table spoons ; if the latter together weigh 28 oz., find the weight of each dessert spoon, and its value at f of a cent per grain. ^6. An estate worth £2178 149. lOd. is divided among ihree children ; the first has £927 lis. 9d., the second has half as much, and the third has the remainder. How much did the third receive ? 4d BZAMIMATION PAPSB8 HI II 1 1 *^ 7. How many times may £2i 11*. 6jcl., be sub- tracted from J68067, and what will the remainder be ? 8. Compound a mixture, 8 parts of which shall each contain 4 oz. 8 drs. 8 grs. of one ingredient, 4 parts shall each contain 6 drs. 2 sc. 7 grs. of another ingredient, and 5 parts shall each contain^? drs. 2 so. of a third ingredient, and determine the weight of each one-twelfth part of the mixture. 9. A person bought 874 eggs at 2 for a penny, and a second quantity at 8 for twopence ; he paid altogether £1 9«. lid; how many eggs did he buy at 8 for two- pence ? 10. A person employs 50 men and 85 boys, who work reepectively 12 hours and 8 hours a day during 5 days of the week, and half time the other day; each man receives 24 cts. and each boy 4 cts. an hour. What is the amount of wages for the year ? BIBASUBES AND MULTXPT.SS. i VII. 1, What is meant by saying that one number is a common measure of two or more numbers ? Also, the greatest common meoMire ? •»► 2. A gentleman has a piece of ground, the sides of which measure 225 ft, 297 ft., and 869 ft. He wishes to enclose it with a fence having panels of unifoiTa length. What is the longest panel that can be used for that purpose ? 8. When is a number a common multiple of two or more numbers, and when the least common multiple ? How many acres of land would admit of being divided into a number of farms containing 150, 200, or 250 acres each ? lf^.tA8UBSS AND mJLTIPLBt. 4. Biiow by examples whether the greatest common measure of two numbers can ever exceed the difference of tiie numbers ; and whether their least common mul- tiple can ever exceed their product. CI. A shepherd on telling his sheep found that when ho told them out by twos, threes, fours, and fives, he had none left, and he knew his flock was above 800 but less than 400. What number had he ? 6. Explain what is meant by one number being prime to another. When two numbers are prime to each other, are they neceessarily prime Give examples. 7. Besolve 182288, 107828, 188216, and 97844, into their prime factors. And find their greatest common measure and least common multiple. 8. The product of four consecutive numbers is 1680 ; find them. 9. A, B, C, and D start together, and travel the same way around an island which is 600 miles in cir- cuit. A goes 20 miles per day, B 80, C 25, and D 40. How long must their journeying co tinue, in order that they may all come together again ? 10. A certain school consists of 182 junior, and 99 senior students. How might each of the two classes be divided so that the whole school should be distnbuted into equal sections ? vm. 1. When a aeries of numbers have been resolved into their prime factors, which of these factors must be taken to form by their product (1) the greatest common measure, (2) the least conmion multiple of the num- bers ? Form the greatest common measure and the H EXAMINATION PAPERS W J least common multiple of 405, 570, 910. 2. Find the least number of ounces of standard gold which can be coined into an exact number of half- sovereigns, if gold be worth 8/. 17«. lOid. per ounce. 8. What is the greatest number of ounces Avoir- dupois that will exactly measure 15 cwts. 1 qr. 27 lbs. 10 oz., and 21 cwts. 2 qrs. 21 lbs. 14 oz. (28 lbs.=l qr.) 4. Prove that every common measure of dividend and divisor is a measure of the remainder. 5. If the step of a man be 86 inches, of a woman 24, and of a boy 18, how many times will aU three step to- gether in walking 5 miles, supposing all three stai-t together ? 6. Four bells toll at intervals of 8, 7, 12, 14 seconds, respectively, and begin to toll at the same instant, when will they next toll together 9 7. Four points, moving each at a uniform speed, take 198, 495, 891, 1155 seconds respectively to de- scribe the length of a given straight line. Supposing them to be together at any instant at the same end of the line, and to move in it from end to end continually, what interval of time will elapse before they are together at the same point again ? 8. A teacher having a school of 144 boys and 128 girls divided into the largest possible equal classes, so that each class of girls should number the same as each class of boys. What was the number of classes ? 9. There is a street 854 rods long, and the land on one side of this street is owned by three persons, A, B, and 0. A has 102 rods fronting the street, B 114 rods, and G 188 rods. They agree to divide their land into village lots in such a manner that the lots shall be of MEASUBES AND SnTLTIPLES. 45 the greatest width that will allow each person to form an exact number of lots out of his land. What is this width? 10. If three bodies move uniformly in similar orbits round the same centre in 87, 224, 865 days respectively : supposing all three in conjunction at a given time, find after how many days they will be in conjunction again. . IX. 1. Define Factor, Common Factor, and Highest Common Factor. State and illustrate the principle on which the process for finding the H. C. F. depends. 2. Find the Highest Common Factor of 15561, 11115, 18585. 8. Suppose that three men in 810, 840, 900 days respectively, do a certain piece of work, express the rel- ative values of the work of the three men in the simplest manner possible. 4. A farmer has 240 bushels of wheat and 920 bushels of oats, which he desires to put into the least number of boxes of the same capacity, without mixing the two kinds of grain. Find how many bushels each box must hold. 5. How many rails will enclose a field 14699 feet long by 10861 feet wide, provided the fence is straight and 9 rails high and the longest that can be used ? 6. Define Multiple, Common Multiple, Least Com- mon Multiple. Show that the L. C. M. of two num- bers is their product divided by their H. C. F. 7. Find the L. C. M. of 68590142 and 85044059. 8. A can walk 8 miles in 48 minutes, B 8 miles in 72 minutes, C 8 miles in 96 minutes, and D 8 miles in 108 minutes. How far can each go so that on their re> i i 46 EXAMINATION PAPERS IN turn they may arrive together at the place iiom -which they started ? 9. If in two days A can build 28 rods of fencing, B 60 rods, G 16 rods, and D 40 rods, find the least num- ber of rods that will furnish an exact number of days' work. 10. An island is 48 miles in circumference. A, B and G have to walk round it till they all arrive together at the starting point. A walks 2, B 8, and G 4 miles an hour. How many times must each go round before the task is accomplished ? FBAGTIONS. X. 1. What are the advantages in arithmetical opera- tions of employing fractions expressed by the smallest number possible ? State how fractions expressed by large numbers may be reduced to equivalent fractions expressed by smaller numbers. Is this always possible ? 2. Explain why fractions having different denomi- nators must be altered in form before their sum or difference can be expressed by one fraction. ^^ 8. Add together the greatest and least of the frac- tions f , i, \i, ^%, and subtract this sum from the sum of the other two fractions. 4. Ghange the fractions |^, ^, and {^^f , into fr-ac- tions having a common denominator ; and express the difference of the first two as a fr-action of the difference of the second two. 6. What fraction subtracted from the sum of f and ^ will have unity for the remainder 9 , nUOTIONS. 47 '^ 6. What fraction divided by f of | of li will give the quotient unity ? 7. Prove the rule for dividing a fraction by an integer, and simplify the following expression : 4Hof^of74 ^ 2i + lM „ _ 12^-2^ + O^-SV'A' v8. Eeduoe 8i-2^ ,«* * u • i xr , f/i:4.n + l^t w "8 simplest form. 9. From the rule for the multipHcation of vulgar fractions deduce the rule for division. V Multiply the sum of i, J, and i, by the difference between ^ and f . V Beduoe to its simplest form 2} + 1 ^ 10. Beduce plest form. 2J~»- . 7 9x10 22^ . 2fTf"^l2'^fe'8-"80'*^ '*« ""*• XI. 1. What is meant by reducing one concrete number to the fraction of another ? Give examples. 2. Explain the method of adding and subtracting concrete fractional numbers : *^' Add £1^, 9|<., 6|if., expressing the sum in the fraction of jeioo. 3. Beduoe 1 lb. Troy to the fraction of 1 lb. Avoir- dupois. How many minutes are there in -^ of a year + ^^ of a week -f ^^ of an hour ? 4. Beduce to its simplest form, i.e.t to days, horns, &c., the following expression : 48 EXAMINATION PAPEBS IN ■; t ( ,- 1} of 4? of ]^Ml of 8 days 2 hours. 6^ £1 "^ 5. What fraction of 2 cwt. 14 lbs. is t of 2 qrs. 14 lbs. ? •vi6. How much ironstone ore must be raised from a mine, so that on I6sing \^ in roasting, and -^ of the re- mainder in smelting, there may result 606 tons of pure metal? V 7. Find a sum of money which shall be the same part of £61 ds. 1(2., that 2 cwt. 2 qrs. 10 lb. is of 86 cwt. 1 qr. V 8. If a mixed metal be composed of 11 parts of tin to 100 parts of copper, how much copper and how much tin will be required to make 24 cwt. of this metal ? 9. On measuring a distance of 82 yds. with a rod of a certain length, it was found that the rod was con- tained 41 times with half an inch over. What is the distance approaching nearest to 77 yds. which can be measured exactly by the same rod ? 10. If a yard measure be incorrect by one-eighth of an inch, find the error in measuring a distance of 600 yds. 2 ft. 6 in. Explain, if there is any difference, whether the error be in excess or defect. xn. 1. Simplify Uof 1Q^|x7^ +7| . f-2^-HA ^ i+4^of^ 8| ^ + ioO^-.iMl- 2. Find the quotient when 8i of — ?il^--_ is divided by 74 of ^ o/ H , 6A + 4of4t ntAOTIONS. 49 8. Beduce 7 weeks, 8 days, 11 boors, 52 minutes, 40 seconds, to the fraction of 865^ days. \ 4. How many yards of paper f yd. wide, will be re- quired for tbe walls of a room which is 20f ft. long, 11 J ft. wide, and 12^ ft. high ? How much will it cost at 44 cents a yard ? /^Q WS \/6. A man lost one quarter of his property in specu- lation ; he afterwards purchased a partnership in busi- ness for $16000, and had still $6000 left. What was he worth at first ? 6. Simphfy ii-^^i- of /j- ^^^^l , and - ^ ^ 8^61 \* 4J-8f/* 8J _f 8-2i 9 ^12 V 7, The owner of a ship which was valued at $10,000 sells \ of his share for $8,800, and then \ of the remain- der for $1,800 ; what did he gain or lose by the tran- saction ? 8. Find the value of 28 ,4^^| ^f ,, ^ ^p^ of£2. 10,. 9. A contract is to be finished in 154 days, and 50 men are set to work at once ; at the end of two-sevenths of the time it is found that only one-fifth of the work is done ; find what extra number of hands will be required to complete the contract, the last men employed work- ing 12 hours per day, while the first lot worked through- out 10 hours per day. 10. Suppose that ^ is represented by unity, what number will represent ^ ? 00 1 * V BXAMINATIOK PAPEBS Dl FBAOTIONS. xm. 1. Define a fraction. Explain the functions of the numerator and denominator. She^nr that ^ of f = |^. (Hamblin Smith, Art. 66.) iieauce ,,- - ^^gj ^ j^^ ^ ^gj ^ ti/ V 8. A, B, and G are joint owners of a ship ; O's share is valued at $2000, A's share is i of B's, and the sum of their shares is i of the value of the whole ship. If A buys B's share, what will be th« value of the part of the ship he then owns ? ^^«» o o 4. Reduce 14 wks. 6 days 28 hxs. 45 min. 20 sees., to the fraction of a year of 865^ days. \ 6. Five brothers join in paying a sum of money ; the eldest pays ^ of it, and the others pay the remainder in equal shares ; it is found that the eldest brother pays $800^77 niore than ^a younger brother's share. Find the sum of money. 1^ 7 if cro ^^ V 6. A can do a piece of work in a day of 10 hours, B can do it in } of a day, and in -^j^ of a day ; A works by himself 2 hours, is then joined by B, and they work together 8 hours more, when G joins them ; how long will it now take the three to complete the work *? i^, \« 7. The dimensions of a room are 29 ft. 6 in. by 11 ft. 8 in.; what will be the expense of carpeting it with carpet f yd. wide, and costing 90 cents a yard ? 8. Reduce to lowest terms 217 mile s 6 f. 18 p. 2 yd. 2 ft. 1 in. 606 iniles 2 f. 28 p. 1 yd. 2 ft. 7 in.* 9. In a regiment consisting of English, Irish and ~Jv\^ nUOfflONB. dl Scotch, } of the regiment were Irish, fg Scotch ; but after 200 Irish and 200 Scotch were added to the regi- ment ^ were English : find the original strength oi the regiment and the number of English, Irish, and Scotch, respectively. 10. FinA the difference in dollars and cents between f of 1^ of 16 times £Q 17*. 6d. and (|-|+2J) of (|i X If-^-^) of $480, the £ being $4.80. XIV. 1. Define a decimal fraction, and taking '4568 as an example, show from your definition tliat *4568^=-i^^^\/^. 2. What are the advantages of dfecimivi fractions over ordinary fractions ? State why decimal fractions are not always used in calculations. 8. State and explain the rule for reducing a vulgar fraction to a decimal. Find the values of J-i- '01001 and of lO'Ol-s-^. 4. State and explain the rule for the multiplication of decimals. s/Multiply the sum of 2-616, '00182, and 1-0448, by •62689. -7 ^f3 f/S'3^6Si 6. State and prove the rule for the division of one decimal by another, and apply it to the two following examples : — 10-886^6'16; 1083-6 + 6-16, and prove the truth of the result by vulgar fractions. 6. In what cases can an ordinary fraction be ex- pressed by a Jmite decimal ? Show that the number of decimal places in such cases may be inferred from the factors of the denominator. 7. Perform the following operations in decimals : — (7iof^+H~-02)--005. (tt EXAMINATION PAPERS IN Likewise find the value of f of *08, determining the recurring period. 8. Show that the product of two circulating deci- mals may produce a terminating decimal. Exemplij^ in the product of -2142857 by -46. ^ 9. In what sense can a finite fraction be said to be equal to an indefinite repeating decimal ? How must the sign ^ be understood in the expression ff =858585 , , , , ad ir^nitwn, in order that the expression may be satisfactory ? 10. How many repeating and how many non- repeating figures will there be in the decimal equivalent to the fraction yHts ^ XV. ,/?..• N 1. Beduce .54 of 7 oz. 15 drs. to the decimal of 4-j'j lbs.; and 2^ furlongs to the decimal of 7J of .8125 of 2 leagues. cL^f*/ ^-o^oij 2. Subtract ol^^tiL from ^l^^li and re- Q duoe to its simplest form 2 +:: 7i — ^ 1+8 6 + 4 6+i n/s. a house and lot together cost $1600, and f of the price of the lot was ^ of the cost of the house ; how much did each cost? ^; ^/ v * 37^ / tut-, , %/ 5. A merchant sold 20 bbls. of flour for $127^, which was W of what he received for what he had left. 1l \ FBAOTIONS. 08 and which he sold at $6| a bbl.; how many bbls. in all did he sell ? ^6/ ^ii^ \J. Divide St^^ + 1 J of ^3^ of IJ + 2| of 4J by the dif- '■^^ fo^ehce between 3jlli. and ?iiili. \ 7. A man bought a horse for $120, which was $80 less than ^ of one-and-a-half times what he sold him for. How much did he make on the sale of the horse ?jf^^^ 8. Simplify ^^^ ^^ ^ It^LM, and reduce to its ouup y 12 of 8i UWof24- lowest terms PJ-^^L^U . ^ Wof8i+^t 2^/ 2} 9. Find the value of .4x(6§+-2.6) of $9.60 -|- 2-26-§of 1^ 16-8 x-95 of $2.>*0+:7r^ cents. X^r. ^^ •2 of S^+U '^-006 N 10. Find the quantity of coal consumed by a steamer for a voyage of 4048 miles, supposing her rate per hour i* to be 14-04 knots, and her consumption of coal 87 tons per day, a knot being f|J" of a mile. ^^ ^ >/, I^-h^ XVI. 1. Show clearly how to change a vulgar fraction into a decimal? Reduce |f$ to a decimal. What is the equivalent decimal fraction ? What is done with |^ to bring it into this form ? S 2. Reduce ^ths of Jg20 to the deounal of £100. \ 8. By what decimal of one farthing does *0009 of one shilling exceed '00008 of one pound ? 4. Show that -026 of Ml is double of -06 of £1 6». 6. Explain the reason why any number of shillings may be expressed in the decimal of a pound by multi- ^ t^vt* ^ 54 ■XAMINATION PAPEBB IM plying the shillings by 5, and marking off two places of decimals. 6. Find the exact values of the following concrete decimals : *879 of an ounce, and *954 of a pound Troy. 7. If the unit of Troy weight, called the penny- weight, contained 14.25 grains inslead of 24, how many grains would make the pound Troy 9 8. Express a pound Troy as the decimal of a pound Avoirdupois ; and conversely, express a pound Avoird- upois as the decimal of a pound Troy. 9. Express in the fraction of a foot, the remainder after *012 of a yard has been subtracted as often as it is possible from 1'087 yard. 10. What decimal of a day is 2 hours 12 minutes 10 seconds? 11. Divide 8 weeks 4 days 5 hours 6 minutes 7 seconds by 5 days 6 minutes 40 seconds, expressing the result as a decimal and stating its nature. xvn. t 1. Divide 27107*67 by '008427, and reduce to a . , , . , A of 2-179-1 of •8684 ^ smiple deonnal 5 _ — ^ . \ 2. After spending $10 less than $ of my money, I had ^iS more than ^ of it leffc ; how much had I at first ? \ 9|oflf 1 4of8i+g H 6. 7. What fraction of £5S 5s. 6d. is ^^ of £17 2«. 8d. ? A man invested f of his capital in bank stock, { of the remainder in real estate, and had still $6000 left. Find his capital. 8. Find the value of 48 cwt. 2 qrs. 21 lbs. at £2 16s. Sd. per cwt. (Qr.=26 lbs.) 9. Find the difference between .26-f.2of8.7 ^ 4.3-1-5.6 -.2 of 11 .48— .014 of 20 & 7.4- 10. A person, after paying out of his income for a year a tax of 4 cents in the dollar, has $7200 left. Find his income for a year. -..»^.j -...,. _ -ii-,'3._.- .■■'-j^ia ■ 66 PAPEBS FOR ENTRANCE INTO DErBMBEB, 1874. IV. 1. The difference between the product of two num- bers and 476 is ten nulHons, ten thousand and ten; one of the numbers is twenty-one thousand and twenty- eight ; what is the other number? 2. A cannon ball travels at the rate of 1,500 feet in a second and a half; how far will it have gone in j| of a minute ? 8. How many grains are there in 9 oz. 17 dwt. 22 grs., and how many acres, &o., in 167412715 square inches ? 4. How many yards, &c., of carpet 2 ft. 1 in. wide, will it take to cover a floor that is 19 ft. 7 in. long by 18 ft. 9 in. wide? 5. After taking out of a purse % of its contents, § of the remainder was found to be IBs. 5^. What sum did it contain at first, and what part of £3 is that sum ? 6. Find the value of , lioff-^lOi''*^' ISiofSJ 7. What must be the length of a plot of ground, if the breadth is 16^ feet, that its area may contaia 46 sq. yards ? 8. A pint contains 84§ cubic inches ; how many gallons of water will fill a cistern 4 ft. 4 in. long, 2 ft. 8 in. broad, and 1 ft. 1^ in. deep ? 9. Beduce to a simple quantity 2.8 of 2.27 . 4.4—2.88 , 6.8 of 8 + rT — T-ITl of 1.186 1.6-1-2.629 2.25 HIOH SOHOOLS AND COLIiBOUTB INSTITUTES. 67 10. The chain for measuring land is 66 ft. long, and is divided into 100 links ; what is the length of a fence that measures 2456 links, and how much would it cost at $8.86 per yard ? June, 1875. V. 1. Reduce to its lowest terms / 2i— f of lf _ 1 \ 1* 01 f 2. A merchant bought a number of barrels of flour for $4600, and sold *hem for $6200, thereby gaining 76 cents a barrel ; how many barrels did he buy, and what did it cost him a barrel ? 8. A paid $60 an acre for his farm, which was ^ as much as B paid per acre for his farm of 160 acres. Find the entire cost of B's farm. 4. Find the sum of ^ of £1 18«. 0^d, + ^ of £1 6«. Sifi+T^^of £2 4^. 8frf. 6. A farmer having 17 cwt. 2 qr. 19 lbs. of pork, sold 4 cwt. 8 qr. 21 lbs. of it, and tlie remainder he sold in barrels, each containing 2 cwt. 6^ lbs. ; how many barrels did he sell ? 6. If it take a man 1 hour and 40 minutes to cut i a cord of wood, for how many days of 8 hours each will be occupied in cutting 186 cords 88 feet ? 7. A man invests i his fortune in land, ^ in bank stocks, \ in debentures, and loses the remainder, which was $8,000 in speculation ; how much was his fortune ? 8. The dividend is fifty-one million eight hundred and forty-six thousand seven hundred and thirty-four, r 68 PAPEBS FOR ENTRANCE INTO the quotient is five hundred and eight thousand three hundred and one, and the remainder 28; find tha * divisor, 9. Find the cost of AQ^ yds. of cloth, when 7f yds, cost £7 18«. Ad, 10. A man paid $2,896,875 for land, and sold 56.25 acres at $81 an acre ; the remainder then stood him at $20.05 an acre ; how many acres did he buy ? December, 1875. VI. 1. Find the amouni'of the following acooimt:-^ Mr. Markham boughi of Mr. Jones, Dec. 8, 1875, 12 yards Scotch Tweed, @ $2.85. 16 yards of Silk, @ 2.12^. 60 yards Peking, @ 14i. 42 yards Shirting, @ 16^. 12i yards Flannel, @ 50. 20^ yards Scotch Plaid, @ 60. 2. I bought from A 97 acres 2 roods and 12 square rods of land ; from B, four times as much, less 7 acres and 1 rood ; and from 0, ) as much as from A and B to- gether. I then sold 120 acres 1 rood and 29 sq. rods. How much had I left ? 8. Beduce to its simplest form i 15 [^A*+ 28 -2^ ,r'\]^'^' 4. State the rule for division of Vulgar Fractions, and show by means of an example the reason for it. 5. A person bought a certain number of barrels of flour for $2200; he reserved 20 barrels for use and mf^n BOHOOLS and collegiate institutes. 00 Bold ^ of the remainder for $1976, which was $804 more than cost. Find the number of barrels he bought. 6. A sum of money is divided among 4 persons. The first receives t, the second i, the third |, and the fourth the remainder. It is found that the first re- ceived $700 more than the fourth. Find the sum received by each. 7. Add together | of £S la. 6d. and ^ of j of 4i guineas, and reduce the result to the fraction of £1 10«. 8. If the annual rent of 46 acres 8 roods 14 perches of land be $870.70, how much will be 4he rent of 70 acres and 20 perches ? 9. If the price of 1.875 pounds of tea is 1.8749 shillings, how much can be bought for £15 8^. ? 10. A hall is 45 feet long and 11^ feet wide ; what will it cost to carpet it (1) with cai-pet 27 inches wide and $1.75 per yard ; (2) with carpet 45 inches wide and $1.26 per yard? Junk, 1876. vn. 1. Bought 19^ yds. Irish Uncn at 6/4, 16f yds. cal- ico at 1/8, and 16^ yds. of silk at 8/4 ; find the amount of the bill in dollars and cents. 2. Add together | of f of £2. 5s., ^ of 8 guineas, and '27 of £1 18s. 6d., and reduce the result to the dec- imal of £25. 8. If a pipe discharge 2 hhd. 28 gal. 2qt. Ipt. of water in one hour, in bow many hours will it discharge 11 hlid. 25 gal. 1^ pt., the water flowing witli the same velocity ? 70 PAPBBS FOR BNTBANCE INTO 4. Add together, 16 H 1 X - f ' i n !i T^of2TS,xJi'l*of8^ A and divide the result by ?t^f |— -* — -^ -^^^^ 5. A man's annual inoome is $2,400; find how much he may spend per day so that alter paying a tax of 2 cents 7i mills on every doUai' of inoome he may save $682 a year (8G5 days). 6. A room is 86 feet long and 24 feet wide ; find the difference in the expense of carpeting it with carpet a yard wide at $1.40 a yard, and with carpet 27 inches wide at $1.15 a yard. 7. If 162 gallons of water will fill a cistern 4 ft. 4 inches long, 2 ft. 8 inches broad, and 2 ft. 8 inches deep, how many cubic inches are contained in a pint ? 8. Three men can mow a field in 6 days ; they mow together for two days, and then one of them ceases work, and the other two finish the field in 7 days ; find how long the man who ceased work at the end of the second day would have taken to mow the whole field by himself. 0. A man sold two city lots for $600 each ; on the one he gained ^ of the price it cost him, and on the other he lost i of the price it cost ^^^n ; find his entire loss on the sale of the two lots. 10. A drover bought a number of cattle for $4376, and sold a certain number of them for $48 a head for the total sum of $8656, gaining $680, for bow much per head must he sell the remainder so as to gain $400 more. high schools and colleoute institutes. 71 Decembeb, 1876. VIII. 1. How many square inches are there in 8 ao. 2 ro. 27 pr. 27 sq. yds. 7 sq. ffc. 28 sq. in. ; and how many tons, owt., &c.f in 87,406 pounds and 4768 oimces ? 2. A person owns f of a ship, and sells f of his share for £1260. What is the value of the ship ? 8. The difference hetween the product of two num- bers and 2481 is three hundred million^, three hundred and three thousand and du-ee. One of the numbers is twenty thousand throe hundred and six. Find the other. 4. Show which (is the least and which the greatest of the following fractions : — i of 9J, ^ of 9, and J J of 8.2. 6. If telegraph posts are placed 80 yards apart, and a train passes one every 4 seconds ; how many miles an hour is it running ? 6. A regiment marching 8^ miles an hour takes 110 steps in a minute. What is the length of the step ? 7. How many yards of carpet 15 inches wide will cover the floor of a room 22^ ft. by 19 ft. ? 8. Simplify 88 -1^ of 2^ of 1^ + 2|h- ^^—7. 0. Find the sum of 6-27, 18-651, and 12-845, and the difference between *84027 and '27. 10. If a room be 12 ft. square, what must its height be in order that the area of the walls may amount to 60 sq. yds. ? is; 11 72 PAPBBS FOR ENTRANOB INTO IX. 1-i 1. Multiply H+H by and subtract j^Hif from ifcyn. 2. At what timo will the hour and minute hands of a watch be together between 8 and 4 ? 8. " The Crystal Palace at Sydenham has the lar- gest dock in the world; the minute hand is 19 feet in length, and moves half an inch in every beat of the pendulum, and its point travels nearly four miles a week." The ratio of the circumference of a cn-cle to its diameter being 8.1416, find the exact distance travelled by the minute hand; also show that every beat of the pendulum measures a little less than four- fift}i8 of a second. 4. Express .88 of 18«. id.-\-.lS8 of £1. is., as a • 20 decimal of M ; and divide 8.064 by .846+- of .2916. 6. A man leavesjrhis property to his wife, a sixth part to each of two childi-en, a twelfth to his brother, and the rest, amounting to $8,000, to charitable pur- poses. Find the amount of his property. 6. The weight of lead is -^vand that of copper -r- of an equal bulk of platinum. How many cubic inches of lead will be equal in weight to a cubic foot of copper ? 7. Find the G.C.M. of 860149 and 2006163. H, Which is the lieavier, a pound of gold or a pound of feathers, and on ounce of gold or an ounce of feathors */ By how mucli in each case ? mOH SCHOOLS AND COLLEGIATE INSTITUTES. 78 9. A mau died in 1873, aged 44 ; his son died in 1827, aged 17. ^How old was the father when the son was born ? 10. A. hrm turns out 60 tons of steel goods per week, using up for that purpose 61 tons of iron, at $27 per ton, 100 tons of ooal at $2.70 per ton, and $180 worth of other materials ; expenses are $300 a week, and rent, taxes, &o., are $870 a year ; at how much per w t. must the steel be sold to give neither proB t nor lo&s ? X. 1. Define the L. 0. M. and the G. 0. M. of two or more numbers. The G. 0. M. of two numbers is 687, and the L. 0. M., 18796 ; if one of them is 106 times 863.87 4i "^ 8.4 find the other. of A 2. Beduoe 22870064 square inohes to acres. 8. A farmer sold 1140 lbs. of wheat and 782 lbs. of jats for $2D.76, receiving 36 cents a bushel more for the wheat than for the oats ; find the price of each per bushel. 4. What part of half a crown is 1 ^j 2i-|of^l| 7 iof3f-h^' of two guineas and a half ? 6. The length of a wall is, aocctding to the French motrio system, 18 metres, 9 deoimotres, 6 oentimotros ; find its length in English feet, the leu^bU of the metre being 39.871 inohes. 6. Bought 21)0 acres of land for $98«0, and sold » part of it for $10000 at $40 an aero ; how many acros had I remaining, and how much did I gain on every acre sold ? / I 74 PAPERS rOB RNTBANCB INTO 7* Sbow that the valne of a fraction is not changed by multiplying or dividing both |its terms by the same number. 8. A man and a boy engaged to do a piece of work for $21 ; when } of the work was done the boy went away, leaving the man to finish it alone, the result being that tlie work occupied a day and a quarter more tlian it '''ould have done ; the boy was able to do in a given time only half as much work as the man, and was paid accordingly; find how much the man earned per day. 0. If the price of a farm of 80a. Ir. lOp. be $8926.12^, what will be the price of another farm con- taining GOa. 15p., if 8 acres of the latter be wortli 4 of the former ? 10. A rectangular cistern whose longtli is 18 ft. 4} in., and breadth 6 ft., contains 294^ cubic ft. of water ; find the depth of the cistern, and the weight of water if one cubic inch weighs 262.5 grains. XI. 1. A persons income is reduced from £750 to £784 In. Qd. by income tax. How much does he pay in the . in po 2. A laborer receiving wages at the rate of $0 a woek through the year, saved 20 cents a week, whioli lie deposited in the savings bank. In consequence of a strike hiH wages wore raised 80 cents a weok, but he found at the same time that witli the cost of Living, and his payment to the trades* union, he had to pay 50 cents, where he formerly paid 45 cents ; find the in- crease in his yearly savings. 8. The fore and liiud wheels of a carnage aie 12 BIOH SCHOOLS AND OOLLSlOIATE INSTITUTES. 75 and 16 feet in oiiciimferenoe; find the least uiimber of revoiutiojuii ui' uiwii wkeel wiucli will give tue bame kiigth. 4. Wliat is moaut by an improper fraotion and what by a lULiLed uumber ? Uow are improper fraotious oou vertud into mixed numbers, and oouversoly ? 6. The sum of ^ and ^ is diminished by ^ ; how often does the dilfurunce contain ^\ of the sum of |, i and ^V ? « 6* What length of cai'pet | yard wide will cover a room whose length is 42 feet 5 inches, and breadth 81| feet '/ 7. Explain whether .007 or .06b is more nearly equal to .0074^1 and express in words the o^ror in ex- cess or defect in each case. 8. A tea dealer has teas worth 90 cents and 00 cents per pound, respectively, which he mixes, taking two pounds of the former to one pound of the latter, and sells the mixtuie at b5 cents per pound ; what does he gain or lose per cwt. '/ U. If 4 men or women can do a piece of work in 20 days, how long will it take 8 men attd 15 women to du Uiu same work ? 10. li a garrison of 1500 men have provisions for 1^ months; how long will their provisions last, it it be iucioasedto2200? xn. . «. ... 202 -lU ^e 122.V j ,• , 1. Simplify ^^\jjj ^^ 20(4 76.078 by 91.868. 9. DtH3a every intomiinate dociraal oirciilato ? Prove 76 PAPERS FOR ENTRANCE INTO 'I li In i fche rule for oonvertmg a " mixed " circulating decimal into a vulgai- fraction. 8. On the 7th of August I lent a friend $1600, which he retained until the 6th of October following ; my friend afterwards returned the compliment by lend- ing me $1200 on the 16th of March ; when should he get back his money ? 4. A Mock of oak a foot square and 6 feet long has I'ound it two bands of iron, each 8 inches broad and 1 inch thick ; find the weight of the whole, a cubic foot of oak weighing 58.87 lbs., and of iron 486.72 lbs., (cwt.=112 lbs.). 5. The distance from Toronto to London via the G. W. B. is 119^ udles ; the distance from Toronto to Hamilton is -j^ of the distance from Hamilton to London ; find the distance from Toronto to Hamilton, and from the latter place to London. 6. If -]^ of a meadow be mown by 12 men in 6 days, find in what time the remainder could be mown by 10 men. i 7. Subtract the cube of the difference of -^ and | from the difference of their cubes, and divide one-fourth of the result by f of the product of their squares. 8. A has 60 shillings, B has 66 francs; how many francs must B give A in order that his money might bo one-sixth of A's, a franc being f| of a shilling? 9. A runs at the rate of 260^ yaids a minute, and B at the rate of 275 yards a minute ; how much start may one give the other so as to win by a yard in a mile race? 10. A man who rows four miles an hour in still water takes 1 hour and 12 minutes to row that distance and start mile BIOH SCHOOLS AMD COLLEOIATB IMSTITUTSS. 7*7 up a river ; how long will he take rowing down again ? xm. 1. Find the amount of the following bill ; 84 lbs. 14 oz. beef (^ 17 cts.; 14 lbs. 10 oz. mutton @ 19 ots.; 7 lbs. 6 oz. pork chops ($ 21 cts.; 16 lbs. 7 oz. lamb (^ 29 cts.; 8 lbs. 9 oz. suet @ 16 cts. 2. Fifty-nine lbs. of a mixed metal are lowered into a full bucket of water, and the water which overiiows is found to measure 195 cubic inches ; find the weight ol half a cubic foot of the metal (supposing a cubic foot of water to weigh 62^ lbs.), and its value at $1.20 per lb. 8. A postmaster is allowed one dollar and a quarter on every hundred dollars' worth of stamps he sells ; find his gain on a sale of 1000 three cent stamps. 4. What must be added to l|_ofJi_ . 1> of 82^+|f44f to make it of 8| of l| + f? '17 of (•00617---00r)82)4--119x-007 •17X-17 6. Fivo-nhiths of all the pupils in a pubUc schoo] wore below the fourth-class ; f of those above the third class went up to the Entrance examination, of whom 8 failed to pass, and the number successful was | of the number above the third class ; find the total number in the school. 7. A. person after paying Id. in the pound income tax has left a net income of £526 Bs. lOd. ; how muob tax did he pay ? 1^ of H of 8^ of 2§ e(xual to 1 28f 6. Simplify mopm 78 PAPBBB FOB BNTBANOB INTO 8. Find the weight of a bar 8 yds. 1 ft. 9 in. long, of which a yard weighs 16 lbs. 7 oz. 8 drs. 9. If I buy 147 gal. 8 qt. of molasses at 26 cents a gallon, and use 88 gallons of it, at how much must I sell the remainder per gallon so as to receive as much as the whole cost ? 10. A and B can build a wall in 80 days, and A does twice as much as B ; how long will it take each to buUdit? XIV. 1. Find the yearly average of profits or losses in seven years, of a merchant who gained on the first, third, fourth and sixth years the sums of $2080, $800, $2800, and $4000 ; and lost in the second, fifth and seventh years, $400, $1000, and $1280, respectively. 2. Divide $4000 among tlu6c persons, so that the first may have three times as much as the second, and the third as much as the first and second together. 8. There is in a manufactory a certain number of workmen who receive $10 a week, twice as many who receive $6.80 a week, and eleven times as many who receive $2.80 a week, and the total amount of work- men's wagi s for one week is $878.80 ; find the number of workrno , 4. If a cent piece is one inch in diameter, how many can be laid in rows touching each other on a table which is 7 ft. 6 in. loi.g and 8 ft. 4 in. wide ? 6. A cask is required which can be filled exactly by any one of the following measures, taken any number of times exactly ; half a pint, half a gaP-^n, throe gall- ons, 6 gallons, and nine gallons ; find the smallest cask for this purpose. mi x 1^ by 19^ + 2^-2^^xU. r- mOH SCUOOLS AND OOLLEOIATB INSTITUTES, 81 iree- from 4. Find the L.C. M. of 11, 14, 28, 22, 7, 66, 27, 81, 6i, and 86; and the G. C. M. of 18616 and 18787. 6. After the losses sustained in two engagements, a detachment of cavalry was found to consist of 1040 men; in the first engagement they lost one man in every twenty-five, and in the second -^^ of the remain- der ; find the numher of men originally in the troop. 6. Divide the sum of {ll^-M)-i-{.05^^) and (^j^ -I- 6.007), by the difference between |(1.85-.72) and 6.0004. 7. The earth's polar diameter contains 41,707,796 feet, and the difference between the equatorial and the polar is one 292nd part of the latter ; find the difference between the two in miies. 8. A man sold 24 horses for $160 each ; on half of them he gained ^ of what they cost, and on the re- mainder he lost ^ of what they cost ; find his whole gain or loss. 0. The standard gold coin of Great Britain is made of gold 22 carats fine, and a pound Troy of this metal yields 46}^ sovereigns ; find the weight of pure gold in 100 sovereigns. 10. Make out in proper form (giving the amount) a bill of the following sales : Jno. Jones bought of B. Jaf- fray, July 10, 1877, 10 yds cassimere @ $2.86 ; 16 yds. silk at $1.12|; 727 yds. ticking @ 14 cts.;42yds. shirt- ing ® 16^ cts.; 12 yds. flannel (^ 40 cts.; 24^ yds. print @ 66 cts. xvn. 1. If the pound Avoirdupois contains 7000 grains, find the greatest weight which will measure both a I! HI I : B2 PAPERS FOR ENTRANCE INTO pound Troy and a pound Avoirdupois; and the least weight which can be expressed without fiactions in both pounds Troy and pounds Avoirdupois. 2. If a boy's school life lasts seven years, and he has 4 weeks 8 days hoUdays at Christmas, and 6 weeks 2| days at midsummer; how many hohdaya has he in 7 years? 8. Multiply £6 11«. 8|(i. by 18|. 4. What sum munt A bequeath to B, so that B mnj receive $1000 after a legacy duty of $10 per oent. has been deducted ? 5. A creditor receives $1.60 for every $4 of what was due to him, and thereby loses $801.05. What wag the sum due ? 6. Of a field | is meadow, f arable land, and the re- mainder is 1 acre, 8 roods, 26 poles ; find the quanti- ties of meadow and arable land. 7. What must be given per yard for carpet 27 inches wide, that the carpeting of a room 26 feet long and 15 feet 8 inches broad may cost $180? 8. Find the value of 9. Find the value of 8.0005 X. 006 " .0009 10. Which is the cheaper, a hat which cost $8, and will last 9 months, or one which cost $2.40, and will last 7 months ? And how much wiU a man save iu 20 years who wears the cheaper kind ol hat, interest not being reckoned ? {^ I I Hion RC^HOOLS AND OOLLEOUTX INSTITUTES. 68 oast )oth Ihe eeks e in xvm. mny . has what b was le re- lanti- lohes d 16 and wiU iu eresi l! \, 1. Show that the fraction 10-H2 12 +U is greater than G ind less than 6 2. A person buys 64 lbs of meat weekly; for 10 weeks tlie price is 17 cts, per lb., for 2G weeks 16 cts., for 10 weeks 15 cts.; what is the amount of his butcher's bill, and the average price per lb. during the year ? ^ Beduce to its simplest form 1+f of J-flf ,»^of (1 + 6J) + 1^ of ,% of (7-2|)-J 4, Find the value of of If 8-8 of 4-4 .786 of 2 sq. ft. 6 sq. inches. ff. A person has four creditors ; to the first he owe» $1248, to the second $1092, to the third $984, and to the fourth $786 ; he fails, and the creditors seize the whole amount of his property, which amounts to only $1640; how ought this sum to be divided amongst them? 6. By selling cigars at the rate of $2.60 for 4 dozen it was found that f of their cost was gained ; find the price at which each cigar ought to have been sold in order to gain ^ of the original cost. 7. Gunter's chain consists of 100 links, and ten square chains make an acre. Find the area of a rect- anj^ular field whose breadth is 78 chains 28 links, and IcnidJi 85 chains 40 liiiks. ll IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I '- IIIIIM j50 i^ ill 3.2 1= 2.2 IM " m iio 1.8 1.25 1.4 1 1.6 ^ 6" ► <^ ■c^ O v: / /A Photographic Sciences Corporation '% 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 L(^. , m - 4f. 4s' r 84 PAPEBS FOB ENTBANOE INTO 11 8. A person expended $66.92 in tea at 87^ cts. per lb., coffee at 18|^ cts., and sugar at 10^^ cts., buying an equal quantity of each ; how many pounds of each did he buy ? 9. Find the duty on 4 hogsheads of sugar, each weighing 1280 lbs. gross, at 2^ cts. per lb., 3'^th of the gross weight being allowed for tare. 10. A clock gains 8^ minutes in 16 seconds less than 24 hours ; at noon it is 2 minutes too slow ; when will it indicate true time ? XIX. 1. Find the difference between 1000 Avoir, oz. and 1000 Troy oz., and arrange the remainder in parcels of 2^ dwts. each. How many parcels are there if 17000 grs. make a lb. Avoir, wt. ? 2. $90.90 are shared among 4 men, 6 women, and 6 children, so as to give to each man twice as much as to each woman, and to each woman three times as much as to a child. What do the women get ? 8. A sheep-dealer bought sheep to the value of $9,000 and after keeping them 4 weeks and paying 60 cents, each for their pasture during that time, sold the whole for $14,000 and thereby cleared $2.00 per head. How many sheep did he buy ? 4. If f of 18 of ^- of a ship is worth $600, what should be paid for .126 of it ? 6. James received a present of some money. He gave ^ of it to his sister, and ^ of the remainder to his brother, and kept the rest, $4, to himself. How much did he receive, and how much did his brother get ? 6. James can dig a garden by himself in 8 days, HIGH SCHOOLS AND OOLLEOIATB INSTITUTES. 85 did ' John can also dig it alone in ten days. The owner is going to pay $27 for the digging. If they dig together, kvhat should each receive ? 7. Little Jane has a card board 21 in. long and 15 in. wide, which she wishes to cover with postage stamps 1^ in. long and ^ inches wide, and wishes to know how many it will take to do it. Make the calculation. 8. How many times will a carriage wheel 4 ft. 8 in. in diameter turn in going 1 m. 1 fur. 1 per. ? The cir- cumference of a wheel is 3| times the diameter. 9. A person owns a ship and its cargo valued at $6000. ^ of the value of the cargo is equal to | that of the ship. What is the value af each ? 10. How many bushels of potatoes can be sold out of a garden in which there are 160 rows of potatoes, in each row 240 hills, and on an average 10 potatoes in each hill, if 6 potatoes make a pint ? XX. 1. A farmer bought land from A at 60 dollars an acre, and the same quantity from B at 85 dollars an acre. The whole amounted to 53215 dollars. How many acres did he buy from each ? 2. A farmer has 66 bushels of com, and 90 bushels of wheat, which he wishes to put into sacks of equal size, and without mixing the two kinds of grain. fl!oTy many bushels must each sack contain ? 8. Define a fraction. Explain how it is that the product of two proper fractions gives a fraction lese than either of them, and the quotient a fraction greatei than the dividend. 4. Beduce to its simplest form : 86 PAPERS FOR ENTRANCE INTO 5. If a shekel contained 240 grains, what was the weight in pounds Avoirdupois of the head of Goliath's spear, which was 600 shekels of iron, and of his coat of mail, which consisted of 5000 shekels of brass ? 6. Find the length of paper |- yard wide required to cover the walls of a room whose length is 27 feet 5 inches, breadth 14 feet 7 inches, and height 12 feet 10 inches. 7. A alone can do a piece of work in 11 days, and B alone can do it in 17 days. How long would they take to do it together ? 8. One person takes 61 steps of 29 inches each in a minute, and another takes 59 steps of 81 inches each ; in walking a mile how much longer will one person take than the other ? 9. Prove that a decimal is divided by 10000 by re- moving the decimal point in the dividend four places towards the left. 10. A farmer sold % of his whole amount of land, at $25 per acre, and received for it $1000. What amount of land did the farmer own 7 XXI. 1. If 4 men mow 15 acres in 5 days of 14 hours each, in how many days of 13 hours each can 7 men mow 19^ acres ? (See £|!amblin Smith, " Complex Problems.") 2. Divide 1 1 1 + 7+i vis of 7iby 1 + 2 3 + ■ TIIOH SCHOOLS AND COLLEGIATE INSTITUTES. 87 ■ 8. The following summary is taken from a sales book : April 3 and five following days, respectively, sold 250 yds. print @ 21 cts.; 1000 yds. @ 18 ots.; 600 yds. @ 19c.; 8000 yds. @ 18 cts.; 1600 yds. at 22c.; and 375 at 20 cts. Find (1) the average selling price per yd., (2) the average number of yards sold daily, and (8) the average daily cash business for the week. 4. Lead weighs 11.4 times, and platinum 21 times as much as water ; find the weight of the platinum that will be equal to 112 lbs. of lead. 5. The rates of two trains travelling in the same direction being 16 and 60 miles an hour, how long be- fore the fast train is due at a certain station must the other leave in order to reach the next station, which is 20 miles further on, five minutes before the fast train arrives ? 6. Find the G. 0. M. of 68590142 and 85044069. 7. Simplify 1.6 of 2.75-3.8 ^^ (.119 -.085)' 1.6-2.76 of 3.8' .1192 -.085*' 8. A plate of copper 2 ft, 9 in. wide, 3 ft. long, and f of an inch thick, is rolled into a sheet 1^ inches wide and 18 inches long. Find its thickness. 9. A tree of 140 feet in length was broken into two pieces by falling, and ^ of the longer piece was equal to |- of the shorter ; find the length of each piece. 10. A |man commenced business with a capital of $8000 ; the first year he gained $40 for every $100 in- vested, adding his gain to his capital; the second year he gained $25 for every $100 invested, adding his gain as before ; the third year he lost |^ of his accumulated capital ; how much did he make in the three years ? IV 88 PAFEBS FOB ENTRANCE INTO xxn. 1. Eeduce | of 7J of .86 of 1^ of 8 m. 1 fur. 6 per. to inches. 2. What are the prime factors of 76676600 ? 8. What No. must be added to 7,869,466 to render it exactly divisible by 8976 ? 4. In going down street John observes that he passes a person every 6 steps he takes. Now if he step 80 in. at a time and walk at the rate of 4 miles per hour, how many persons will he pass in a walk of 16 minutes ? 6. A can dig a garden in 6 days of 8 hours each, B can do it in 4 days of 12 hours. How many days of 10 hours each will it require to dig the whole garden when both work together ? 6. What will be the size of the largest measure with which 2 bins which contain 89 bush. 2 pks. 8 qts. 1 pt. and 46 bush. 1 pk. 1 gal. 1 qt. 1 pt., respectively, can be emptied by an exact number of fills of the meas- ure ? Give answer in pints. 7. A farmer laid out $71778 in pm-chasing an equal number of sheep, hogs, and cows. Each sheep cost $6, each hog twice as much as a sheep, and each cow twice as ranch as a hog. How many of each did he buy ? 8. A purse and its contents are worth £1 6«. Qd., and the purse is worth 7 times the contents. What la the value of each ? 9. A owns f of a ship and B the remarnder, and f of the difference between their shares is $1500. What is the vessel worth ? }0. There is a number which when multiplied b^ - HIGH SCHOOLS AND COLLEOIATE INSTITUTES. 89 24-, and the product diminished by 1400, and the result divided by 2^, and this new result increased by 8, and the sum divided by 4, gives 42 for a quotient. Find the number. xxin. 1. A speculator gave $18810 for horses, and sold a certain number of them for $7990, at $85 each, losing thereby $10 each ; for how much each must he sell the remainder so as to gain $2180 on the whole ? 2. In 161884 inches how many miles ? 8. A man bequeathes ^ of his property to his wife, ^ of the remainder to his son, and ^ of what then re- mained to his daughter, and the balance, $1000, to es- tablish a scholarship in a High School ; find the amount each person received. 4. Simplify {8^ of 6A ¥ .12t}x(8J-(4J-2i)) I** (2i-H)xi 5. A boy starts to rim 800 yds., taking three steps in a second, each step three feet long ; he is followed after an interval by a dog which makes two bounds of 6 ft. each in every second ; find what start, both in time and distance, the boy must have so as not to be over- taken by the dog. 6. In a certain business one partner whose share is T*T of the whole, receives from it a profit of $869.20 ; what share is owned by another whose profit is $1969 ? 7. Fifteen cubic inches of copper of specific gravity 8.7, five cubic inches of tin of specific gravity 7.4, and two cubic inches of lead of specific gravity 11,4, ar© 90 PAPEBS FOB ENTBANCB INTO molted together; find the specifio gravity of the bronze formed by the mixiaid. 8. Show that /2i _2881 aiidl.2^8_^4^5^6_ ^^.^ .211 "2821 that 2^+ 23 "^ 2* 2* 2« 2>— ^ ^ 9. Find the price of 184 tons 17 cwt. 8 grs. 14 lb. of copper @ £87 17«. lid. per ton. Qr.=28 lbs. 10. Of the nmnber of candidates that presented themselves at certain entrance examination ^ were plucked in arithmetic ; ^ of the remainder were plucked in grammar ; and of those that still remained ^ were plucked in other branches ; the number of succesBfuI candidates was 26 ; £nd the entire number of candi- dates. > XXTV. 1. Multiply 60788 by 4620, and verify the result by dividing the product by the factors of the multipHer. 2. If 6 articles cost $14.30, how much will 13 cost at the same rate. 3. The sum of $288 is to be divided among 24 men, 86 women, and 72 children, so that the shares of two men shall be equal to that of three women, and each woman's share equal to that of two childi-en ; what will be the share of each ? 4. If 68 bales of linen contain 67048 yards, and each bale contains 84 pieces, and each piece the same number of yards, how many yards are there in each piece ? 6. If a merchant mark his goods on credit 20 per cent, above cash price, what ready money will he ^e for an article marked ^26 ? niOH SCHOOLS AND COLLEGIATE INSTITUTES. 91 6. Two workmen could complete a piece of work, woiking separately, the one in 6 hours, and the other in 8 hours; what part of the work could they get through in 1 hour, working together ? 2^-1^ , , 22.4 . 250 . 1.2 7. Simphfy ^ 22.4 250 and -^- + -^ + 21-i-lJ' """ .26 ^ .8 ^.0075* 8. A bought of £ 84 yards, and of 46 yards oi cloth, at $5.60 per yard. Having sold \ of these pur- chases to D, at a profit of $1.25 per yard, at what rate must the remainder be sold that his profit may be $160 on the whole ? 9. A farmer mixed fifteen bushels of oats worth 40 cents a bushel with 5 bushels of com worth 80 cents a bushel, what is the mixture worth per bushel ? 10. If 5 oxen or 7 horses eat up the grass of an en- closure in 74 days, in what time could 5 horses and 7 oxen eat up the grass of the enclosure ? 1. XXV. Beduce to simplest form ll^-r^l of Vtt 5|of 8A^2^ li^of 1«- 2. If a sovereign weigh 128.274 grains, how many sovereigns will weigh 21 lbs. 4 oz. 16 dwt. 10 grains? 8. A, B, and are joint owners of a ship ; G's share is valued at $2000, A's share is i of B's, and the sum of their shares f of the value of the whole ship ; nnd the value of the shares held by A and B. 2' 8^ 4. Express as decimals -^.; and -771 ; and find the 10* 10* difference beti^een .„ \^.^ . on *^^ ■ •48— -014 of 20 4-8 f 5-6 7-4 -2 of |1 92 PAPERS FOH ENTRANCE INTO 6. A farmer bought 48.125 tons of hay ; for 20.26 tons of it he paid $16 per ton, and for the rest $18.2625 per ton ; he sold the whole at the average price of $.945 per owt. ; how much did he gain or lose ? 6. What will it cost to cover with lead a cistern whose depth, length and breadth are 8 ft. 6 in., 7 ft. 10 in., and 5 ft. 4 in., respectively, at $2.48 per square yard ? 7. If IJ 'guilders are equivalent to 9 shilUngs, and 10 shillings are equivalent to 12*5 francs, find how many francs to 24 guilders. 8. The expense of carpeting a room was $45 ; but if the breadth had been three feet less than it was the expense would have been $86 ; find the breadth of the room. 9. A, B, and met; A had 5 loaves, B had 8 loaves, and C had 40 cents ; they divided the loaves fairly, and C divided the money fairly between A and B ; how much did each receive. 10. A mechanic earns on an average $1.87^ a day, and works 22 days per month; if his expenses are $25.75 a month, how many years will it take him to save $1116, there being 12 months in a year ? XXVI. 1. A farmer has three tracts of land. The first and second contain 280 acres each, and the third contains twice as much as the other two ; how many acres does the farmer own ? And what would the whole amount to at $201 per acre ? 2. A cistern whose capacity is 15000 gallons is sup- pUed with water b^ two pipes, each discharging 32§ BIOH SCHOOLS AND COLLEGIATE INSTITUTES. 98 gallons per hour ; but, by leakage, the cietem loses, duriug the fiUing, at the rate of 100 gallons per hoiu*. In what time would the two pipes fill the cistern ? 8. An upholsterer has 125 yards of carpeting of one kind, 176 of another, and 226 of another. He wishes to divide the whole into pieces of equal length, and the longest that can be thus obtained ; what must be the . length of each piece ? 4. One person expends $6 for coal, at $7 per ton ; and another $6, at $9 per ton. Which of them obtains the greater quantity of coal ? 6. Find the value of the expression (4+*of*of*of20).^-. 6. Multiply 10.5 by 1.05, and reduce the result to a fraction in its lowest terms. 7. How many square feet of glass are required to glaze 6 windows, each containing 14 panes of glass, the panes measuring 17 inches by 15 inches ? 8. A man buys 25 sheep for $144, and 80 more for $184 ; what will he gain or lose by selling them at $6.10 apiece ? 9. A person who has -f of a mine sells f of his share for $6000. What is the value of the whole mine to him? 10. A person contracts to do a piece of work in 80* days, and employs 16 men upon it ; the work is hah finished in 24 days; how many additional workmeui must be then introduced in order to perform the con- tract? > 94 PAPERS FOR ENTRANCE INTO i:i xxvn. 1. Define prime numbers ; numbers prime to each other ; composite numbers ; abstract and concrete num- bers. 2. Gunpowder is composed of nitre, charcoal and sulphur, in the proportion of 16, 8 and 2 ; find what weight of gunpowder would correspond to 46 cwt. of nitre, and find also the corresponding weights of char- coal and sulphur. 8. Express | of 17*. 6d, + .125 of 16«~..627 of 18s. 9c?. as a decimal fraction of £5. 4. How many bricks 9 inches long, 4^ inches broad and 4 inches thick, will be required for a wall 80 ft. long, 20 ft. high, and 4 ft. thick, allowing the mortar to make up one-sixteenth of the entire wall ? 6. In a cricket match the highest score was ^ of the whole number of runs, the next five scores amounted together to ^ of the whole, the remaining five scores to ^ of the whole, and there were seven wides ; find the total score. 6. Eeduce .769230 to a vulgar fraction in its lowest terms, and find, to eleven decimal places, by how much 8-1-=-^ differs from 8.14169. 7+tV 7. What number is that which increased by 2 and smultipUed by 8, the product diminished by 60, and the ^remainder divided by 826, gives the quotient of .1206? 8. Simplify 1 1 + i+* 1+^, and (-^r-Tj) of^^^u HlOn SCHOOLS AND COLLEGIATE INSTITUTES. 05 9. A sum of JB260 17«. Qd. is transmittod from London through Paris to New York ; ,€1 EngHsh = 24^7^ francs French, and 6^ fr- 9 = $2.26 ; find the value of the sum in American ou^jency. 10. A piece of work can be done by A alone in 6 days, by B alone in 5 days, and by C alone in 4^ days; they all begin it together, but A only continues to work till it is j&nished, B leaving off 2^ days, and C H days before its completion; in what time is the work ac- complished? , , xxvin, 1. A merchant bought 290 yards of cloth at 9 dollars per yard. Having sold 137 " yards of it, at 14 dollars per yard, and 81 yards, at 16 dollars per yard ; what would he make on the whole by selling the remainder at 16 dollars per yard. 2. A can build 7 rods of fencing in a day, B can build 9 rods, and C 12 rods, in a day. What quantity of fencing would afford a number of full days' work for any one of the three ? 8. The working wheel of a locomotive is 226 inches in circumference. It turns 91 times in a minute ; through how many furlongs, perches, &c., does it draw the train in a minute ? 4. A contributed towards a charitable purpose 28^ dollars, B contributed twice as much as A, C as much as B, D as much as A and B together, and E as much as all the rest. What was the whole contribution ? 6. WTiat is the difference in the gain per cent, be- tween selling goods at 2d., which cost 1^., and seUing goods at 2^. which cost 2d, ? '-r * \ 96 PAPERS FOR ENTRANCE INTO^' 6. How may the relative magnitudes «ffTwo or more fractions be compi*red ? Express by thjB least integers the relative magnitude of the fractions fj^, ^ and §^. 7. Beduce to the simplest form : — (2^+li + 8^)-lof f of 1|. 8. Find what decimal multiplied by 8750 will give the sum of 17.6, -^ of 86, ^ of 1801, and 96.812. 9. Find the difference between 4^^ + 5.81 -2.5 and Tff "^ IT of .876. 4^2^ of 82 of .46 10. A and B together can mow a meadow in 5 days, and B could do it himself in 8 days. In what time could A mow the meadow ? >- i* ■ XXIX. •■'*■. w 1. Find the cost of 13 lbs. 8 oz. 17 dwts. 11 grs. at SX 2s. %d, per lb. " ? '.v 2. Two clocks point to 2 at the same instant ; one loses 8^ seconds and the other gains 4 seconds in 12 hours ; when will one be half an hour before the other, and what time wili each clock then show ? 8. Express 2| of 1^ tons-^ of 4 lton8 + 2f of 1^ cwt.— 4^ of 1 ton 12 cwt. as the fraction of \ of 10|^ of a ton + 1^ of V> cwt. 4. The specific gravity of atmospheric air compared with water is .0012 ; I ask for the specific gravity of common gas, and am told it is .46 compared with air ; find its specific gravity compared with water. 6. A quantity of tea was sold for one dollar a pound, the gain being one-tenth of the cost price ; the total gain was $67.60 ; how much tea was sold ? V X HIGH SCHOOLS AND COLLEGIATE INSTITUTES. 97 6. An engine, A, is pumping 10,000 gallons of water per minute from a mean depth of 200 fathoms, on a consumption of 14,400 lbs. of coal per day, while an- other, B, is pumping 16,000 gallons per minute from a depth of 60 fathoms, on half the quantity of coal ; which is working most economically, and in what ratio ? 7. Divide l,„izi2i^f /l+§\ 1-^ i-i/ H 3 2 1-4.^ of i^-l- 1-i 1 + 5 8. Find the cost price of lead per cwt., if the sale oi 48 cwt. for $218.70, give a profit of one-eighth of the original price. ,..,.■-.:'■'■ -^'"-'^ \;."^''' ^ , • :„. ' ''.■ -'i''-', '^-?'.. 9. Simplify < :/ 91.81^+ .0298 .1-. 692674' and 8.875 x 3.5-i-5.68 x 8.05 8.05 10. A and B engage in business, A contributing $12,000, and B $8,000; B is to have one-tenth of the profits for managing the business ; how should a profii of $10,000 be divided ? -! ^ , 11. An income first pays the water rates, and on the amount thus reduced an income tax of 2^ cents in the dollar, and then only ^ of the grosb income remains ; find the water rate, '.h - : ,■ "-' ::-'-'^i ^\:'-'l' ■ XXX. ":"^"-,-' ■^■■' --^m^. 1. E:?duoe to its lowest terms the following fractional expression : — 767 acres 9 chains 279 yds 4 ft. 208 sq. miles 181 acres 93 yds. 4 ft. 2. A horse-power will lift 88,000 pounds one foot high per minute ; how many gallons of water per day s > y 98 PAPERS FOB ENXBANCE INTO of 24 hours will an engine of 120 horse-power lift to the height of 140 fathoms, a gallon of water weighing 10 Ihs ? 8. What must he added to .856 of £2 17«. \M, to make up -^ of £8 19s. l\d. ? 4. Water expands when freezing so that a ouhic foot of water becomes 1.089 ft. of ice ; find how many cubic feet of water there are in an iceberg which is 900 ft. long, 88 ft. broad, and 220 ft. high. 6. Simplify *°^«*-(^°^2i^4) 2* 14 4 of X _1^ 1 5 6. If eggs are sold at the rate of 85 for 48 cents, and the gain at this rate is one-fifth of the outlay, find at what rate per dozen they were purchased. • 7. Find the cost of 20 tons 16 cwt. 8 qrs. 22 lbs. of coal at 25 shiUings per ton. 8. A reservoir is 66 ft. 8 in. long by 17 ft. 6 in. broad ; how many cubic feet of water must be drawn off to make the surface sink 2 feet 6 inches ? 9. A parcel of 12 lbs. weight is carried 80 miles by rail for 66 cents, and the rate for the distance over 60 miles is [two-thirds of the rate for the first 50 miles ; how far can a parcel of 8 lbs. be carried for 16 cents? 10. Bought 100 bbls. flour @ $5.12^, and 250 bushels wheat @ f 1.06| ; sold 75 barrels of the flour @ $6.50, and all the wheat @ $1.87^ ; find at what price per bbl. the remainder of the flour must be sold in order to gain $221.87^ on the whole investment. f i * f mOH SCHOOLS AND OOLLEOIATE INSTITUTES. 99 XXXI. 1. Define divisor, dividend, quotient, remainder, ^ow many of these are abstract when the dividend is abstract ? How many are concrete when the dividend is concrete ? 2. Reduce to its simplest form, (3^ a-) of 12f 3|- . 2 TT ^^?+ (12|-2^) of (71-A of (15f-2|) } 8. At what price per lb. must a grocer sell sugar which cost him $15.40 per cwt., so that on every $44 of outlay he may gain the cost price of 80 lbs. 4. Find the expense of papering a room 80 ft. 6 in. long, 24 ft. 8^ broad, and 11 ft. high, the paper being 2 ft. 8| in. wide, and costing 81 cents a yard. 6. Prove the rule for changing a mixed circulating decimal to a vulgar fraction. Find a recurring decimal equal to 6.874 + 1.621— .28— 1.748126 + 2.2428. 6. A and B commence a piece of work on Monday morning, and by Wednesday night have done -^ of it ; A then leaves, and B completes the work in 9 days ; in how many days could each working separately have done the work? 7. A man bought 2400 bushels of wheat at 90 cents a bushel, and found that, by mistake in measuring it, he had more than he paid for to the extent of 2.25 bushels in every hundred ; he sold the whole quantity at $1.06 a bushel; find how much he made by the transaction. 8. The first and second terms of a proportion are .0836 and .6875 respectively, and the fourth term is | of the sum of these numbers ; find the third term. ifr 1 ( I f I ^ i 100 PAPERS FOB ENTRANCE INTO 9. I bought 4250 lbs. of wheat at $1.02 a bushel, and 8408| lbs. of oats at 64 cts. a bushel ; I sold the oats at a certain loss per bushel, and the wheat at an Eidvance of 14 cts. per bushel, gaining on the whole 98 cts. ; at what price per bushel did I sell the oats ? 10. Make out in correct form (with tlie amount) the following bill of goods : Jas. Smith sold to Jno. Brown, 460 lbs. sugar @ 12^ cts., 240 lbs. do. @ 11|, 320 lbs. rice @ 10^ cts., 220 lbs. coflfee @ 22^ cts. ; 80 boxes oranges @ $3.75, 16 do. lemons @ $3.37J, 16 do. raisins @ $4.12|. XXXII. 1. Define multiplicand, multiplier, product. What kind of number is the multiplier in every instance ? Find area of board 4 ft. long and 8 ft. wide, and explain clearly what kind of units the two factors respectively express. Shew why, when the multiplier is greater than 12, each successive partial product is put one place farther to the left. 2. Find the number of rails each 24 ft. long, and weighing 20 lbs. 8 oz. to the foot, that can be made out of 100 tons 8 cwt. 16 lbs. of steel. 8. Eeduce to a decimal, 7ix3^ I of 11 1 T of 233 iof tV of i of ^ of 8|. 6i of U ' 4. If a model of the earth were made with a diameter of 20 feet, express as the fraction of an inch the height of the highest mountain, taking the earth's diameter as 7912 miles, and the actual height of the highest moun- tam as 80,000 feet. 6. If wire fencing cost 28. 4rf. per yard, find what must be paid for enclosing a field 806 yds. long and 166 yds. wide. Answer in dollars and cents. HIGH SCHOOLS AND COLLEOIATE INSTITUTES. 101 8}. 6. A garrison of 1000 men, provisioned for 60 days, was reinforced at the end of 18 days, and the provisions were exhausted at the end of 80 days from that time ; of how many men did the reinforcement consist ? 7. Find how many cubic yards of water are dis- placed by a ship whose gross weight is 750 tons, grant- ing that a cubic foot of water weighs 64 lbs, 8. There are four village lots t the first contains ^ of |- of an acre, the second 40§ rods, the third | of an acre, and the fourth ^ of f of an acre ; find the quan- tity of land in the four lots. 9. How much water must be added to 68 gallons of brandy, worth $4.40 a gallon, in order that the mixture may be worth $8.60 a gallon ? 10. Find the value of .79 of 5.126 shiUings -^ .725 of 18.8 shillings — .126 of two shillings + .76 of a penny. Answer in shillings and pence. >vr^ 1. Simplify , , , .,i 2. The amount of duties collected at the Toronto Custom House on the 26th January, 1877, was $8421.98. Assuming that the average duty was 17^ per cent., find the invoice value of the goods on which the above amount was paid. 8. A can do in 10 days, B in 12 days, and in 15 days, a piece of work for which $64 is to be paid ; they all begin together, and work 8^ days, when B and C leavu, and the work is finished by A. How should the money be divided ? it 102 PAPERS FOR ENTRANCE INTO 4. Express an English mile in terms of the French kilometre, the kilometre being 1000 metres, and 64 metres being equal to 70 yards. 5. " Autliorized rate of discount on American in- voices, 6 per cent." — (Mail, Jan. 29.) Assuming this, find (in Canadian cy.) the duty at 17^ per cent, on goods invoiced at $4880. 6. A and B have equal incomes ; A's expenditure is to B's as 6 : 6 ; at the end of two years A has saved $600, which is ^j of B's savings ; what is the income of each? 7. Find the cost of an embankment a mile long, 4 ft. high, and 18^ ft. wide, at 12 cents per cubic yard for the first foot in height, and 2 cents a yard extra for each successive foot in height. 8. If a new unit of weight were instituted contain- ing 1 lb. 1 oz. 8.826 drs. avoirdupois, how many such imits of weight would make 587 lbs. 11 oz. 16 drs. ? 9. A railway train travels 80 miles an hour, in- cluding stoppages, and 85 miles an hour when it does not stop ; in what distance will the train lose 2 horns by stoppages ? 10. Of the candidates at an entrance examination, .07 failed in grammar, ^ of the remainder in arithme- tic, and 67 parsed ; find the number of candidates. XXXIV. 1. Add together 5 rods, 7 fathoms, 8 cubits, 6 Eng- hsh eUs, 8 chains and 8 inches ; express the result la feet. 2. Take the G. C. M. of 448, 728, 822, and 952, *Tom the L. 0. M. of 2^, 6, 12^, 17^ and 85, and divide HIOH SCHOOLS AND COLLEGIATE INSTITUTES. 108 the difference diminished by 23^ by the sum of 82^ and 76. 4i 8. Reduce ^, |f, ff . f^, *A and "f to equivalent 6V 9i fractions having the same numerator. H 4. A can do as much work in one hour as B can do in one hour and a half, and B can do twice as much work in the same time as C. K A, B, and C can do a piece of work in 6 days, in what time would each of them doit? 6. Fmd the sum of ^l^^s _ 4 yds. £7 5 French Ells 1 oz. Avoir. 1 dr. Avoir. 1077 , 461 "T :; — ^ — -, I pcTTPrr-i- 1 scruple. Idwt. 2804 1920 6. Multiply /f +44 - ^ — 8+ -L •^•^ I ^ f of 7 4 + J 5 + 8+. n by 8f-f 7^ 51 V 7. K 6 ao. 8 r. 18 per. 4 yds. of land cost $200 ; find the price at the same rate of a square piece of land one furlong in length.^ 7^ Z. ^ p(/ n^ju^uU^ 8. A traveller sets out from Toronto to Brampton, and travels uniformly at the rate of 8 miles an hour, and returns at the rate of 4 miles an hour : he was an hour and a half longer in going than returning : find the distance fi'om Toronto to Brampton. y^ -Jk--^^/ 104 9. PAPERS FOR ENTRANCE INTO Beduce to its simplest form, — -_ _'. ^ 111 X 01 + •87 £4 17s. 6d. 4-8G8 miles •8 +-29 11 1 mile, 18 per. 1 ft. "^ 80 £1049 4 tons 18 cwt. ~6-876 1b8. • 10. If 48 pioneers in 5 days of 12 J hours long, can dig a trench 189*75 yds. long, 4-6 yds. wide, and 2*5 yds. deep, how many hours per day must 90 pioneers work during 42 days in order to dig a trench 1686.6876 yds. long, 4-875 yds. wide, and 8*2 yds. deep ? XXXV. 1. Simplify -iofj_^10f-^i of 1^2.8 '+ a T •8 a 6" OixiofJ 2H-Tix^ 2. Reduce 2^ of S\ of ^ of 8i English ells to the fraction of f of f of 5^ French ells. 8. A can do a piece of work in 5, B in 6, and C in 8 days. If A and B work at it two days each, how long will it take B and C to finish it ? S^ ^i^lw V 4. A man buys land at $60 per acre. If he sell \ of it to A at $80 per acre, ^ of the remainder to B at . $22 for J of an acre, and the rest, wliich is 120 acres,3^ to C at $76 for ^ of an acre ; what is his gain or loss ? /QfiJ ) // /"^ // ^' ^^^^ *®* ^* ^^ cents per lb., having gained -^-^ of , {)^i-% ^e cost , find the selling price per lb., if he had lost ^. tji cost , find the selling price per lb., if he had lost ^. 6. A man can row a boat from A to B (a distance of 80 miles) in 7^ hours if there be no current ; how long would it take him to row it if there \^s a current of 1 J miles per hour from B to A ? *^0v» man schools and oolleoiate institutes. 106 7. If A can do ^ of a piece of work in 2 J days, and B can do -f of tlie same work in 8J days, how long will it take A and B working together to do it ? ^ -cr >^^> 8. Divide $2880 between A and B so that | of A's^ share will be equal to f of B's. Z '^ ^ ^ o » ^ Sr//j^ 9. A man divided his pro^ierty as follows:— He gives to his eldest son \ of his property, to his second son i of the remainder, and to his wife what was then left. If he had given his second son twice as much he would have received $800 more than the eldest. Find the share of each. >/ 10. Bought 180 gals, wine @ $2.60 per gal. ; paid for carriage $8.60; for duties $5.80. If ^ of it be lost by leakage, at what price per gal. must the balajice be sold to gain by the whole transaction $10.60 ?^ J, Z Z< T^ 11. A can do a piece of work in 4, B in 6, C in 6 days. If A and B work at it 1^ days each, how much will it be worth to finish it if A and C can eani $2.80 per day? .•>..";■ ;:/;^,^;^-. /^,.'::.;':^ - >•' '^ ./:;;:\// ;^'^"; '.-. XXXVI. .''"■■ 'vj-' ' "' •'4-:,,,/ 1. Distinguish between abstract and concrete num- bers ; in multiphcation show that the multiplier cannot be concrete. c, . , . - 186 -t- 7980 X 7080-^7847 - (491 - 805) Snnphfy ^225^160-5-^8^ ■' 2. If 8 turkeys and 5 geese cost $4.75, and 2 turk- eys and 7 geese cost $8.60, what is tlie jprice of 10 turkeys ? 8. Define reduction ascending. " With the difference between &\ VJs. 9d., Halifax cur- rency, and $8.68i, I purclmee an equal number of oranges, figs, and apples; the oranges costing 6(i., the rlflF 106 PAPERS FOR ENTRANCE INTO I figs 2d.f and the apples Id, each ; how mauy of each did I purchase ? 4. What is the difference in length between 6 perches 21 yds. and 17 EngUsh ells, 8 qrs. 8 nls. ? (Answer in inches.) 6. What is the distinction between the simple and compound rules ? A farm containing 486 acres 2 ro. 14 per. 12 yds. 2 ft. 72 in. was divided among A, B and C, so that B received 79 acres 1 ro. 89 per. 28 yds. 8 ft. 108 inchee more than C, and 41 acres 12 per. 12 yds. 2 ft. 86 in. less than A ; how many inches in A's share ? 6. By what must 141 miles 1 fur. 1 per. 8^^ yds. 1 ft. he divided so as to give 6 for quotient and leave 8 m. 5 fur. 88 per. 2 yds. for remainder ? 7. Define a fraction. How is fraction reduced to its lowest terms ? Give the reason for the process. Reduce the difference in weight between 2 lbs. of lead and 2 lbs. of silver to the fraction of 6 drs. 2 scrs. 8. An estate worth $10,000 is left to A, B and C ; | to A, f to B, and the remainder to ; find CTs portion and its value. 1 8 9. If -;r- + 2i-^4^ + f X1.2-5-.8 of an acre of farm land cost /oTTVr-^ ^^ ^^^^» ^^^^ <^"&^* * village lot to cost which is 182 feet long by 880 feet wide, if land in the village be worth 2^ times as much as farm land ? 10. A does t of a piece of work in 4 hours, B does I of what remains in 1 hour, and C finishes it in 20 minutes ; how long would it have taken all working to- gether to do the work ? I mOH SCHOOLS AND COLLEGIATK INSTITUTES. 107 XXXVII. « 1. When on ounce of gold costs $19.45, what is the the cost of .04 lb. ? 2. An imperial gallon contains 277.274 cubic inches. How many gallons would a vessel contain whose capa- city is 98^ cubic feet ? 8. Required the mean of the following observations of temperature :— 41° 29', 41«> 27^, 89* 18', 41» 88', 87® 47y, 44° 28', 40° 18'. 4. Feb. 6, 1877: "Gold in New York opened at 105^." At this rate, how much gold must be paid for $4210.42,^^ currency? 6. There was a question whether the indemnity to be paid by the King of Ashantee was 6,000 oz. of gold or 60,000 oz. ; what was the amount of money in dis- pute, gold being reckoned at £8 17«. lO^d. per oz. ? 6. A man instructed his servant to lay out equal sums in buying oxen, sheep and horses, and to spend as little as possible. The servant agreed to forfeit $2 for every ox, $1 for every sheep, and $4 for every horse which he bought more than was necessary to obey or- ders. He bought the oxen at $40 each, the sheep at $5 each, and the horses being at the prices of $50 each and $60 each, he bought those at $50 each. What should be the forfeit on account of the mistake ? 7. A, B and run a race. A starts at 9 a.m., anii goes at the rate of 8 miles an hour ; B starts at 10.16 a.m., and goes at the rate of 10 miles an hour ; when should C start, who goes at the rate of 12 miles an hour, so that when A is overtaken by B, C may be one mile behind them ? 108 PAPERS FOR ENTRANCE INTO i; 8. If 2 cwt. 8 qrs. 21 lb. sugar cost $58.40, find the value of 17 cwt. 2 qrs. 14 lb. (Cwt. = 112 lbs. 9. A block of stone is 4 ft. long, 2 ft. 6 in. broad, and 1 ft. 8 in. thick ; it weighs 27 cwt. ; find the weight of 50 cubic inches of the stone. 10. A candidate at an Entrance examination ob- tained as an answer to a question 27 ft. 8 inches ; but found that he had used 5.4 instead of 5.2 as a multi- plier ; find the corz-^ci answer. ' , ,'V ' ' 1. The dividend decreased by 18 is equal to 88 times the remainder ; the difference between the remainder and divisor is 9 ; the quotient is 21 ; find the divisor, dividend, and remainder. 2. Prove that t of 1 =^ of 5. Simplify (8^+-i42867) X 2125. - ^ 8. A has four times as much money as B ; they play together, each staking 10 shillings ; A wins the first game, but loses the next ten games, and then three times A's money is equal to seven times B's : what had each at first ? 4. In a school there are 168 scholars in the lower form, and 119 in the upper form. The scholars are so divided that the number in each class in tl j lower form and upper form is the same, and the number of classes as feuj as possible. Find the number in each class and the total number of classes. 6. Suppose unity to represent '0012, what number represents '0001 ? HIOU SCnOOLB AND COLLEGIATE INSTITUTES. 109 6. A man buys 100 gallons of wine at $2.00 a gal- lon, and keeps part for his own use. In selling at $2.25 a gallon, by using a false measure ho gives 8^^ quarts for a gallon, clearing $26.00 by the sale. How many gallons did he keep for his own use ? 7. A company of boys is met by A, who gives each boy 40 cents ; afterwards the boys are joined by 10 others, and the money received from A divided equrlly among all the boys, who are mot by B, and ho gines each boy 80 cents ; afterwards the boys are joined by 18 others, and the money is again equally divided, when it is found that each boy has 20 cents. How many boys in tlie company when met by A ? • - ' 8. A grocer buys tea at 64 cents a lb. and sells it so as to gain ~- of the cost price ; find his receipts on 6048 lbs. 9. A man divides the value of his estate equally among his three sons. The first son gains an amount equal to one-third of what he has ; the second loses one- third of what he has, and the third gains one-third of what he has, and then loses one-third of what he has after his gain ; and now the sons together have $800 less than the value of the estate. What was its value ? 10. I sold $20,000 stock of Consolidated Bank at 98^ and invested the proceeds in Bank of Commerce stock, selling at 120, and paying a half-yearly dividend of $4^ on every $100 of stock ; find my half-yearly income. ., XXXIX. 1. What number divided by 86821 will give a quo- tient 5627 with remainder 824 ? ;i 110 PAPERS FOR ENTRANCE INTO 2. In multiplying a number by 89, 1 begin the par- tial product of 8 and the multiplicand under the figure in the tens' place of the product by 9. Why do I do so ? Show that the sum of the partial products is the com- plete product. 8. Addition, Subtraction, Multiplication and Division are called the fundamental rules of Arithmetic; why are they so named ? 4. In making out a bill for 65 bushels of oats at 40 cents per bushel, I multiply 65 by 40, and give the re- sult $26.00. Am I correct? Give reasons for your answer. 6. The less of two numbers is _54|_ i of 8§' and their 1* difference is ~ ; what is the greater number ? 6. How much must be paid for 860 feet of boards at $12.00 per M, 250 shingles at $2.60 per M, and 760 feet of timber at $1.00 per ? 7. A and B set out at the same time from places 88 miles apart, and meet at the end of 12 hours ; A travels If miles per hour more than B. How many miles did each travel ? 8. Sold a house for $4800, and gained i of its cost. What did it cost ? 9. If 10 men can do a piece of work in 12 days, how soon after beginning must they be joined by 8 more so as to finish the work in 10 days? 10. If a man fill ^ of a cask with brandy, } with wine, and i with water, and it lack 21f gallons of being full, how many gallons will that cask contain ? BIOH SOHOOLa AND OOLLEOIATS INSTITUTES. Ill in the par- • the figure do I do so ? Ls the com- jid Division aetic ; why oats at 40 ^ive the re- ns for your and their of boards at and 760 feet m places 88 ; A travels y miles did of its cost. n 12 days, i by 8 more dy, J with ns of being ? XL. 1. In 1284567 sq. in., how many acres, roods, &c. ? 2. The remainder 8 is f of the divisor, and ^ of the quotient ; find the divisor. 8. If I purchased 2f yds. of black cloth at 16«. 6d. B^r yard, 2f yds. doesldn at 7s. 6d. per yard, SJ yds. alpaca at Is. 6d. per yard. If yds. linen at Is. 8d. per yard, and 6^ yds. flannel at Is. lOd. per yard. What change should I receive out of a twenty-five dollar bill ? 4. Add f of a peck to 2f gals., and reduce the result to a decimal of 4 bus. 2 gals. 2 qts. 5. Beduce to its simplest form, ^ ^^" tV(2*046--6). 6. The bottom of a cistern measures 7 ft. 6 in. by 8 ft. 2 in., how deep must it be to contain 76 cubic ft. of water? 7. A boy gives j- of his marbles to A, ^ to B, and the rest to 0. loses 20, and has then 70 less than A. How many had each at first ? 8. A man lost f of the value of his horse by selling it for $60 ; for what should he have sold it to gain |^ of its value ? 9. A man has $4000 in the bank. He drew out ^ of it, and then ^ of the remainder, and afterwards depos- ited ^ of what he had drawn out. How much had he then in the Bank ? 10. A man after paying a tax of 2 cents on every doUpT of his income, and also spending $2 per day, is still able to save $495 a year (865 days) ; what is his income? 11- Irr^ V s v V CHAPTER IV. EXAMINATION PAPERS TOR CANDIDATES FOR THIRD-CLASS CERTIFICATES. .. ,„. July, 1871. ";'-■'" ''^'"''" \ 1. Write in figures and express in words the num- bers seven hundred and one units in the 6th period, fourteen in the 5th, one hundred and twenty in the 3rd, fouteen in the 2nd, and nine in the 1st. >7^ . , , 2. Shew that the corresponding operation in the simple and the compound rules, are based on the same principles. How many years, months, days, hours and minutes from 20 minutes past 4 o'clock P. M., July 15th, 1862, to 25 minutes past 11 o'clock, June 29th, 1871 ? J^i^V? // -r^«> fhtL ,ef4^ J'-i^M. 8. State the principles on which is based the rule / for finding the G. C. M. of two numbers. Apply them to find that of 8621 and 1581. >('/ 4. The driving wheels of a locomotive are 17^ feet \ in circumference, and the trucks lOf , what distance must the train move to bring wheel and truck into same relative positions as at starting ? 2^ ^ y X^ y 6. State the general principles on whirth the rules XillBD-GLASS CIEBTIFIGATEa. 118 : into same of fraction. s depend; and find the simplest form of (7J^6i) of { (li X J) + IJ } X (3J - -ft), i/ »^ n' 6. From the sum of 2^| acres, f of 8:|^ acreg, xv, K roods, and ^ of 1-^ perches, take 4 acres, 26 perches, 12 square yards. 3 /V , ^ /^ , ^2- 7 '/^ i^^ 7. A man divided a farm among three sons ; to the ', first he gave 80 acres, to the second ^ of the whole, and -.^^ to the third f as much as to both the others. How many acres did the farm contain ? ^ ^d C'^-t^J^c? 8. Find the sum, difference and product of 8*456 \ and -426. 3 , S i , 5 ' 6 "b / , Y A^y/C^O^j 9. Find values of 2-7345 according as the unit is £2 5s., or 6 acres, 2 roods, 10 perches, or 6 oz. 10 dwt., 16grs.^^''i /• 'il2 10. dold 20900 feet of lumber for $881-624, gaining / thereby $78-87^. What had it cost per C ?// i/ jl^ 11. Explain the difference between simple and com- pound proportion. In Nova Scotia the Sovereign is -^ worth $5, and in Ontario $4-86f ; convert, $2720-40 Ontario currency into Nova Scotia currency. for investing, with instructions to purchase certain goods, deducting his commission from the amount of money sent him : find his commission. ' 10. A coal dealer bought 784,000 lbs. of coal, at $4.60 a ton (2240 lbs.), and sold 624,600 lbs. of it at the rate oi $6.60 per short ton (2000 lbs.), and the bal> ance at $1.20 per short ton : find the ^ hole gain.^ ^/J'^^l THIBD-CLASS (;ERTIFICATBS. 115 1 tbe cost on can be aging the ^, B, and , and G, '(y* 10 md 9 feet days, of [ong, and len in 7^ he latter bi-ds long, J6 a yard,y % ^(^ nts a lb., lb. must , and 18 inMon- ictions to tion from ission. viur S coal, at of it at the bal- /f 7S July, 1872. 1. The demand of 10 hours' pay for nine hours' work is equivalent to a demand of what increase % in wages? >/.( ■'-/ 2. What number divided by (A+tV)-5-(3-4) x a + i)wiUgiveAofy|of ?^of247? ^ 8. Find amount of following account: — 448 lbs. butter at 23 cents, 486 lbs. cheese at 9^ cents, 240| lbs. lard at llf cents, 254^ lbs. tallow at 1^^ cents, 40| dozen eggs at 16f cents, 15 bbls. salt at $1*40, and 481|l lbs. ham at 12^ cents. / J, <^3 '^l-V/L 4. A bankrupt owes four creditors as follows : — A $2500, B $8300, C 4200, and D $4000; his property ^^' ' is worth $10500 ; what does each creditor receive ? JL 6. A lumber merchant bought 106250 feet of lumber at 14| per M., and retailed it at $1*75 per C. Find his gain. S $3a*S }f 6. Find the expense of plastering a room 20 feet longf, 18^ feet wide, and 11|^ feet high, at 18 cents a yard.jj^^, ^%/i 7. K 25 men build a waU 16 ft. high, 2 ft. thick, and 50 ft. long, in 12 days of 9 hours each, how many hours per day must 40 men work to build a wall 60 feet long, 8 feet thick, and 20 ft. high in 25 days ? 8. How much water must be mixed with 600 gallons wine, at $2*50 a gallon, in order to n^^^ke the mixture worth $2 per gallon ? / ^ ''^ -^^ ^t-* 9. If $120 gain $5-84 in 126 days, find the gain in 860 days. ^^4<» f) S K 10. A merchant bought 500 bis. of flour at $6*25 a ts' tv%i i IIG KXAMINATION PAPEBS. bl., on a credit of 8 months. He sold it at $6*50 a bl. on a credit of 4 months. What was his net cash gain, money being worth 12% ? ^ ^ 3 / -^ IV, July, 1878. 1. Define a fraction and fully explain the terms numerator and denominator. 4 of 4 ^xU ^^ Simplify 6i-6A'Ax6i ^^^ '"ti r \ « »■ ^ 2. Bought \ of 4^ cords of wood for \ of | of $80 : what were two cords worth at the same rate ?^^ < ;? 1 8. Show how to convert pure circulating decimals and mixed circulating decimals to vulgar fractions. Find the sum of -478, -82*1, -82, -78504, '\ and •4826, and the product of 8-466 by -426. ^'^ ^'^U-3i;rt/i (^) '¥if 370 4. How many feet of lumber will be required to in- close a building 60^ feet long, 40J feet wide, 22 feet high, and each side of the roof 24J- feet, allowing 628^ feet for the gables, and making no deductions for doors and windows? ji%^-^^ ^ 6. Find the difference betwi^en the true and the bank discount of $2600, payable in 90 days, at 7 per cent^ ' 7 ^> 6. Find cost of plastering the walls of a room 80} feet long, 18} feet wide, 12 feet high, at 18 cents per square yard (no allowance for openings) ; find also the cost of carpeting such a room wijbh carpet 27 inches wide, and costing $1.80 per yard.jJ^2.3-X'l- -^ S(J^ ^u, 7. Ten per cent, of an army ^as slain on the field of battle, and 6 per cent, of the remainder were mor- tally wounded: the difference between the killed and THIBD-OLASS OE51TIFIOATE8. 117 mortally wounded was 1100 ; how many men went into battle ? l!l4r^^P^if^ 8. Having received a stock dividend of 8 per cent., I find I am now the owner of 297 shares ; how many shares did I own at first ? 1, "^ S '^ 9. Given, that pure water is composed of oxygen and hydrogen in the proportion, by weight of 16 to 2, find the weight of each in a cubic foot of water.// 7 «^ ^2^/7 10. How many railway shares (100 each) at 40% discount must be sold in order that the proceeds in- vested in bank stock, which is 4% below par, and pays a dividend of 7^, may yield an income of $1680, %iQ 11. A railway company pays $24.76 per acre for a portion of road 100 miles long and 94^ feet wide, find the whole amount paid. ^ ^ J^ 4 S "6 12. An insurance company took a risk at 2^yo, and reinsured f of the risk at 2% ; the premium received exceeded the premium paid by $42 ; find the amount V. of the risk. ^ ^ December, 1873. 1. From a pound Troy are coined 46^J-^ sovereigns ; find (in £ s. d.) the price per oz. of gold. -^ ^^ ^ / \ • 2. Divide $29.50 between two persons, so that one shall receive half as much again as the other. % //'W y '"d ^7' 8. Simplify i of J4 - ^^ of iS + A of-|°'. 4. The sum paid for 494 gallons oil, including k duty on each gallon which amounts to \ of the cost price of a gallon, is $1719.12 ; find the duty on a gal^or. ^ . i "S 0. A merchant tailor bought 27 pieces of cloth, ^aqli •7 A 7" ■ f i 118 BXAMINATIOM PAPEBS. containing 19^ yards, at $4.81^ a yard, and paid freight $9.62^ ; he sold so as to gain ^881.87^. At what price per yard was the cloth sold ? il d", ^ 1' '^ 6. A and B can do a work in 8 days, B and in 6 days, and A and in 4 days. If $16 be paid for the work, what is each man worth per day ?)ft{ ^t , ^^k 7. Find the value of 80 cwt. 1 qr. 15 lbs. of sugar at $10.20 per cwt. (qr.=26 lbs.) J^ ^/^> Oi 8. A person, after paying an income tax of 2 mills in the dollar, has $ 1 681 .98 left. Find his gross income^ yra '^^ 9. Find the cost of covering a room 27 feet wide and 80 feet long, with matting 2 ft. 6 in. wide and costing $1.62^ a yard. i^ /y^T.^t 10. A miller has a bin 8 ft. long, 4^ ft. wide, and 2^ ft. deep, holding 76 bushels; how deep must he make another bin which is to be 18 ft. long and 8f ft. wide, so that its capacity may be 460 bushels ? 7-^^ 11. A man, engaged in business with a capital of $10920, is making 12^ per cent, per annum on his capital ; but, on account of ill-health, he quits the busi- ness, and loans his money at 7f %. How much does he lose by the change in 2 years, 5 J months ? i /H i % ^/^"^ VI. July, 1874. I. Simplify o. ^ ioff x7i 7,1^ ^^^'^^^'^'Kaok •'- ^ ^TTj-oTS ' ST150A-741 ^ ^25. 2. Water is composed of two gases, oxygen and hydrogen, in the proportion of 88.9 to 11.1; what weight is there of each in a cubic yard of water ? (cubic foot of water weighs JOOO oz.)^ /irr9 Ji /^ THIBD-GLASS CERTIFICATES* 110 8. The sum of $1,416 is to be divided among 15 men, 20 women, and 80 children in such a manner that a man and a child shall together receive as much as two women, and all the women shall together receive $480; find the amount received by each man, woman, and child, respectively.^ J 3. <^ .'^ ^, ^/<^/' ^'^ 4. A bankrupt who is paying 87^ cents in the dollar, divides among his creditors $6,800 ; what do his debts amount to? / /ii^ 6. It costs $96.26 to carpet a room 22 ft. 6 in. long, with carpet 27 in. wide and $1.75 a yard; find the width of the room. /^ \ 14 6. If 8 men or 6 boys can do a piece of work in 17 days ; in how many days will 5 men and 8 boys do a piece of work three times as great. ;£ :2 -j ^a/u>V 7. Find the cost of 88 yds. 2 qrs. 8 nails of cloth when 3.76 yds. cost $8,826. ^ Zfit/i -| 8. A man invests half his fortune in land, a fifth of it in Bank Stock, a sixth in provincial debentures, and loses the remainder ($8,000) in speculation — What was his fortune at first. J ;^, ^r^UU 9. Bought 9,000 bushels of wheat at $1.12^' a bush,, payable in 6 months ; I sold it immediately for $1,06 a bushel, cash, and put the money at interest at 10 per cent. At 'the end of the six months I paid for the wheat; did I gain or lose by the transaction, and how much ? 10. In an examination. Arithmetic and Grammar are valued at 200 marks each ; Education, Geography and History, at 160 marks each. A candidate obtains 70 i> in Arithmetic, 66 y* in Grammar, 60 % in Educa- tion, 60 7^ in History, and 40 % in Geography , find his average rate per cent. (i. e. rate per cent, obtained of the aggregate marks.) ^-^ fl ^^ >I0\ yt ^ 120 BXAHINATIOlf PAPBBt. vn. July, 1876, 1. Simplify, .1 3 M 74 llf-2^ "64 10A-7i} 844) m llj-f2| 2. A wine merchant pays $175 for a hogflhead oi wine, and bottles it o£f into an equal number of quart, pint, and half-pint bottles: how many dozen of each has he, and at what must he sell it per dozen to gain A of his outlay ? /^ ^ . ^ ^';/ st ^ /^Z' 7^? ./-^. 8^^ 8. What must bo the face of a note so that when discounted at a bank for 4 months and 9 days, at 9 pei cent., it will give $240 ? ^^ 4/^. ^/V- 4. A, B and C having equal shares of a ship, sell respectively one-third, one-quarter, and one-fifth of their shares to D, who dies and leaves his share equally among them : If B's and C's interest in the ship be now worth $37,800, what is the vame of A's share ?i/4^7/^ 6. A farmer hfts 600 bushels of wheat ; he can sell it at once for $]..20 a bushel ; by storing it for six months at a cost of $20 paid in advance, he can realize $1.80 a bushel ; he adopts the former course ; money being worth 8% per annum, determine how much he has gained or lost by so doing. 5^ 5 ' -- c^-v*^ ' ^^ "^^ 6. Express the value of *8d of 88. + '05 of 2 guineas -I- 1.8 of 6«. /pj o ^rj^ 7. A merchant bought a number of barrels of floui for $1800 ; he used 20 bbls. and sold ^ of the remainder for $1568, which was $224 more than cost. How many barrels did he buy ? ^^iTV 8. When gold is quoted at I884, what is the gol^ value of a $10 greenback ? ^ aM THIBD-0LA88 CERTIFICATES. 121 9. A piece of land whose length is 151 yds. 1|^ ft., and breadth 85 yds., is to be exchanged for part of a a strip of land of the same quality, whose breadth is 16 'P^ yds. 2^ ft. Find the length of the equivalent strip. ^^Lf k^ 10. What is the duty on 4 hogsheads of sugar each weighing 1280 lbs., gross, at 2} cents a pound ; tare 14 - per cent. ^ /^ /, ^ f / 11. A merchant in New York wishes to remit to London a bill of exchange for ^293 1«. 0(2.; what is tiie cost of this bill when exchange is at 9|^ premium *t/f/^2-o '//^ ^ vni. N. 8., June, 1876. 1. Find the value of 27 6-Hi-l) of 4 shil- 'U lings, and express in decimals. 2. 7xl0^''"8xl03 A. and B. agree to divide their travelling ex- penses in the proportion of 1§ to 1. A. pays on the whole $129, and B. $76.26 ; what has the one to pay and the other to receive in order to settle the account ? 8. Acertamnnraberofn.er.,ai4^'24io4B, and three times as many boys earn $124 in 5_days; jl each man earned $1.20, each women 66| cents, and each boy 68^ cents per day. How many wese there of ^ach? ^ n^^/t ^ ^ /S cJv^ 4. Seven-tenths of the selling price of certain goods is two per cent, less than cost. Find the gain per cent, at which the goods are sold. C/ ^/^ 6. At 2^ per cent., what will be the cost of insuring property worth $8600, so that in the event of loss ^c) 122 BXAMIN4TI0N PAFBM. \h ■^! i i i 1 i worth of the goods and the premium of insoraiioe may be recovered ? ^ ^^ J^ 6. A, B, and 0, do a work in 10 days; A does 1^ times what B does in the same time, and B does } what C does iu the same time. How long would it take euch todothework?^!?f^^(J^^^y fftf^i'^d 7. Bought a number of oattle for $2000 ; had I bought 20 head more at a cost of ten dollars per head less, my entire outlay would have been $2800. How many cattle were purchased ? V^ 8. Find interest on a note for $616.62, dated March 1st, 1878, and paid July 16th, 1876, at 8%.|^.^-f -^ 9. A man mowing grass walks at the rate of *86 ^ miles an horn*, and in 70 minutes mows a grass plot of 1066 square yards ; how broad does he mow ? A^ ^ /- 10. A tradesman has a cash price for goods aM a nine months' credit price: money being worth 8% per annum simple interest, find the ratio of the prices. '{V ^ IX. July, 1876. 1. Hni what q[uantity must be added t6 If ofH . 2iof 6^ ;3^of2f ^^ l?of82f "^Si of_6J\ of H/ , / 1 of BiofSiof ]4xi\ to make it equal to \t^^ } 2. Beduce to its simplest form (•076)^+(-026)» - . (•076)a - (-0767^0267+ C025p~; ^^ ^^^^ ^'^"^^^^ ^^ §'36^ giving the result to the end of the first period* THIBB-OLABS GEBTinOATEB. 128 / / 8. Express ^ of 12«. 6d.-{-'fgof 8 guineas + A ^^ j^4 _ ^ of 2J<^"4<' - - ''W /y ^^»^^^ >a.£ 6. A vessel worth $12886 is lost, on whicn the own- ner had paid a premium of 8^ j^er cent ; what had he insured for if he recovered all moneys paid, in addition to the value of the vessel 9-^ ^J?/^ f 3 ' ^' 7. A banker lent to the same merchant $2804 on I \ ^^^' j^the 28rd of March, $1680 on the 16th of June, and ""^T^, $1728 on the 29th of September ; the merchant repays the whole sum, with interest, on the 2iid of January. Find the amount repaid, interest bein^ 7^ per cent, per annum. ^^-C/V^, ^^W^ J KroMiiai i ' . THIRD-GLASS CERTIFICATES. 126 cost as iud the of J. of 161* rs; how 7ork of $8765. ing for )r wear t'a.0. ' francs gulden nother ) miles Find ) other eown- lad he dition 04 on and epays iiiary. per 8. The true discount on $1286.68^ for 210 days is $31.18^ ; find the rate per cent. ^/:S '*^ 9. What sum of money must be divided among A, B, and G, so that A may have $1.44, and $2.25, and / that B may have as much per cent, more than A as G has more than B ? ^ i>fC/^ 10. Divide the number 474 into three such paits that three times the first may be equal to 5 times the ^ second and to eight times the third, i^i^h /^^i^ ^ ^0 XI. 1. Beduce to its simplest form (•05)3-(-025)» / <^0 (•05)2 4- (-05) (•025) + (-025)» 2. " Sterling exchange in New York is quoted at $4.86 for demand bills, and $4.86A for 60-day bills." A merchant in New York owes another in London £1500, which he can either pay at once or in 60 days with interest at 6-j^j per eent. per annum (865 days); find whether it will be more profitable for him to dis- charge the debt by a demand bill or a 60-day bill, and how mudi he , will save bv the more profitabjie/joi^m. . 8. If 60,000 bricks are required for a wall 50 yards''^ ir,\ long, 15 ft. high, and 1 ft. 10} in. thick ; and if each ' brick be 9 in. long and 4^ wide, find its thickness. ^ 4. A grocer sold, at 51 cents per lb, a portion of a stock of tea, incurring a loss of 15 per cent., and a total loss of $18 on the quantity sold ; he then increased the selling price so as to gain 20 per cent., and having sold the balance of his stock at the increased rate found that he had gained $78 on the sale of the entire, ^tock. Find the quantity of tea at first, / d o Q -^-^^ -« /i I- ■ I » I* «, 126 EXAMINATION PAPERS. 6. $500. Toronto, Feb. 1st, 1876. For value received I promise to pay Thwaite, Eby & Co., or order, five hundred dollars, three months after date; with interest at six per cent, per annum ; endorsed as follows: May 1, 1876, $40; Nov. 14, 1876, $8; April 1, 1877, $12; May 1, 1877, $80. How much was due when the note was finally paid Sept. 16, 1877 ? 6. If 18 were added to a certain number, f of jf of the sum would be 40 ; find the number. /^ / 7. A person investing in railway stock paying 4% re- ceives 5 per cent, for his money ; find the price of the stoak. yc 8. The average of 21 results is 61, that of the first 8 being 64, and of the next ekven results 69. Find the average of the last two. ^ C 9. The French kilometre contains 1000 metres, and 64 metres are equal to 70 yards ; how many yards are there in a kilometre ? y{) ^3 ^y^ ^^ 10. Coals are 20 per cent, cheaper this year than last ; if the price were to rise $1 a ton, they would still be fifty cents a k)u cheaper than last year; find the price last year. j[ p^ xn. 1. A, B, and C can do a work in 84 days. A, B, and D in 72 days. A, 0, and D in 63 days, B, 0, and D in 56 days ; hflw long would it take each alone to do it^ 2. A gallon laeasure contams fragments of a mixed met il, and these are found to weigh 56 lbs. ; 2^ pints of water are then poured into the measure and exactly fill it; find the specific gravity of the metal a gallon of water weighing 10 lbs. f, /J^i^ and a ths, re- alue of I among in the . irst two lums. and a and 16 liuch 82 days' Ives 1-^ ns will ie sides length ji^sed in 1 worth 66 cents a stone, but uses a false pound weight of 15| oz., what must B charge for his flour that the exchange may be fair? (i6 iU^^itT 4-9. A man finds that his half-yearly income will be $3^ more by investing in Dominion Bank stock at 126 and paying 4^ y- half-yearly, than by investing in Bank of Commerce stock at 120 and paying 4^ % half-yearly. How much has he to invest '^jf ^j^^tMf^o 10. Gold is sold at the mint at £2 lis. 9d. per oz., and is mixed, with aUoy worth 5s. 2d. per oz., in the ratio of 11 to 1 ; if Sovereigns are coined of this mixture each weighing 5 dwts. 8.247 grains, find approximately what is the Mint profit on 100 Sovereigns. ^ **", cv v XIV. ^ 1, Find value of ' ; /-f |^|+i(u3i-li)-(7f-6,); yf 2. Divide '0564 by 14*1 and give reasonr^for the position of the decimal point. « ^/-^ (J 8. What vulgar fractions are reducible to finite decimals? Beduoe to its bimplest form 1 \i i. *0| •008^ 25 tX 207 600' ■I I — 4. A man bought a store a£d contents for $4720 ; he sold the same for 12^ % less than he gave, and then lost 16 i> of the selling price in bad debts. Find his entire loss. / /lO 9^^ " 6. Paid three sums of money in succession, each ==:;=; 180 EXAMINATION PAPEBS. of which took ^ of the money I had before paying it less 60 cents, after which Lhad $83^ remaining. How much had I at first ? /^/^ / // J <^ ^ 6. Sold wheat at $1.00 per bushel and gained $80 on the quantity sold; had I sold it at $1.12} I would have gained $42 on the same quantity How many bushels did I sell ? C^/ ^-7^^.^. .4/ A/ — 7. Se^ m men engage to do a piece of work in a certain time, but three of them failing to come, the work was prolonged 7} days. In what time would the seven men have do^ie it ? ■ — 8. -. aioi" $76, the t^ a ; i) cents, and the coffee at 40 cents, per lb. ^ How many Ibd. of each did he sell ? ^c [uL //^ ^'^ •=- 9. A gi vicei ■'?. Sv I :/'ant sells 90 lbs., of tea and coffee for / / 7 XV. ..I II 1. Find a decimal multiplier which wiU convert Troy ounces per inch into tons per mile ; use this multipHer to find the weight in tons per mile of wire which weighs y^ of an ounce Troy to.one, in<;Ji in length. ^j-^'^^-^^*^ V- 2. If tiio vaifti^ 01 one poun^ of gold is 14 times that of a pound of silver, and the weight of equal bulks of ' gold and silver are in the ratio of 19 to 10 ; find the value of a bar of silver equal in bulk to £1750 worth of gold. //5'',, /) V ,, ^-y.a^ .*- :^ J^.^^4iZ^^ '••^. Find the true and the mercantile worth on a note i £^/c " /1/4 j^il6"'^^ /{ Ji THIBD-OLASS CERTIFICATES. 181 tless How L $30 ^ould many in a )work seven :ee for ts. per pound, to the price, ig at Troy [tiplier weighs 3B that klks of id the Irth of note for £219 drawn on the 4th of June at 4 months, and discounted on the 14th of July, discount bemg allowed at 4^ per cent. (Keckon days of grace.) ^ 4. When the 3 per cents were at 90, I found that by selling out and investing in Indian 4 per cents at 95, I could improve my income by £24 Qa. Find the amount of my stock in the 8 per cents. ^Jt S^ 1 ^ ^ 5. A owns f of a vessel and B the remainder ; the Tessel is sold, A receiving 60 per cent, of his shai-e of the money, and B 20 per cent of his ; B afterwards re- ceived $4000 from the purchaser, and the balance then due was divided equally between A and B. What is the ship sold for ? ^ / / / ^ —6. A man sells out f of stock in a certain railway, O paying 2 ^o half-yearly dividends, and invests in Bank of Commerce stock at 120 and paying 4 ^ half-yearly divi- dends ; he finds that his income is thus increased $dd|^ ; find the amount of his railway stock, ^ii^- /^(^ > —7. A man's income is derived from the proceeds of $4550 at a certain rate per cent, and $5420 at one per cent, more than the former rate ; his whole income being $453, find the rates // 7^; / ^ y ;<; S^ — — 1 -c-/ / /i' - 8. A mixt^e of black and green tea weighing 1^ lbs. is worth $8.70 ; if the proportion|^of each are inter- changed, the mixture will be worth $6.90; the black tea is worth 80 cents per lb. ; find the price of the green tea. ^ ^ tu-^ - 9. A, B, and can together do a piece of work in 20 days ; after 6 days A gives up and is succeeded by D who does half as much again as A, B, or C can do in a day. When will the work be finished ? / 2^ ^i.i''c<^'y "%-< vy^i ** 10. K I geti^ Londdlis^ for 25'fran,(?s 20 centimes, what shall I gain'iBclose p^l^-Mjjt. by taking French /• I J *■■ 188 EXAMINATION PAPERS. /^ I II !*/ . money into Bavaria, where ttjB»;jxchang^i^l gulden Vi 40 kreutzerd for JBl, tmd,,*8gula^!B^^a(1'^ln"eiit^^ a Napoleon ? (1 giiMe!f=^^krjwitzer^>»J^ t/Oi XVI. 1. Find the difference between •004 -r -0005 2-423 + 8-676 + 2-0001911 of £2, and ^ n of \ of j^. f + ? — 2. A, B, and are employed to do a piece of work for $26.46 ; A and B together are supposed to do f of it ; A and -j^ of it, and B and G ^ of it, and are paid on this supposition. Find each man's j^are^^ ■^8. In a certain constituency the total niimber of votes is 2500 : 20^0 of these refuse to vote at an election at which A, B and C are candidates ; 6 per cent, of those who vote spoil their ballots, and of the number of votes counted by the returning officer, 20 per cent, of A's equals 26 per cent, of B's, and 10 per cent, of B's equals 4 per cent, of C's. Find the number of votes for each. Ci "- ^nn> ^h - Oo"0^ (i -^ /crU — 4. A farmer gave for a horse a bill of $272, due in two months, and sold him at once for a bill of $316, due in 6 months ; find the former's gain or loss, true discount being rjMjkra^ed at 4* per cent. iO^/'2,C' 6. In a certain factory irore employed men, women, and boys; the boys received 8 cents per hour, the women 4, and tlie men 6 ; the boys worked 8 hours a day, the women 9, and the men 12 ; the boys received $6 as often as the women $10, and the women $10 as THIBD-OLASS OERTIFIOATES* 188 ii^^ ■I often as the men $24. How many men, women, and boys, respectively, were there, the whole nmnber being — 6. A crew can row down stream a distance of 4 miles in 80 minutes, and up stream the same distance in 84f minutes. Find the rate of the stream. -^ 'y^^iic 7. A grocer increased the price of sugar, charging for 7 lbs. what he before sold 8 lbs. for ; he made 25 per cent, profit at his former price ; find the profit after the rise in price. /^*it y^ —8. At what rate must a note payable 18 months hence, without days of grace, be discounted to produce 7y- interest? ... 12^^^ % 9. The area of one of the faces of a cubical block is 660.49 sq. ft.; find the volume. // <^ yc/' . ^ '^3' —10. I sold 260 yards of cloth for $846, receiving ' $1.80 a yard for part of it, and ^1.60 a yard for the re- mainder. How many yards did I sell at each rate ? /i^, /<^^ xvn. / 4..-^/' 1. Simplify {(2-6 + l-12 + -32)x(7-24674-2-684)} -^56-3. 2. A man having $128 spends a part of it and after- wards gets 3^ times as much as he spent. He then has $353. How much did he spend at first ^ yf iO 8. A and B go into business with equal sums of money. A gains a sum equal to ^ of what he had at first, and B loses $60. A then has 1^ tii^e^ as much as B. What sums had they at first ? c^ A (fi) 4. A fruiterer bought equal quantities of apples of two different kinds. For the first sort he pays 8 pence for 6 ; for the second 5 pence for 7. He sells them t^t 184 I 1 1 ■XAMINATION PAPEBS. ^ ly would he need to sell at 11 for 7^ penoe^. How many this rate to gam 19 cents ? V6 ^ 6. The side of a field is 19^ rods in length, and the end 16y^7r rods. What is the longest board that can be used in fencing both side and end of the field, so that / no fraction (of a board) may be left ? f^^-- iu^ rv /^i"^ 6. A boat can sail with the current from A to B in 40 minutes, and back in 50. Compare the rate of the current, with the rate of the boat while going down. / ,' /(J 7. A boy can split a cord of wood in one hour, and a man can do it in half an hour. After the boy has been working for half an hour he is joined by the man. How long wiU they take, botl^ working together, to finish the cord ? / ^ 4vvvi/'»-^ 8. The distance between the post office and school- house is half a mile. A carriage stands on the pave- ment in front of the schdolhouse. The fore wheels are 10^ feet in circumference, the hind wheels 15f feet. A chalk mark is made upon the upper side of each wheel. How often wiU the 4 chalk marks be all up together while the carriage drives to the pest office ? <^ '^ iCyytCJ 9. A and £ sit down to play. A has 5^ times as much money as B. At the first game B wins ^ of A's money. What fraction of B's money must A win back so that they may have equal shares ? 5^^ 10. A merchant agrees to take cordwood from a farmer, and pay for it in tea. When the wood is de- livered he finds that the farmer, by using a false mea- sure, has given 7-| feet to the cord instead of 8. How much must he raise the price pf the tea so that ^e may be even with him ? ^/. ^if I / TRIBO«0UlSB certifioatkb* xvm. 185 1. Sterling exchange is quoted in New York at $4.86^ for demand bills ; at this rate, how much will a New York merchant have to pay for a sight bill for £226 128. 6d. ? //^ (/ '7, /^j -g"^ -^ 2. A pipe whose section is 4^ square inches, delivers water into a reservoir with a velocity of 11 ft. per second : Li what time will it cover half an acre 19 inches deep ? ^*1 ^^ia^ J "Xr i***-*--!^ • 8. Multiply ^ oi -175 by -285714, and divide the result by -00425. 4. Two partners, A and B, gained $700 in trade. A's money was 8 months in trade, and his gain was $800 less than his stock ; B's money, which was $250 more than A'^, was in trade 5 months. Find A's stock. 5. Beduce oflf-ioff TV i of ^ ux ^ of A /vo of a rod to 4~f + 1- the fraction of 2 furlongs, 6. A grocer, by selling 10 Iba. of tea for a certain sum, gained 20 per cent. ; afterwards he increased his price, giving only 9 lbs. for the same money. How much per cent, did he make at his increased price ? ^ ^ "a 7. Find the expense of papering a room 21 ft, long, 16 wide, and 12 high, with paper 30 inches wide at 18 cents a yard, allowance being made for a dopr 7 ft. by 8 ft., and two windows each 5 ft. by 8 ft. (^ Z'^* 6*^2.^ 8. Bought a quantity of goods for ^50 cash, and sold them on 9 months' credit for $1000. Find the gain on the transactjion, allowing true discount at 4^ per cent, per annum. ^^ ^ / "1 ^ 3 A^ "h 9. Supposing that a cubic inch of gold weighs 20 oz., and an equal bulk of silver weighs 12 oz„ and a / "•■sia 186 EXAMINATION PAPKBI. \ lump composed of gold and silver weighs 82 oz. less than if it were all gold, but 66 oz. more than if it were all silver ; what is the actual weight of the lump ?/^/i^ ^ 10. If the second-class railway fare for 70 miles be $2.10, what must a first-dass passenger pay for travel- ling 126 miles, if the first-class fare for 8 xnHes be the same as the second-class fare for 6 miles ? S^ ^ 3«q XIX. 1. Simplify 4*8 X 2-7 8i '^21•6xl8i-^.•26/ ^ r^^^^ 9 multiply . • I of a mile . 146 oz. Avoir. 27 ao. and by 146 yds. ^ 146 dwt. Troy ^ 184 sq. chains (f«.-4--76(i.-12). O 2. If A and £ in 7 days make 19 chairs, and A and in 6 days make 18 chairs, B and C in 9 days make 26 chairs ; how many chairs could A, £, and 0, make in 680 days? S'^'^V 8. If a decimal system were adopted in which £^ 16«. 9|(/. would be represented by 8''47, express the unit of money in shillings. ^^ t^^' * ^* 9^'^'^ Z^i 4. Find the G. C. M. of £4 l^^S.; £7 16». 4cf., and £,1 18a. %d,t and> express the answer decimally in shillings. » * \ 6, If 68 inches be equal to 16 decimetres, a litre equal to a cubic decimetre, a gallon equal 277 i cubic inches ; find the number of litres in 20 bushels. (1 ■.)' 6. What sum must be insured on a house worth $666, so that in case of loss the owner may receive \ of this snm, and ulso f oi the premium, which was at 6 per wnt. ? ^ ^^.^ , ^r^ ■u / esB ere be rel- the uid by and 3 26 eiu ^8 the u. and in itre ibio >rth V I of It 6 ■. V J 187 >1 Douse tc THIBD-0LA88 OEBTIFICAVES., 7. A lad undertook to go from the school his home by jumps, and it was found that each jump y^ of an inch less than the preceding ; his first jump iivas 1^ yards, and he ceased to advance just lialf way between his home and the school house. Find the dis- tance from his home to the school house. 8. A and £ were employed to cut 4 acres of grass, for which $24 was to be paid ; the men were to be paid in proportion to their abiUty to work, which was as 8 to 4, and also to the time each was engaged in the work^ which was 2 to 8. Find what each received, o , " c' 6 9. An article was bought on 8 months' credit for $208.60, and four months afterwards it was sold for $260,204. Assuming mon^y to be worth 7% per annum, find the gain per cent, on the arf'ole. ^ ( /^-/- y^ 10. Assuming that the earth's orbit is a circle, and that the earth is 96,000,000 miles from the sim, and that the circimiference of a circle is 8| times its diameter ; how many days would there be iii a yeai- if the earth, in each of its revolutions, advanced in its orbit the length of its circumference, which is assumed to be 26,000 miles? ^'^i^V-^ XX. Ill 1. Eeduce to its simplest form "ogog — "4844^ ■*" 76201 • 1 1 1 and find the product of 24 "^ 44 -+6^ -IT i>y Tr + Tr"!" 8 r+ir+ 13 6i 1 1_ J_ 2* 'ff X II of 7 J. 2. The old wine gallon is 281 cubic inches ; the cubip inch is -000016886 cubic metres, and the imperial ^^ BB m 188 EXAMINATION PAPBB8. I gallon is 4.64102 litres. How many imperial gallons are there in 157 wine gallons ? /SOt *2^(:y4 8. A has twice as muoh money as B ; thoy play to- gether for a certain stake, and the first game B wins ^ of A's money. What fraction of the smn B now has must A win back in the second game that they may have exactly equal sums ? «4t 4. A merchant deducts from his pricey at 6 months 6 per cent, for cash and 4 per cent for 8 months' credit; find what profit he makes at his 6 months prices, if he sells, on 8 months credit, an article whose ^sh price is $4.70, at an advance of 95-,^ cents on ^SSi^ ^^o /^ 6. In what time will Jg8699, 9 florins, 9 cents, 9 mills, amount to ten times itself at 5 per cent., and at what rate per cent, will 99/. 19«. 9|«{. amount to .20 tunes itself in 20 years ? / ^ ^X^ V c' / '^<^ 6. The whole time occupied by a train 176 yards long, going at the rate of 20 miles an hour, in crossing a bridge is 25 seconds. Find the length of the hndgey 7. A bill is due in 2^ months, and interest is reck^T^ ed at 4 per cent.; what fractions of the principal are the interest and the true discount ? Find the price of Union Bank stock if $1800 stock can be paid for with a bill for $1258.40 due as above. j;%,^ ^ 7^-i ^ ' '/o 8. A room whose height is 10 ft., and length 1^ times its breadth, takes 140 yards of paper 2 ft. wide to cover its 4 walls. What will it cost to carpet the Aoor^ with carpet 27 inches wide and costing $1.50 a yard ^B^^ 9. By the sale of goods which cost me $19 I lost a sum equal to 5f per cent, of the proceeds ; and by the sale of another quantity which cost $24 I gained a sum equal to 81^ per cent, of the proceeds ; what did I gaip jper ce»t. )n ihe whole ? J ^ I '0 n THIBD-0LA88 0EBTIFI0ATE8. 189 illona i,y to- ine J N has may onths redit; if he ice \a of. its, 9 ad at to 20 yards »ssing "^ are 3 of itha li le to \st a the 3um raip 5^f^ 10. I want an alloy oonsisting of 19 parts hy weight of mdicl, 17 lofid, and 41 tin ; the only nickel I can oh- tain is 10 lbs. of an alloy containing 11 parts of nickel to 7 parts of tin and 5 of lead. How much lead and tin must I add to make up the alloy I want ? XXI. ff y*7 a,^ 1. What fractions is ^11 5i"^10^/ j/2i + 3| % ^ 1 i of 24 l|fl? ^^st) 2. Sterling exchange is quoted at 9| for sight bills ; what must be paid for a draft for £42 Is. 6rf. ?>i^ j i"! Vl%l^ 8. A person taking two tickets, a first and a second class, from Toronto to Napanee, pays one dollar more for the first than the second ; what did they cost each if a first-class ticket from Napanee to Belleville cost 81 cents, and a second class cost 68 cents ? 6 3 ■ >> ^ ^ ^'^ 4. Divide %1,111.11 among A, B, 0, and D, giving A %mil more than 40% of what B and D receive, B $88.88 less than 60% of what G and D receive, and $99.99 more than 88^% of what D receives. 5. A person walks to a town at the rate of 8f miles per hour, and, after resting half an hour, rides back at the rates of 7^ miles an hour ; he finds that he has been absent 4 hours and 10 minutes. Find the length of hii journey. Ql^^^ ,j^^^ 6. If the truel^scount at 6 per cent, on a note for $249, be $9, for what length of time is the note dis- counted? C^ 'H^<^. 7. The sum of f 177 is to be 4ivided among 15 n^en, V 140 EXAMINATION PAPERS. 3 A V: !«i 20 women, and 80 children, in such a manner that a man and a child shall receive as much as two women, and all the women shall receive $60. Find how much Q^ each man, womnn, and child will, respectively, receive. ■ 8. A sovereign weighs 128^^^ grains ; find the least nimher of pounds of gold that will coin an exact nWber of sovereigns. ^q 9. Bought $64 worth of apples at 80 cents a bushel, part of which being damaged and rendered worthless, I :sold the remainder at an advance of 50%, receiving :$76.80. How many bushels were damaged ? /(-^ 10. The expense of carpeting a room 20 feet long was $66.66f ; but if the breadth had been 8 ft less than it was the expense would have, been $58.83^. Find the breadth of the room. / \ ^ jfY xxn. ^^ 1. 40 % of a mixture of wine and water is wine ; but when 10 gals, of water are added the wine is only Sis % of the whole. How many gallons in the mixture at fitst^ y^ a$X 2. A man boug&t 1200 bushels of wheat for $1500 ; some at $1.50 and the remainder at another price ; but had he bought the second lot at $1.50, and the first lot at the price at which he bought the second, he would have paid $240 more. What was the cost of the second lot per bushel ? ^ /, ^-O 8. By selling a lot of land for $600, thereby gaining 20 % ; a second for $600, losing 20 % ; and a third at an advance of 20 % on cost ; I find I have made $75 "^on uhe wnole transaction. Find the cost of each lot. 4. Divide $7,200 among A, B, 0, D, giving A $900 . 67S THIBD-OLABS CERTIFICATES. 141 liat a men, nuch seive. least tm^ij tkti exact ishel, BBS, I iving > long than dthe only ;ure 500; but ) lot ould cond Qmg d at $75 )900, more than 40 % of B, C, D, and B $600 dollars less than 70 % of C and D, and C $400 more than 40 % of a sum which is greater than D's by $2,300. 5. A merchant supported himself 3 years for $600 a year ; at the end of each year he added to that part of his stock not expended a suin equal to -^ of this part. At the end of three years his stock was doubled. What was his original stock ? 6. A and B leave London for Toronto at the same time that leaves Toronto for London. If A goes 8 miles each hour, B 12 miles, and C 9 miles, when will C be equally distant between A and B, if the distan^ between London and Toronto is 114 miles ? ,ivv ^ ^^f^^^ 7. I bought an article for f of what I would have sold it for had I received $2 more for it than I did ; but had I reahzed the $2 more I would have gained // $17.38^. Find buying and selling prices. 0^^i/ V yj^^*0 8. If J of A's money equals f of B's, and ^ of B's money equals f of O's, and the simple interest on aU their money for 4 yrs. 8 mos. at^Cy/ is $497. How much money had each %^^ y i ^ ^^-v"*^ ^ to i "^^ 9. (a) Can ^27" \/37~a^d v/io7 be sides of a tri- angle ? : J- /^ (h) The perimeters of a circle, a square, and a rec- tangle (which is not a square), are each a. The area of the circle is A, of the square B, of rectangle C. Show that A>B>C. 10. If A owes me $100 due at the end of 3 months, and $100 due in 9 months, and I accept his note for $200 at 6 month^ do I gain or lose by the operation ? Explain. ^ ^a.^ t i ^ OHAPTEB V. SECOND CLASS INTERMEDIATE EXAMINATION. JtJLT, 1871. / »'V >i ^, 1^ /^ 1. Explain fully how to state and solve a question in simple proportion. A grooer sells 14-j^ oz. for a lb., how much does he cheat a customer who buys to the amount of $78-92 ? 71V rv^7,t/4 2 Give exumples of the difference between Simple d Compound Practice. Convert Jg296 IQs. lO^d. ster- ing into Canada currency, the £ being worth $4'86f . 8. What vulgar fractions will produce finite decimals, a- L (84)* and why ? Beduce to a decimal , x -.q + 4. A and B can do a work in 7 dayc, 6 and C in 8 days, and A and C in 9 days ; in what time will (1) each ,, . separately, (2) working all together, do the work ? fi) i'-r*, ff. Explain folly the terms Numerator and Denomi- nator. Prove that both terms of a fraction can be multiplied or divided by the same number without changing tliu value of the fraction. Examine whethor ->t,,,^, -'TTi' - i h i i t m-''f- ' " '• " " ' ■■■•'—"' 8B00ND OLASB AHD INTEBMEDIATB. 148 in 8 each lout Ithar the oommon definition of multiplioation holds in the case of fractions. 6. Examine the different oases of profit and loss. A merchant asked 80 i' advance on cost of goods, but v finally took 80 % less thanthe^prioe asked; how much did he gain or lose i' ? , //)-^/ ^ '' ■ -^7. Show how to find the present worth of a debt payable at a future time without interest. I have 2600 bis. of flour for sale and am offered $6*80 cash, or v $6*55 on eight months. How much shall I gain by accepting the better offer, money being worth 8i % ? ;p { V'"*-- ' ■■■ ■ ^ ■■' '-A. « 8. Define msuranqe, poHcy, premium. A person insured a house for ^ iis value at 1^ ^ annually ; after paying 6 premiums the house was destroyed, tho entire ^ loss being $1946. Find value of the house. ^ iCf ^ '76 "^ •^9. The poUce returns for a certain year give 1860 male offenders, and 1150 females ; the next year's re- turns show a decrease of 5*4 ^ in the number of male criminals, and an increase of 8*4 % in number of female. Find increase or decrease % in whole number of orimi- nals. • --^ 1^/ X yi^'-i.'t-- I'C^:^^''-- ! a./4 V :W 10. A board is 8 feet wide and six feet long, find its area; show clearly that your multiplier is not concrete. Find cost of carpeting a room 22 feet 6 inches long by 17 ieet 9 inches wide ; the carpet being 27 inches wide and $1-60 a yard. ^iii' - ^,. > ^ 11. The sides of a right angled Wangle are 80 feet and 40 feet respectively, find the perpendicular from the right angle upon the hypothenuse. ^ C/ • 12. It is required to lay out 70 acres, 8 roods, 26| /<» perches of land in the form of a rectangle whose length /^ shall be three times the breadth. Find the dimensions. / / y- /" '^' -iL^. U4 EXAMINATION PAPEBS. n. Deobmbbb, 1871. \ y I i (• 1 1. Prove the rules for converting pure recurring Decimals and mixed do. into Vulgar Fractions. 2. Simplify {f|t-f|of8i-(AofHf-«}^(i| >_»ofi). ^^- V ^ 8. A dealer received an invoice of glassware, 15% \/ of which was broken ; at what % above cost must the remainder be sold to clear 20% on the invoice ? ^/-^- //I .^ 4. Give the Rule for Equation of Payments^ what is assumed in this Rule ? A person owed $8000, pay- able in 10 months ; he paid $§0? in 4 months, and $1000 at the end^f 9 months ; when was the balance due ? — /L'^, 'T-v^U) . /V fv** « 6. A and B agree to do a certain piece of work for $25 ; A could do it in 8 days, and B in 10 ; but G join- ing them, the work is done in 8 days : how should the money be divided ? h -^'A ^ i'l'h- •» ^- , r 6. Stat« the difference between ' * True ' ' and * * Bank ' ' discount. I owe a man $575, and gave him a note at 60 days : what must be the face of the note to pay him the exact debt, when discounted at (Bank discount) H% a month? . iJS,u^ «• 7. A drover bought oxen at $40, cows at $80, and sheep at $10 a head; there were 2^ times as man/ cows as oxen, and 5 times as many sheep as cows, and the whole cost was $1440 ; how many of each kind did he buy? ^ C'i^C^\ /s'^^^, 1 ^'^^<^^ f] 8. Find the cost of painting a room 20 ft. 8 in. Dy 18 ft. 6 in., and 10 feet high, having two windows, each 7 ft. by 4 ft., at the rate of 50 cents a squftre yard. ^ -^i/ *rf / /' / 8BG0ND GLASS AND INTEBMEDUTB. 145 cumng 1 U4 > re, 15% LUst the ^ ■ rj 4. what '0, pay- is, and balance ork for join- ad the /: ank" lote at y him sount) ^» , and man/ and ddi4 ^i n. by each '/^. ^ 0. An importer pays for freight and duty lO^o on cost price, and sells to the retailer at a profit of 20% ; the retailer sells to the consumer at a profit of 25 per cent ; find the amount paid by the consumer for goods which cost the importer $8260. S / ^ ^ / !Z \, ^ 10. The boundary lines of a field are the following : the first runs north 86 rods ; the second, north-east 60 rods ; the third, south 72 rods ; and the fourth, west to the place of beginning, 48 rods ; required the nr^mber of acres in the field. /(^ t- ^ ^vv 8. Prove the rules for converting the various lands of decimals into vulgar fractions. Shew that, in converting a fraction in its lowest \^ terms to a decimal, the result wiU be a finite decimal, or a mixed circulating decimal, or a pure circulating de- cimal, according as the denominator contains only the factors of 10, otlwr factors also, none of such factors. 4. The officers of a regiment are '042 of its whole l» strength ; 50 privates are added, and then the officers *§? 4'v«^r ?• UOONO OLABS AND INTBBMBDIATS. 149 loney ) pur- se of By at iving P'ain. 27 A. f the re 80 onals IS in itors, that ded ex- laud ids rest »al, de- Ithe lole lers /1 76 are *040 of the whole. Find the number of officers and the entire number of men in the regiment at first. 6/ Z Y/(/U^ 6. Prove the rules (without formulas) for (1) Sim- ple Interest, (2) Discount, (8) Compound Interest. 6. A man has capital which he invests to produce 6 ^ per annum ; every year he adds one-fourth of his income to his original investment : in how many years will his income be three times what it was the first year, given log. 2--801080, log. 8--477121 ? 7. Give complete explanations of the analyses of the following questions : (1.) An agent received $66 y for selling grain on a commission of 4 % ; find value of f"l ^i^ grain sold. (2.) A person receives $600 from an 8 % bank dividend ; how much stock does he own ? (8,) Sold stock at a discount of 7| %, and make a profit of 6 % ; at what rate of discount was the stock purchased ? (4.) A shipment of flour was insured at 4f 7^0 to cover f of its value, the premium paid Jbeing $122.60 ; what was the flour worth S^J^ijl^^f^^' 2 % If 8. My agent in Montreal sold a shipment of flour at $8 a barrel on a commission of 8 % ; I then instruct him to purchase certain goods for me on a commission of 2 % ; his whole commission was $600 ; find how many barrels of flour were shipped. j *^ IST^ 9. Give analyses for (1) the different cases of Profit and Loss ; (2) Partnership. — 10. The rain which fell during a certain shower on the roof of fi rectangular building, 186 feet long and 99 feet wide, filled a cistern 8 f^t Jong, 6 feet deep and 8 feet broad ; how many (long) tons of water lell during that shower on an adjoining field of 6 acres ? /£ i^ i 160 EXAMINATION PAPEB8. <. il VL DSOBHBER, 1878. 1. When greenbacks ore at a discount of 16f , what is the price of gold ? ^ ^ 6 2. State and prove the rules for converting the dif- ferent kinds of decimals into vulgar fractions. •*• 8. Water expends 10y<> in freezing ; find the weight of water in a sohd piece of ice whose dimensions are 12 ft., 8 ft., 6^ ft. (cubic foot water weighs 1000 ounces.) ^C ^*>»o 4. Show that the sum of ^^0.79012846679 and v/0.6l2846679 is unity. 6. Show (no formulas) how to find the (true) dis- count on a sum of money for a given time and rate. How much may be gained by hiring money at 5% to pay a debt of $6400, due 8 months hence, allowing the present worth of this debt to be reckoned by deducting 6% per annum discoimt ? ' '^ '■'•■■, 6. A person having $6000 Bank Stock, sells out when it is at 40% premium ; what amount of money does he receive, brokerage being |% ? ,, k^ \. < 1\ — 7. If a piece of silk cost 80 cents a yard, at what price shall it be marked that the merchant may sell it at 10% less th^ the marked price, and still have 20% profit ? J . 00 ;5 8. A merchant m Toronto has $4800 due him in Halifax ; how much more will he realize by havii draft for this sum on Halifax and selling it at }% t • county than by having a draft* on Toronto remitted to j . him, purchased in Halifax for this sum at \i» premium ? 9. A and B are partners. A's capital is to B's as 6 to 8 ; at the end of four months A withdraws i of his 8ECONO 0LA8B AND INTERMEDIATS. Iffl capital, and B f of his; at the end of the year their ji& ^"^v/^ whole gain is $4000 ; how much belongs to each ? H^-2 x ^ v-i' 7 f , what the dif- weight i are 12 ces.) 'C^i^Ko 7- le) dis- d rate, to pay [ig the ucting Is out noney 7r what it at 20% im h 1 ed to t lun ? as 5 his 10. A commission merchant in Montreal sells for a Toronto merchant 800 hbls. flour at $6.87|, on a com- mission of 8%, and buys certain goods required by his Principal, on a commission of 2% on the price paid for the goods, taking his commission out of the money in hand. Find whole amount of commission. ^ -J, S O 11. A person sold two horses at $160 each, losing 20% on one and gaining 20% on the other. Did he g^ , or lose on the whole transaction, and how much ? . t stO* <^iU'ii/ Nv Four men begin at the same time to walk round "' 152. IXAIONATION PAPEBS. an island 86 xniloB in ciroumference. They travel at the rate of 8, 8}, 8^, and 4j miles per hour respectively. When will tiievaJLbe toge^er a^un 2 /{j'^'d '/i-rwU ^ 5. A sold B a biU of go^ amounting to ^7,600, but B not having the money gave Aji note for 8 mos., which when discounted at the bankj|£id the debt. Ke- quired the fiioe value of the note f^ / ? / i "^ *?*/ •* 6. If £5 be allowed as discount off a bill of £125 due a certain time hence, what would be the discount aUowoa if the biU had hrioe as long to run y-Vf J 7. A gentleman has $25,000 of Bank ol Commerce stock which pays a dividend of 8 %. When money is worth 7 % he sells out, and invests in Bank of Toronto ^ stock at 205, which pays a dividend of 12 %. What difference in his income after allowing his agent ^ % commission for each transaction ? ^ J JS& « ^Q J^ ^ aA /La ®* -^ grocer wishes to mix 60 lbs. of tea @ 4o cts. '^ J with tea at 60 cts. and 70 cts., so that l^e mixture may A o4 yO\)Q worth 50 cts. How many lbs. of the other teas must he take ? Give reasons for your solution. 9. A column 1^ feet in diameter and 80 leet high has a spii'al gold thread on it which makes a complete circuit in every foot of the column. I^eqiiired the length of the thread ? /'T^' ^^J'fp ^ (/ \ J- 10. When the course of exchange between London and Paris is 9^. per franc^ and 8*68 francs are equiva- lent to 1 Prussian thaler, and 24*5 thalers to 84 Aus- trian florins, and 25 Austrian florins to 12*6 Venetian ducats, if a London merchant owe to one in Venice 1000 ducats, will it be more advantageous to remit by way of Paris, Berlin and Vienna, or direct to Venice, supposing a ducat to be equivalent to 4«. 2(2. ? /^^ f^j k tfOcJ 4^ 'J lX\Vi 4^ UlSCOND GLASS AND INTEBMSDUTB. vm. 168 ^ June, 1874. 1. Explain clearly the terms Numerator and Denom- inator. Prove the rules for multiplication and division of fractions. 2. From the sum of -628125 of a £» -109875 cf £6, ' .7 V 47-8126 of a ^ing, and j of y, of 1-2421876 of 18*. 4(£., take 2-91658571428 of a guinea. / 2) '^ 2 ^/ ' ^ 8. If 12 men in 94^ days, working 10 hours a day, dig a trench 88^ yd. I'ong, 2| yd. deep, and 2| yd. wide, how many hours a day must 217 men work to dig a trench 28{^ yd. long, 2^ yd. deep, and 1^ yd. wide, in 11 days? 2. -^^w ^ 4. If -08 is the yearly rate of interest (compound) /''irO/^.^ per unit, what is the rate per qtuirter ? If the quarterly rate of interest be -02 per imit, find the true yearlyrate.^^! ^^-si^ 'Jf \/ 6. Three men form a partnership, each contributing ^ the same amount of capital ; one of them is appointed manager, and as such is to receive 12^% before the ^ dividends are paid. When the business is wound up the manager receives altogether, $6000. What were the total profits ? >*„ „. . ^^ 6. One company guarantees to pay 6% on shares of $100 each ; another guarantees at the rate of 6|^% on shares of $80 each ; there price of the former is $124.50, ^ and of the latter $84. Compare the rates of interest which they return to the purchaser. L/ ^ «^ ^' "jn ^ 7. By selling doth at $1.20 per yar^, a tradesman ' gained 2^% on his outUy ; at what price must ho sell it togaml2J%«./,3/i2:^ IH ■XAMIMATIOll PAPEBB. N 8. Find the length of the longest chun, in terms of which 88 yds. 2 ft. 6 in., and 119. yds. 2 ft. 1 in. can both be expressed as integers. ///J- - y 'Vi^ 9. A person has $10000 Bank of Montreal stock which is at 186, and pays a half-yearly dividend of 6% ; he sells out, and invests in Dominion Bank stock, which is at 108, and pays a half-yearly dividend of 8^%. Find by what amount his semi-annual income is increased or diminished. 4^ ^^►J'VJ^ -*.t<...-cA^-^cf t^.^ y 4. A grocer intended to gain 8 % on a stock of tea, and fixed his price accordingly ; when he had sold two- thirds of the stock he was compelled to reduce the price 10 cents a pound, and so gained only half as much as he had intended. What was the original cost per lb. of the tea ? F 3 ' C V 5. Shew that ^^f"^;^'^ = 17-488. 6. A sells goods to B at a loss of 4 %, B sell? them . to C at a loss of 6i %, sells them to D for $890.60, ^ gaining 8^ % ; find the prime cost of the goods, ^ ^' (fij 7. A and B invest capital in the proportion of 8^ to i . ^, . 4. After five months A withdraws one-half his capital, r and B withdraws two-thirds of his. At the end of the^^) /3C' year they have gained $7,090 ; find each man's share. 8. A bankrupt has book debts equal in amount to his Uabilities, but on $24,000 of them he reaUzes only 66f cents in the dollar, and the expenses of the bank- ruptcy are 5 % on the book debts ; he pays 65 cents in «, the dollar ; find the amount of his liabiUties.^ ^ d SS^d "'- 9. A merchant in Boston has 10,000 francs due him on account in Paris ; he can draw on Paris for this amount, and negociate the bill at 19f cents per franc, or he can advise his correspondent in Paris to remit a draft on Boston, purchased with the sum due him, ex- change being at the rate of 5 francs 20 centimes per dollar. What sum does he save by adopting the more profitabfe course ? / / ^ , - -y 10. How many flagstones, each 6 '76 ft. long and 4*15 ft. wide, are required for paving a cloister 12'46 ft. 70 166 EXAMINATION PAPXB8. \ wide which encloses a rectangular court 46.77 yds. long and 41*98 yds. wide ? jU^-v> 11. When the 8 per cents are at 96, how much stock must he sold out to pay a hill of £1,664, 9 months he- fore it hecomes due, real discount heing allowed at 4|^ % per annum ?^/^ 7^ '^^♦'^ -p- 12. A pile of hricks in the form of a parallelopiped contains 8000 cuhic feet, and the length, hreadth and thickness are as 4, 8 and 2 respectively; find the dimensions of the pile. >^ / ''^ T ^^^ July, 1874. 1. Capital originally invested so as to yield an an- nual income of $22500, at the rate of 9%, is re-invested at 10%, and then divided among three persons in shares which are as 4, 7 and 9. What is the yeaiiy income of each ? : ki\-j ^ '- r 2. If U. S. 6's 6-20 can he purchased at 107^ in cur- rency, interest payable in gold, and railway bonds bear- ing 7% interest payable in currency can be bought at 86%, determine the respective rates of yearly interest yielded by these investments, assuming that the pre- mium on gold is 25%, and that the railway bonds are subject to a tax of 1^%. 8. A merchant sells i- ri two quahties of flour, the i^ it superior at $6 a barrel, the inferior at $6 a barrel ; in the month of April he sold 160 ^aiTcls, receiving there- j^^ for $810. How many barrels o. each kind did he sell ? 4. If a merchant sells on credit to a retail grocer, on the let of November, goods to the amount of $100 ; on the 6th, goods to the amount of $225 ; on the 18th, mmmm SECOND OLABB AND INTERMEDIATE. 167 .long stock IS be- 4*% piped I and I the 1 an- ested lares leof cur- ear- tat rest re- are le in re- )n goods to the amount of $180 ; on the 22ud, goods to the amount of $76 ; and on the 29th, goods to the amount of $120. Find the equated time at which the whole debt for the month becomes due. /Urv ^U ^'■ 6. A man having bought a lot of goods for $760, sells one-third at a loss of 4% ; by what increase per cent, must he raise that seUing price, in order that by selling the rest at the increased rate, he may gain 4% on the whole transaction ? ; ;^ 7^ 6. The value of paper required for papering a room, supposing it f of a yd. wide, and 4^. a yd., is £2 8«. \^d.'y what would be the cost if the paper was two feet wide, and ^d. a yard ? i. 7. A New York merchant shipped to Liverpool 10,000 bushels of wheat which cost, delivered, $2.16 in currency per bushel, he sold it for Is. 6d. a bushel, and invested the proceeds in cottons at Sd. a yard, which, after paying an ad valorem duty of 80%, he sold at 80 cents a yard in currency. Determine his profits from these teftnsactions^old h^in^ at 87^% premium. ^ i'3 7^ 8. K 86 meiF working 8 h 9. A man sells 676 bushels of wheat at a profit of 8%, and 296 bushels at a profit of 12% ; had he sold the whole at a unifojtin ]N:ofit of 10%, he would have re- ceived £2 14«. flEd. more than he actually did; what was the yrioefet bushel paid for the wheat ? ^7<^ , * 10. (a) The height of a tower on a river's bank is 60 feet, the length of a line from its top to the opposite bank is 66 feet ; find the breadth of the river. ^'iTS^ , i//. i 3 . / 168 EXAMINATION PAPEBB. ^ (b) The content of a oist em is the sum of two cubes whose edges are 10 inches and 12 inches respectively, and the area of its base is the difference of two squares whose sides aie 1^ ft. and If ft. xespeotiyely ; find its depth. -73^^ wv XL Decembeb, 1874. 1. The first of six boys can copy 8 lines as soon as the second can copy 2 ; the second 6 as soon as the third 6 ; the third 7 as soon as the fourth 8 : the fourth 9 as soon as the &fth. 10 ; the fifth 16 as soon as the sixth 14 ; how many lines will the sixth copy while the first is copying 186 ? J 1 i " 2. The hour, minute and second hands of a clock turn on the same centre and are together at 12 o'clock ; how long before the second hand will be midway be- tween the other two ? J.<> -Lli ■ rA - 8. A person imported a quantity of goods, paying 16% for freight and insurance, and 10% duty. He sold them at a loss of 10% ; but if he had sold them for $600 more than he actually received, he would have made a profit of 2%. Find the original cost of the goods. y^-o tUx^ > 4. When elbhange at New Ywk on Paris is 6 francs 80 centimes to the dollar ; that at London on Paris 26 francs 20 centimes to the pound sterling ; and that at w^n^^*^ York on London 9% premium ; how much less will it cost a merchant to remit 2000 francs to Paris by circular exchange through London, than by direct ex- change? * y^i' r 6. A ooutractor tenders for a certain work at $20,000, ^ iWfa SECOND GLASS AND INTERMEDIATB. 169 to be paid at completion of the work; another tenders for it at $19,400, stipulating that $2000 shall be paid him every three months ; find the difference of the ten- ders supposing the work in both cases to be finished in two years, and money to be worth 8%. > »^ ra«' **i / 6. Two partners gain $4800 ; A puts in $5600 more /^/i-^o than ^ of the whole stock, and his share of the gain is $2600. Find the stock contributed by each, j^ 7. A rectangular court is 80 yds. long and 50 yds. broad ; it has paths 6 feet wide joining the middle points of the opposite sides, and also paths of the same breadth running all round it on the inside ; the re- ^ mainder is covered with grass ; if the paths cost la. &d, "c/k ., y- per square foot, and the grass 8 shillings per square yard, find the whole cost of laying out the ooMii^f^^^^ • 8. A speculator paid $1400 for two lots, the price o. one of them being 40% that of the other. He sold the cheaper lot at a gain of 60%, and the dearer one at a loss of 80%. Find his ^ain or loss per cent, on the Wihole transaction. l^j^ -^v ^ v > ^, ^ / 7 /^ 9. A has £90,000 stock in the 8% South Sea An- ^ unities and is offered by Government the choice of be- ^?fi^^^ ing paid off at par at the end of the year, or of receiving ^ jeilO of the new 2^% stock for each £100 ; he choses ^y ^^ the former alternative, and invests his mbney in the 8 % consols at 92. Find the amount of his stock in con- sols, and the excess of his income above what it would ' " yt have been if he had agreed to the proposed conversion. _ ^ 'J 10. (1) A rectangular piece of ground whose sides are in the ratio of 2 : 8 contains 2800 square yards ; find Uie sides. ^ 0i" A^-^V./ t-^*^ 7. A merchant sold goods for which he received a 46 ,%^ -y . days' note, which he immediately discounted at the fj-t^^iti. Bank of Commerce at 6%. >The discount was $88.7()f J ; find the face of the note.^ti^Z 3 2. • ?6 ^ 8. Exchange between Paris and Amsterdam being at the rate of 2 francs 20 centimes to the guilder, that between London and Parts at the rate of 26 francs 80 centimes to the £, and that from New York on London at 9|% premium, what will be the cost of a renyttance for 1000 guilders from New York to Amsterdam by bills of exchange tlurough London and Paris ?^e- 4. A Toronto merchant owes £900 in Liverpool, G, B. He determines to remit to Paris at 6 francs 60 cen- times per $1 ; thence to Hamburg at 186 francs per 90 marcs ; thence to Amsterdam at 18j^ stivers per marc ; thence to Liverpool at 220 stivers per £ sterling : how much must he remit to discharge his debt in Liverpool, and how mudi does he gainpver direct exchange at 9i% premium "i W^^a q V^& to #»*U. 6. A man invests $19460 in Bank of Montreal stock at 194, and $19,850 in Bank of Toronto stoek at 198, paying his broker in each case \% on the amount of stock purchased. If the former pays a hah'-yearly dividend of 6^%, and the la^r a half-yearly dividend of 6^%, find his total income for the hah-year. \ 8B00ND OLABB AND INTFJIMEDIATB. 165 rom i feet is is ohi^i and paid lay? and aaU I that the ,G. cen- r 90 .re; .o^? 1. i% real at of C. Coffee, costing 86 cents per pound, is mixed witli ^ry wortli 10 oeutu a pound, in the proportion of 6 pounds of coffee to 2 pounds of chicpry, and the mixture / is sold for 84 cents a pound : find the gain %. 2*2 ^-/ .. ^ . / 7. A person invests the present worth (true dis- count) of $80,102 (due six months hence, at 4% per annum) in Bank stock paying 6% yeaily interest and seUing at 92} ; liis taxes amount to 6§% of his gi-oss in- come from the ahove investment : find his net annual income. ^ y7f 2. 8. A and B invest capital in the proportion of 4 to 5 in business ; at the end of 6 months A withdraws | of his capital, and B f of his. At the end of the year there is found to be a gain of $4,050 ; how is this to be divided? A^^n^^ liKnyf 9. (1.) In multiplication, why are the successive partial products not placed directly over one another ? (2.) Can the multiplier be a concrete number ? Explain clearly the meaning of tlie factors in 5 ft. x 8ft. =15 sq. feet. (8.) Is a fraction a number ? Explain fully why { has the same value as •^. 10. Find within an inch the length of a side of a square field which contains two acres. XV. iNTERlfEDIATE — DECEMBER, 1876, 1. Divide '0076 by 26*6, and explain the reason foi fixing the position of decimal point in the quotient. 2. Supposing the rate of carriage to be diminished \ after the first 50 miles, find the cost of carrying 18 ! SB mum 166 EXAMINATION PAFBB8. owt. for 80 miles, w^n 24 owi. can be carried 75 miles for 6#. lOd. '^ '.yi^ 8. If the difference between the simple and com- pound interest on a smn of money for three years at 5 per cent, be $87.86, find the smn. iTf^ ^79* ^7 -t 4. A passenger in a train travelling at 80 miles per hour, observes that in just one minute he overtakes the length of a freight train running on a parallel track at 18 miles per hoar ; how long would he have been in passing the same train if it had been moving at the same rate in the opposite direction ? /^^yo-c^-^t^i*^ 6. A merchant spends $168 in purchasing black cloth at the rate of 11 yards for $10, and blue cloth at the raie of 7 yards for $4, and buys twice as many yards of blue as of black. Discovering that the black is much worse, and the blue much better than he expected, he determines to retail each kind at the rate paid for the other, and finds that had he received 7 cents more on his entire sales, he would/ ha;^e/ exceeded his usual profit by 10 per oenttj Wuat^al ms usual per- centage of profits on cloths ? /J' f^ 6. A bookseller allows teachers l!0 per cent, on all cash purchases. For ordinary customers his of his for laud, and B lost by trading a sum equal to 28^ % of what both had at first, when both together had $50.25. What sum had each a^ first, and how much had each left ^-j7 1 •' AF/f /;^i,2j SECOND CLASS AND INTERMEDIATE. 1G9 1. Simplify ^^^^ 4 ft. 7 in. 16s. Sd. A'i^B. 2 ft. * ila. did. "^ ^^^ xvn. £7 5s, 2 tons 2 qrB. 'L) lbs. 4 tons 1 qr. 21 lbs.' and ±fZ. //j-c^x-ZJ 2. Three vulgar fractions, of which the first is t\, the second y^, and the third has for its numerator 7, are reduced to approximato decimals, and being then added together the sum is 1'00080|. Find the thiid fraction. 7/^ 8. A mercnant bought 126 yards of cloth at a uni- form price per yard, and gained 8^^ per cent, by selling 88 yards of it at $8.62 per yard, and the remainder at $2.60 per yard. What did the cloth cost him per yard ? 4. If 6 yards of silk cost as much as 16 yards of '! wmel or 40 yards of caUco ; and if 19 yards of silk, 17 of flannel, and 22 of caUco, together, cost $87.88 ; had ^ the price per yard of each ai-ticle. ;'* // ^ ' ^'2- \/f— 6. If 69 German thalers, of which 9 parts in 10 aio fine silver, weigh 41 ounces, and English standard sil- ver ^ fine is worth $1.28 per ounee ; find the value of a thaler in English money, assuming the £ sterling to be worth $4.80. ^f^Jt^L ^ 0. Along a certain path 1000 yards long, there is a house every 60 yards, and a tree every 20 yaids ; how mauy houses will have a tree in front ? / 7 <*«- -H^r / o^-^-^fu* 7. A young man's salary increased \ every year ; his expenses each year were J of his salary, and at the end of 4 years he had saved $1001^^. Find his first year's salary. J X3/ ^f^^ ^ ^ LLi A 8. What will be the amount (compound interest) of $2,400 for 1| yea;rs, at 10 per cent, per ^innum, paic] ^%yy ♦ a<- /o ^ <*-■ 170 EXAMINATION PAPEB8. l^alf-yearly ; and at what rate, simple interest, will it amount to the same 'sum in the same time ? ^ > 0* Four persons form a partnership, the second /* puts in twice as much capital as the first, the third ^y^y^^ ^ha]i as much as the first and second together, and the ^JJJ3'j fourth as much as the other three. How should a profit of $20,000 be distributed among them ? 10. An importer sold cloth to a wholesale dealer at 10 per cent, advance; the wholesale dealer sold it to a K many guns firing 7 rounds in 9 Mi 172 BXAMIMATION PAPEB8. J-VV'i i minutes will kill 980 men in 25 minutes at the same rate ? J/^a 4 8. with the condition that for every day he is idle, instead of receiving anything he is to pay 24 cents for his board ; he receives altogether $12.48. How many A boy is engaged for 28 days at 60 cents a day, days was he idle ? ^.^^ 4. The exchange between Russia and England is 6.28 roubles for i>l, between Russia and America 6.28 roubles for $4.66, and between America and Enghuid $4.86 for £1. Find the gam in transmitting 6000 roubles through England to America. J^ f^ , ^"L-h 6. A coin whose weight is f^f f of an ounce con- tains 87 parts in 40 of gold, and 8 in 40 of silver ; the gold is worth $17 an ounce, and the silver $1.10 per ounce. Find the value of the coin. J^J — 6. A and B form a partnershq), A contiibuting $6600, and B $8600 ; they agree that $120 shall be annually put by as an insurance fund, and the remain- ing profits be divided in proportion to the capital con- tributed; at the end of the year A gets $485.41|. Find tlie percentage of profit realized on the entire capital. y f/t^ y(^ 7* Ov\aig a m^ $588.05, I give him a 60 days' note ; what must be the face of the note to pay him tlio exact debt, when discounted at the r^ of 10 per cent. per annum ? Allow day.^ of grace. JTi/Ti^Kiii j'jbT 8. A speculator sold stock at a discount of 7f ?(>, and made a profit of 5 i»; at what r^te of discount had he purchased the stock ? /X ^^ 9. I paid 6 i» interest on a sum of borrowed money; after a time I paid an instalment of $200, and had the Interest on the remainder reduced to 4 %, and tlic SECOND 0LAB8 AND INTKRMEDUTB* 178 yearly interost was now 88^ % less than before. Find tlio amount of the debt. j//%.Co 10. The periods of tliree planets which move uni* formly in cucular orbits round the sun, are respect- ively 200, 260, and 800 days. Supposing their positions relatively to each other and to the sun to be given at any moment, determine how many days must elapse before they again have exactly the same relative positions. i^«-tr-o cC^^ XX. 1. Find the value of 11 05- 6-976 /• 629 of 2-138 1-18 of 1-2 \ 7-26 + -088 2. of 8-G18-6-218 \ ^1,(^^11 6-6 of -46 ' The annual consumption of spirits in a country is 4,600,000 gallons, and the duty is $2 a gallon ; the duty is reduced 4 per cent., and the consumption is in- creeed 6 per cent.; how is the revenue aflfect«d ? jf/^"^ U-OO 8. If 12 men do a piece of work in 21 days, in what time will 10 men do a piece of work IJ as great, if 8 of the first set do as much in an hour as 4 of the second ^ set do in an hour and a half, and tlic second set work half as long again as the first ? ^ 'f If^- ^ssCmy^ 4. If at Toronto exchange on Liverpool is at 9f premium, and at Liverpool etchange on Paris is 26 francs 86 centimes per &\ ; find the arbitrated course of exchange between Toronto and Paris through Liverpool, and what a Toronto meBphant must pay to dkcharge a d bt of 10,000 francs^*/ ^ Of ^/ tfif'^f 6. A lump of metal worth $186n is formed by a fusion of gold and silver, the values of which are $16.60, and $1.20 an ounce respectively ; the weight of 174 EXAMINATION PAPSBS. I J' I* the gold is *76 of the whole weight. Find the weight of each metal contained in the mixture, ^t ^ ^t/iC j^y^ 6. A man invested a certain sum in Bank of Com- merce stock, which is at 120, and pays 4f % half-yearly dividends ; and 62^ per cent, more than that sum in Dominion Bank stock, wh^ohis at 180, and pays 4^% half-yearly dividends ; his^^ffioDme from hoth invest- ments is $222.60. Find uie amount of n^ney invested in eaoh kind of stock. fX ^ ^ o '^^3^i> o 7. A person mixes 22 lbs. of tea with 10 lbs. of an inferior quahty costing 24 cents a lb. less, and gains 16% by selling the mixture at $1.74 per lb. Find the cost of each kind of tea SfM'y-t, f/, 3S/^ 8. If li ounces of gold 18 carets fine be worth £5 lis, Bd.f of what fineness must gold be in order that 18^ dwts. of it may be worth £2 la. 9d. ? ^o C^jx*^ 9. A person bought a quantity of goods for $227.92 payable in 12 months' time, and sold them at once for ^ $275.66 payable in 9 months' time. What is the gain^ in ready money allowing true discount at 4^ per cent. ^#.fj 10. A sum of money is divided between A and B in the ratio of 6 to 8 ; and A's share exceeds $60 by 66| per cent, of the whole sum divided. each. /<^J-» ; /^7^ XXI. 9(8^ of ,1^) '• -« j(:Op.5 e^si anu reduce ^ \ of 1} of £8 14«. 9(2., to the fraction of £6 IO9. ^\d, •% 2. There are three fractions whose sum is W\, and 9 times the first, 1 ^ times the second, and 14 times the third are equal. j.ind the fractions. 9x ^ i^ Tf ^j ii SECOND OLABB AND INTERITEDUTE, 176 sight of f Coni- ^yearly sum in invest- Qvested I. of an L gains ind the worth lor that 227.92 tnce for ^ le gain^ cent. f^t»fyl id Bin lare of reduce and Ics Uio /4 '92/ 8. A hanker in Montreal remits $8,000 to Liyer]>ool as follows : first to Paris at 6 francs 40 centimes per $1 ; t leuce to Hamhurg at 185 francs per 100 marcs ; thence to Amsterdam at 85 stivers per 2 marcs ; thence to Liv- erpool at 220 stivers per £1. How much sterling money will he have in bank at Liverpool, and what will be his gam over direct c 4. One-^alf of a debt ( mouths, ^ in 12 montlis, \ in 16 months, and the re- . mainder in 20 months. When might the whole be paid at one payment ? /^ iA^ .»*,.^ 6. A merchant bought 80 yards of oloth 1} yds. wide, at $8.60 a yard ; but the cloth having been wet, ■* ihiunk 5 % in length and 5 % in width. At what rate ^^ per yard must it now be sold to gain 12 % on the out- lav? ^U.X¥ y,f 6. If 60 cubic inches of lead, together with 64 cubic inches of cork, are equal in weight to 16d8| cubic inches of fir, and the weights of equal quantities of lead and <^ fir are represented by the numbers 11*824 and '46; what number represents the weight of an equal quantity of cork ? • ^ ^ 7. If 40 lbs. of green tea at 60 centb a pound, mixed with 80 lbs. of black at a different price, and the mix- ture, sold at 80 cents a pound, realized a profit of 22 1 per cent.; what was the price of the black tea ^^'Ji. ^ 8. Find the sum of money of which, in the space of four years, the true discount is $24 greater at 6 per cent, than at 4 per cent, per annum. 6^ C f • iT'^^ 9. A person invests « certain sum (gold) in U. S. 5*8 10-40 which are at 6 % discount, and tliree times the amount in U. S. 6*8 6-20 which are at a. premima /;^fJ5yj iX^'T L*j^A^XA^^^ ?-* >^ s J. '%4^- 176 EXAMINATION PAPRRS. of 8 %, the interest on both being in gold, and gold at a promium of 8 % ; what will these seourities cost him if the income from both together is $1184 in currency? 10. A speculator bought a number of sheep frr $2160 ; 26 of them having died he sold } of the re- mainder for $1200, which was $62^ less than cost; how many sheep did he buy ? F//> xxn. I 1. Reduce to its simplest form : .fvr r-L^ (95)*-C026)«(;0r26)«~(-0876)* _ ■£^ kuu^ (•0876)8 -(•06J«(-0i26)-(-026)(-6l26)« 2. 1 >^ A n D If v/2- 1-414218, find the values of ;__£ i > flj^nHf. 2yi0 7^48^ 4v/16 , ^ /288, ^-^5-^3. Smiphfy ^--^ ^ ^^^ ^^ i^y^ 8. A's rate of working is to B's as 7 to 5, B's to C *■ / ~ ^^ as 4 to 8, and C's to D's as 6 to 6 ; A's time of working -/X*r^ each day is to B's as 9 to 10, B's to O's as 10 to 11, ^A and C's to D's as 10 to 7 ; also A's number of dayH is '*\ *** to B's as 16 to 7, B's to O's as 11 to 20, and C's to * /'S o j).g ag 7 to 6. How should $1220, which is paid for the whole work, be divided among them ? 4. Two men start from the same point and run round a ring with different uniform speed ; if they run in opposite directions they meet at 72 yds. from tlie starting point; if they run in the same direction, they are at the starting point together, after one has been seven times round, and th6 other six times. Find the cucumferonce of the ring. ' /J"4 ^^ 6. A person marks his goods so that he may allow « r.iscoimt of 4 %, and still make a profit of 16 %. 'P ■BOOND (JLAB8 AND INTKBMKDIATB. 177 >lcl at a i him if moy ? eep fcr the re- n cost; i/i* 1 Jrrr v/60, ¥'Z. r^ 4v/16 16^/21 '8 to C'i working 110 to 11, |f (layn is id G'h to paid for and run I they run rom tlie bon, they lias hoen iFiud the ^ay allow »C 15 %. What must be the marked prioe of an artiole that cost him|1.87J? jf2..%y *^ 6. A man is in the habit of walking from hit house to take a certain train, in 20 minutes ; being one day detained beyond his usual time of starting, he quickens V his pace to y of his accustomed speed, but is too late by two minutes. How long was he detained beyond his usual time of starting ? g" •jc.cJ*.^ # 7. The true disoourt on a sum of money at 1\ \>et ooiit. being $40, fin. 'he true discount on the some sum at 8i per cent, lor one year. /^ y^/ 8. If 21 bricklayers and 8 carpenters earn $451.50 in one week, and 6 bricklayers and 4 carpenters earn ^ $80.50 in 8i days, find the daily waftee of a bricklay- er and a carpenter. / 3, z i ^ m,Yi 9. What must a person have ^vested in Consoli- dated Bank stock at 90| paying 8 per cent half yearly dividend, if a transfer of 60 per cent, of his capital to Bank of Commerce stock at 115 paying 4 per cent half ^ dividend would increase his half yearly income $88.60 j^^^J^^ 10. From un official return it appears that there were entered for a certain week at the port of London, oxen, calves, sheep, pigs, anA horses as follows : the \/ number of oxen was \ that of sheep, the number of pigs was 18^ per cent, of the number of sheep, the pigs were 112 per cent, of the calves, the horses were 4iftper -y^ cent, of the whole, and the horses and oxen togotlier were 8687. Find the number of oxen. 3i^2o XXIII. - a- vt 6* of A r 11 / 6^ of /^ . 8i 1. Simphfy ^^^^ of A of ^»^-^|J of -^ v/ IMAGE EVALUATION TEST TARGET (MT-3) is i! 1.0 I.I 1.25 '- IIIIM u 1^ si? it. I-. illM m 14 ||M IIM 2.0 1-4 I!! 1.6 V] /2-l 2n/2+^/3-1 . .. . ... >/2 + 73' \/3Ti * ^^^^^^ ^^'^ product by unity; and find the value of — ,1 ^^ » .. » Z*^^*^ ^ 10. A person rows from A to B (1^ miles) and back in an hour ; how long would it have taken him if he had rowed equally hard, and there had been o. stream of 1^ miles an hour running from A to B for the first 30 minutes, and then ceasing ? 4"^^" '•'««-^- XXIV. 1. If 8 oimoes and 160 grains cost 127. 9«. 7^., and 1 ounce and 80 grains cost 4/. lOd*. lOcf., how many grains are there in an ounce ? %, 2y -^ ^ i^ 2. One farmer asserts that his and nis neighVo -*s farms are in the proportion of 6 : 2 ; his neighbor says they are in the proportion of 3 : 1, and the quantity of land thus in dispute is 57^ acres. If the actual ratio/ are 5^ : 2^, find the quantity of land in each farm. //oo. J'bo 8. An Act of Parliament declares that 2n.27i cu. in. of distilled water, at a temperature of 62^E.« the 180 EXAMINATION PAPEB8. barometrical pressure being 80 in. of mercury, shall be considered as weighing 10 lbs. Show what fraction is omitted in a lb. when the same Act says that half a grain is the ^^ part of a cu. in. of distilled water, and that the lb. avoirdupois is 7000 of these grains, /t ^"^^ 4. A clock is set in motion at 12 o'clock on Satur- day night. At noon on Tuesday it is 8 minutes too fast. Supposing it to go at this rate until it strikes 4 on Thursday afternoon, at which time the regulator is altered, so that at noon on Saturday the clock is found to be 6 minutes too late. Continuing the rate what will be the true time when the clock strikes 8 on Mon- day afternoon ? ^'/^fti/ V ^/f,.//^ >'/ / , 5. It is proposed to cux a tunnel under the straits / of Dover at a cost of 10 million pounds. Suppose the working expenses to be 40 per cent, of the fares, what must be the income to pay 1^ per cent, on the cost of the tunnel to the shareholders as promised by the proprietors ; what must be the iBBOidfr receipts to pay this dividend .2a£/ :2- 2- Iz^i, ^1^ y^ -^ ^ chsi. v 6. Show that the true discount of any sum of mt)ney is the present worth of the bank discount for the same time and rate. If the true discount of a certain sum for 8 years 4 months be 88^ per cent, of the simple interest for the same time, and their difference be $24, find the rate per cent, and the sum of money. ^ &^ V^Fy i.4> 7. If 28 men can excavate 760 cubic yards in 4 days, working Of hours a day, what uniform length of day will 24 men require to excavate 922^ cubic yards in 8^ days, supposing that any 5 of the latter party can do as much in 4 hours as any 6 of the former can do in i7 SECOND OLABS AND INTERBtfEDIATE. 181 11 be on is Lalf a -, and '¥00 -i-i^y iatur- B8 too ikes 4 itor is found what L Mon- straits iupi)Ose e fares, on the ised by lipts to mWey le same 8 j- hours, and that 2 men will be withdrawn Tropa the latter party after 2^ days' work. /^ i^^ ^^a%^ a. j^r-/* 8. A, B, and C, start at the same time to plough a piece of land ; B works every day ^ longer than A, and C works -jJy longer than B ; B can do in a f^'ven time f of what A can do, and C | of what B can do. In what time from the commencement will each have finished an integral number of acres at the same time, suppos- ing that A can plough 7 acres in 4 days ? ^/ ^ ^^lafcyt 9. A person in Chicago directs a New York broker to buy $6000 U. S. 6's 6-20 at 7% premium. How much must he pay for a draft on N. Y. to cover the purchase, exchange being ^ per cent., and the broker's commissiont ^ per cent. ? Jv yi'^'fo-f- 10. If $8 be allowed as 9 months' discount off a bill of $68, and at the same rate $8 be allowed off for how long was the latter sum discounted ? /i' XXV. Edoab Frisby, M. a.. Naval Observatory, Washington. 1. I bought a horse for $160 cash and sold him for $160 taking a note payable in 8 months. How much per cent, did I gaia by the transaction, money being worth 6 per cent, interest. ^ ^?^^ /*> 2. A person engages to do a Certain piece of work for $1 per day, but for the first half of the work he is able to earn only 90c. per day, and thinking it an equit- able arrangement, he agrees to take $1.10 for the remaining half, but finds that he has lost $1 by this arrangement. How many days did he work and what should he have received daily for the latter half of the/ work ? J^n^tfT-*^^/*-^ ^*- f^S^^zL^ /dzUf-f ^ 182 EXAMINATION PAPERS. u t^- 8. I remitted $3999*976 to a banker to invest in stocks ; 6 per cents being quoted at l05, and 6 per cents, at 98. I desire to have 8 times as many 6 per cents as sixes. How many of eaciv did he buy allowing ^ per cent, for his commission ^^ <^^'>^ fg-^ y^^^"^- ^ ^-^ 4. A bankrupt has liabilities to the amount of $1500 and his assets are $460 cash, one note of $200 payable in 6 months, and one note of a $100 payable in 8 months. How much will he be able to pay his credit- ors, the bank discounting his notes at 6 per cent, per annum f ^.^O ^^ l(^ ^le^^L^^ /U d^i'^^ 6. The difference between the true and the bank discount of a note, payable in one year after date, is $1. What is the face of the note, 10 per cent, discount being allowed and no days of grace ? S//6 6. A and B together can do a piece of work in 8 days ; at the end of 5 days A is taken sick and C is taken in his place, and B and working together finish it in 2i days ; but if A had continued well, the three working together could have completed it in 2 days. How long would it take each separately to perform it? 7. Two trains whose lengths are 210 and 230^ feet respectively, when moving in the same direction pass each other in 16 seconds, and when moving in oppo- aite directions in 3f seconds. Find the velocity of eacl^ train in miles per hour, ^o €»/- 4^o t^vu^ iuA/ ^/\y 8. A and B are partners in business and have amounts invested which are in the ratio of 8 to 6. They take in a third partner C, who pays them $8000 in such a way that all 8 may receive equal shares of the profits. How much of this money will A and B individually receive, and what was the value of their stock ? SECOND CLASS AND INTEBMEDIATB. 188 9. The population of a town at the end of any year is found by substracting 15 times the population of the previous year from 14 times that of the succeeding year. Two years ago it was 1960, this year it is 2260; show that it increased in Geometrical progression ; find the ratio and the population last year. 10. A vessel is worth $4000; for what amount must the owner insure her, so that if she be lost, he will receive back the value of the vessel and the amount paid for insurance, the policy costing IJ per cent ?^^ o^'O' 43-f XXVI. J. H. Johnston, M.A. — Thobold High School. 1. An agent sells goods on a commission of 8%, and invests in certain goods on a commission of 2/<>, deducting his whole commission before investing, and calculating the 2^0 commission on the amount remaining after deducting his first commission ; the amount invested was $1901.20. Find the amount of his commission^i^^S^' 2. The sum of $45 paid as premium of insurance at f % entitles the owner, in case of loss, to be paid the / value of the property, the premium, and $10 besides. Find the value of the proj^erty. jtj /^/•^t/" , 8. A sells ^gOQds which cost $27^^ B ; andB^sells 5n ^ them to C, who difipogespf'mem fOT"^a6^r99^. aO-^^ ^ what prices did A a]^(i'^D>«lLthe goojii^eacb^sQj^the three having ma;^M^ same rate per cent, of prij^^t ? 4. A and B csieB tteether do a piece of work iii V days A £ i^^ of 9 hours each ; A a^d in 6 days of 11 hours each ; and ^ ,y ^ B and C in 8 days o§10^ hours each. In how many *5 '^/^ days of 12 hours can each of them perform the work ? (I /^/^ 5. A note for i^lOOO. drawn February 16th at 11 ^C V 184 EXAMINATION PAPEBB. months, is discounted September 12th at B^'fc Bank dis- count, and the proceeds invested in tlie 4 per cents, which are at a discount of I^. Fin^ the annual income from the investment. Jpjy ,, // ^^^^ 6. If, on a certain day, the time from noon till sun- set was \ as much again as that from sunset till mid- night ; find the hour of sunrise and the length of the night. ^nyj •h./^ ^ ^*^t. \\ «^// 6. A grocer who sells 7 lbs. of butter for the price which he pays for 8 determines to cheat, both in buying and selling, by means of a false balance, ISlbs. in one scale balancing 14 lbs. in the other. By his dishonesty he increases his profit by $29 on a quantity of butter. What does he pay for that Qiiantitv ? ^ /^''^t ft'f' 186 EXAMINi.TlON PAPERS. 6. A mortgage on a farm is payable in four equal annual instalments of $1000 each. When the first in- stalment falls due the mortgagor offers in part payment $2000 in 6 per cent, municipal debentures upon which interest is due, and which mature in one year. What balance in cash should the mortgago». demand in ex- change for the mortgage, money being worth 10 per c|nt. ? 7. A merchant consigns 6160 bushels 6i wheat, valued at $1.40 per bushel, to a broker, who sells it at $1.60 per bushel, and invests the proceeds in dry goods. The merchant pays $160 freight, and . sells .the dry goods at 10 per cent, advance on^iSiSSi^^^leSu^'isiB on the whole transaction. The broker's commission on purchases being 8 per cent, find his commission on sales. -^z yf ^/^ . o of the mixture ; find the proportions of wine and water in the original mixture. 4r»^o :c^^:: j .' ! 2. What amount of draft payable in 70 days can be bought for $lQp8, interest being 6 ^ and exchange 2 % premium ? m/coo 8. A owes B $800 payable in 6 months, but in 2 months he pays B $1000 receiving B'p n0t§^;;^^the Vjk^ ance. When ought the note to BSjteSeeT^ "^o '^'jy'*" 4. A boatman can row with the current fromA ^ B, a distance of 44 miles, in 4 hours ; w^en the current is f as strong, it takes him 11 hours to row from B to ^ A. What was the rate of the current ? ^ -J^ f^itAf ^ BBGOND-0LA8B AND INTBRMBDIATE. 180 not al- $2080 or both ition of 5cepting ).70 per pound. en with a mix- wine is Irtions of rs can be ige 2 % )at in 2 [>m A fo current 5. For what sum must a note bearing interest at 10 % per annum for 8 months 27 days be drawn that if immediately discounted at a bar^' at 12 )(> per annum, the proceeds may pay the prenu: u at 2 % on a policy which covers both the value of a quantity of goods in- sured and the premium paid, the goods being valued at 6. Tea worth 60o per lb. is mixed with some worth 75c. per lb., and the mixture sold for 76c. per lb., gain- ing 10 % on the price of the first and 12 % on the price of the second. In what proportions were they mixed ? 7. A'c^pitalist^Bolding B. B. Bonds to the amount of $20000 disposed of them at 96| for Capital Stock in a Bank at 79|^„b|oker^ i Voj^ ^^^ ^^^^' ^^'^ Bonds drew 10 % annTOlJ^ffiB B&ofe'ffljk paid 8^ % the first half-year and 4J|^ % the second half-year, the dividend in both cases being payable in gold which is at 120. Upon the receipt of the first half-year's dividend it was invested for 6 months at 8 % per annum on its currency value ; what difference is made in currency in the yearly income by the transactions? ^JA'^.^v 8. A merchant in Montreal wishes to pay £50000 in London. Exchange on London is 9| % premium, on Paris 6 francs 60 centimes per $1, and on Amster- dam 46c. per guilder ; between Amsterdam and London 12| guilders to iBl, between Paris and London 25 francs to £1. Which is the most advantageous, the direct exchange or through Amsterdam or through Paris, and by how much in each case ? ^^^tf-tf- J-c/ 3^'i^'j /'j.^^irti'vv 9. An express train left Suspension Bridge for Windsor at 12 P.M. at the rate of 40 miles per hour including stoppages, except that at London o.t 80 min- utes. A special kain left the Bridge at 1-51 P. M. and \i 7 7 31 /// - i i 190 EXAMINATION PAPEBS. i I arrived in London 46 minutes after the express had left; after a delay of 10 minutes it proceeded with an increas- ed speed of 10 miles per hour. When the express due in Windsor in 84 minutes, passed Belle Biver Station, the special was at Stony Point. The distance from Windsor to Stony Point is 26 miles, and from Suspen- sion Bridge to London 120 miles. If the speed of all trains from Belle Eiver to Windsor is limited to 80 miles an hour, how far is it from Suponsion Bhdge to Windsor? ^n.'f^J^ 10. A contractor was to receive a certain price for a a piece of work. If he employed a certain company of boys he would have to give them \ of the contract price ; but if he employed a certain company of men, he would have to give them § of the contract price. To faciUtate the work, he employed both companies and he received $2000 less than he would have received if he had employ- ed the boys only. Find the contract price, "k J ^^^ XXX. ^ James Bbuoe, Esq. — Waterdown High School. 1, Divide $8000 among A, B, 0, and D, giving A $40 more than \ of the other three taken together, and B $60 less than 60 % of what G and D receive, and C $80 more than 40 % of D's share. ) v«^ srv/i^^aii^^ 2. Two trains start at the same time, one from Hamilton to Toronto, the other from Toronto to Hamil- ton, both travelling uniformly. If they arrive in Tor- onto and Hamilton respectively in 2^ hrs. and 4 hrs. after they passed each other, compare their rates of travelling. 3 ,' i-*' 8. If I place a cent piece which is one inch in diam- eter on a map of one of the townships of Canada, and SB00ND-CLAS8 AND INTEBMEDUTK. 191 Eld left; ncreas- 3SS due Hation, e from ^uspen- 1 of aU I to 80 idge to ce for a pany of ct price; le would Facilitate received employ- Tit iy OOL. jiving A her, and ive, and He from Hamil- in Tor- 1 4 hrs. rates of indiam* Eida, and it covers 602 ac. 8 r. 17 per. 4 yds. 2 ft. 128^ in. ; find " ' 7 the scale on which the map is drawn, j ^J^^ -^ /^ t**^^ 4. If a rectangular cistern 6 ft. long, 4 ft. broad, and 8 ft. deep, be made eight times as large without chang- ing the relation of its dimensions; find its length, breadth, and depth, and how many gallons of water it will hold, assuming that a cubic foot of water weighs 1000 oz. Avoir., and that a gallon of water weighs 10 lbs. /a^x^X/^y^ f^cro^^^ 5. If a debt of $4000 due at the end of 4 years, were discharged by four equal annual instalments ; find the amount of each instalment, assuming money worth 6 % per annum compound interest. S^^Y ' ^^'^ 6. Simplify (12-964-8|x8-i + Vx8i) (3-6x8|~ V'xV + 65*790128466) + {12-96 x 12-96 + V x V xVxV + (VxV)a}. 7. A merchant bought goods for $30 with 6 months credit, and sold them forthwith at $86, with such an al- lowance of credit as made his gain 10 % ; how long credit did he give, reckoning money worth 6 % per an. simple int. ? ^^ M ^, /^%^\C^ '^^'0 "*-*- 8. When wheat was |il.lO a bushel a 4 lb. loaf was sold for 12 cents, but when wheat fell to $1.00 a bushel the 4 lb. loaf was sold at 11 cents. Assuming the cost of converting wheat into bread to be 80 cents on every 100 lbs. of bread, and that the baker was clearing 10 % of his receipts at the former price ; what percentage of his receipts would he gain or lose at the latter price ? ^ 9. If the three sides of a triangle be 8 ft., 10 ft., and 12 ft., find the length of the segments into which the greater side is divided by a perpendicular from the op- po^te'an^le; also the length of the lines drawn fiom 11)2 £XAMINATION PAPEBB. the middle of the perpendicular to the angles of the tri- , and sublets it so as to ^ake 20 y« profit. B, the sub-con- tractor, after finishing ^ of the contract, and receiving pay for th^ whole of it, abandons the work, and by so doing makes a profit of 25 y<>. A has to complete the contract at the same proportionate cost as B was put to, and finds Jthat he will clear $5000. How much was A's tender ? ^^j "0,0 7. A rents a house for 5 years. He is to pay the taxes at 2 cents in the $, make repairs on entering, which wiU cost 20 % of the value of the house, and pay annually $100. The house is assessed at -f of its value. and the taxes are $82 per annum. Find the actual umaa^ rent A pays, money being worth 10 Vo^a ^i/ ^ ^ -f 7. 3 ^ . ^-z 4. A vessel contains a certain number of gallons of 8. wine, 20 % of water is added, and the mixture is found to be too strong ; 16 gallons more of water are added, which increases the amount of liquid previously in the vessel by a percentage equal to i the number of gallons of wine in the vessel. How much wine in the vessel? 9. The population of a city increases 82604 in 8 years. The increase is due to an immigration of per- sons, 2000, and to tl^e births exceeding. the deaths. The J^O^aZ < "^ ^ /7J >7( c-^. '2/ / 194 EXAMINATION PAPSBS. births are -^ of the population, and the deaths ^, an- nually. Find the population of the city at the end of the period. i/**3 2- ^O^ 10. A field of 1 acre, on a new farm, contains a cer- tain number of stumps. The productivness of the field increases 10 %, when 20 % of the stumps are ex- tracted. 20 % of the stumps are taken out annually, at a cost which diminishes yearly 10 % of the oii^al cost. The field produces 20 bushels of wheat per acre before the stumps are extracted, and wheat sells at $1 per bushel. During time the field is being stumped, the produce exceeds the expense of stumping by $90 Find the number of stumps in the field, if it costs $1 to remove a stump th^ first year, J^ f^Z^L*^^ a/u^ -t^J^ o^ .JLU^ i^"* 7. A merchant's selling price is 6 % less than his marked price ; 6 % of his sales are bad debts ; his pro- fits are 25 % on his outlay. What per cent, above cost is the marked price ? ^^ -?^^ y^ 8. Suppose a clock has three hanc(s moving round the same centre — an hour, a minute, and a second de^. hand. At what time after 12 a.m. will (1) the minute ^V ^^/^f and second hand, (2) all three be first together ? 9. A merchant charges 6^^ per annum on all ac- counts overdue. What reducSTpercentage on the bal- ance of a bill of $460 paid one month after the bill was due, would be an equivalent to prepayment of $1^0 2 months before the bill was due ? ^""/_ ^ 3/0 /" ^^^^ 10. Find the value of v/2 by only once extract- v^54-2 ing a root. The diagonal of a rectangular field is 5 chains 40 links, and one of its sides is three times the length of the other ; find the side of a square field of equal area. y, ^ X ,^ ^^. ^^ ^ (^ 11. The amount of a certain principal in a certain time for a certain rate (simple interest) is $280 ; and 196 EXAMINATION PAPBBS. I * •/' the amount of doable the same principal at same rate for half the former time is $800. Find the principal. xxxin. ,/^ James Brown, M. A. — Upper Canada College. 1. Distinguish between Interest and Discount. If the discount of a certain sum be f of the interest of the same, what is the rate per cent, of the latter? /x\ ?.. (1) On March 20th, a merchant sold goods to the value of $1168, and received a note, due June 8th, next, for that sum with interest at 7 % per annum. For what amount was the note drawn ? ^// fy, <:^2.- (2) The above note was discounted on the 27th of March ; what sum should the discounter advance so a^ to receive interest at 12 % per annum on his money ^ Vtf "XViJ 8y^,^$560 be accepted as present payment of a debfiSue^i^ve months, wh^t is the rate of interest }^ cent. ^ annum ? ?^ ^ 4. A person sells |d500 Dominion Bank stock @ 180, and invests the proceeds in stock of the Bank of Toronto at 182. The dividends being respectively @ 8 and 12 per cent., and the brokerage t^ per cent, (in- cluded in the above prices), find — (1) The amount of stock purchased, fh- i '^^ (2) The alteration in the income. jt^Xo (8) The brokerage on the transactions. jfj,i ^a 6. How much mone}cmust be^inve^d in Dojninion ^ank stock, @ 181, to pW^jyJe an aim^^Mncome of $1800, after paying an incoB^ tax of 'ft cents on the dollar ? 6. What is the difference between 8 % per annum 8E0OND-0LA8B AND INTBHUBDUTB. 107 le rate incipal. ?e SOE. it. interest .tter? /X\j\\ Is to the ine 8th, m. For 27th of ice so M oney ?,7/J'XV2ij ent of a interest stock @ Bank of ^ely @ 8 ent. (in- o >opEiixiion icome of on the \x anntuu and 2 % per quarter, at Simple Interest and at Com- pound Interest respectively ? /i^ tj SX. '^^it/Lji t^(?._ 7. Prove the equivalence of the two quotations of Sterling Exchange, 108 and $4.80. If Sterling Exchange, in Toronto, be at par, and Ex- change on Paris be, in London, 1 franc^Oic?., what will be the equivalent quotation in Toronto of exchange on Paris ? /A ?.<-~*-'iS 8. If Sterling Exchange be @ $4.82 (gold) and gold at 106, in New York, while in Toronto SterUng Exchange is @ 108i, and U. S. currency @ 96, find how mnch may be saved on a draft fo^Jl|^200 by remit- ting through New York. i9\^ • i/^^ 9. A manufacturer who employed men at $1.60 a day found that he could save 16 % by employing wo- men ; what wages were paid the latter, supposing a man could do one-third more than a woman in the same time ? p /, Q V 10. A school is divided into three classes, of which the second contained one-fourth of the whole school, but 12 new pupils having been admitted idto the third class, and 16 promoted from the third to the second, and 6 from the second to the first, the classes are now equal ; how many pupils are there ? ^ v Lu^/jl/C XXXIV. i Thomas Oabsoadden, B.A. — Bichmond Bjll Hioh School. 1. Define an abstract number, a concrete number. What is the difference between 86« divided by 17 and 85«. divided by 17*. ? 2. The net rental of an estate afiier deducting 9(2. in 198 EXAMINATION PAPEBB. 1 the pound for Income tax, and Is. in the pound of the remainder for poor rates is £877 16«. ; find. the gross rental. ^ f^o 8. The difference between the interest of a certain sum for 1 year and the discount on the same sum due a year hence at 6 per cent, per annum is 76 cents ; find the sum. ;/S3/S'^ 4. Show from first principles how to multiply one fraction by another. Find the value of H of li If of 2i of $82-76 cents. Ifof 8i • lTVof2| 5. If 9 men or 12 boys can do f of a piece of work in 8f hours, in what time will ten men and 15 boys do the rest? X f^ ^ 6. Sh )W how to change a vulgar fraction into a deci- mal, and prove that the decimal will terminate or recur according to the form of the denominator of the given fraction in its lowest terms. What kind of a decimal will |^ produce ? 7. A merchant buys goods ; the cost of freight is 8 per cent., and that of insurance 12 per cent, on the original outlay ; he is obHged to sell them at a loss of 7 per cent.;*but if he had received £20 8«. more for them he would have gained 1^ pe^* cent. Find the original outlay. ^^6 6 8. A person rowed a distance of 8 miles down a stream in 45 minutes, but without the aid of the stream it would have taken him one hour ; what is the rate of the stream per hour and how long would it take him to return asjainst ^l* ? / / / ^ r ^ 8B00ND OLABB AND INTEBUEDIATB. 199 9. A merchant buys coffee at the rate of £S l&r. per Gwt., and chicory at £1 Ss. 6^. per cwt., and mixes them in the proportion of 10 lbs. of coffee to 7 of chicory ; at what rate must he sell the mixture so as to gain 4^V per cent. ? ^ ^ ^ ^^^^ 10. Explain the method of pointing in extracting the sq. root of a whole number, and also of a decimal. (a) If the surface of a cube is 89 sq. ft., find the lenc^h. of its edge. S^ pet gallon, the 44 consols being at 90 ? XXXVI. . Bev. George Grant, B.A. — SmooB High School. 1. A storekeeper buys six boxes of goods, two be- ing damaged sold at 6% loss ; but selling the whole for $660, he gains 10% on the whole cost. Find his gain ^ on the good boxes ? /7^ •^ w 8B0OND GLASS AND INTERMEDIATE. 201 2. A merchant has teas at 80, 60 and 40 cents pei lb. respectively. He wishes to make a mixture amounting to 1089 lbs., so that selling at 70 cents pei lb. he may gain 10%, and at the same time give one-hali \ oz. on every lb. to his customers to turn the scale. How many lbs. of each kind must he use ? V^i'^' JJ ^' 3J 1^ 8. A party numbering 120, made up of men, women, and children propose to go on an excursion. It is Agreed that each man, woman, and child pay in the ratio of 8:2:1. The total outlay is $500. In conse- quence of the failure of 4 men, 6 women, and 6 children to join the party, the aggregate of the men's shares is to that of the women's and children's shares respective- ly as 6:6:7. Find the number of women that went with the party. ^ yj ii^n^n^vcw 4. An excise duty of 90 cents per hogshead is levied on crude petroleum. The producer reaUzes 20% on his sale. The refiner after allowing for a shrinkage of 20% in the process of refining, makes a profit of 25yo on his outlay. In like manner the wholesale dealer and retail merchant each clear 12% on their outlay. If the tax were abolished, what reduction in price per gallon on the refined oil could be made to the consumer, supposing each dealer to make the same rate of profit as before ? O A I - 1 - - - ^ If stock bought at 6%jpay 6% on the investments/, /^y )er cent, will the broker make who buys^stocITat o 6. what per cent, will the broker make who buys^. 10 discount, and after drawing the dividend sells out for 106 American currency, gold being worth 105 ? /^ ^9 6. Three circular flower-beds, each bounded by a line 856 inches in length, are situated so that their cir- cumferences are in contact. Find the area of the triangular space lying between and not included within tlie flower beds, ^ ''z U . f /U -f S ^ y^'7(, ^ -^ Y 202 EXAMINATION PAPEBS. 7. The directore of a joint stock company resenre $1000 of their capital for current expenses, and in the first year increase the remainder by ^ of itself. The same operation is repeated in each succeeding year, until at the end of the fifth year the company is worth $20,000. What was the capital at first ? "^/yfa^ff^o 8. A farm is sold for $2500. The purchaser pays \ down and gives a mortgage for the balance, principal and compound interest at 8 per cent, per annum pay- able at the end of 6 years. The mortgagee immediately barters the mortgage for a fixed sum, to be paid in four equal payments, one at the end of each year. If money be worth 10% per annum, what should be the amount of the annual payment ? i^' ^i"* f:>b-h- 9. The price of a loaf is 10 cents, when the outlay for flour is 60%, the cost of delivering 10%, and other incidental expenses 20% of a baker's receipts. The price of flour falls 20%, and the cost of delivery rises 20%, what should be the price of the loaf so that the baker may still make the same rate of profit as before ? 9. If $20 be the discount off a bill of $200 due some time hence, what would be the discount off: — (A) If the bill had twice as long to run, and at double the rate of interest. (B) If it had half the time to run, and at half the rate of interest ? XXXVII. J. Deai;ness, Esq. — ^Public School Insp., Middlesex. 1. What part of 1^ of \ of 7^ of 5 pints of wheat is 8^ oz. of the same grain ? 2. A grocer's scales weigh light by \ oz. per lb. H^ g^B for cash at an ^vance of 20 per cent, on invoice UOOND-OLASB AND INTERSfEDUTB. 208 rates, on whioh by paying cash he receiveB a discou :t of 6 per cent. What is his exact gain per cent, on goods he weighs out ? 8. A goldsmith pays \ as much per oz. Avoir, as he sells for per oz Troy. What is his exact gain per cent ? 4. Olock No. 1 loses *06 per cent ; the rate of clock No. 2 is one hundred and one per cent, of the rate uf No. 1. They are set right, and on Saturday at 9 p. m. No. 2 is 56^^ minutes fast. When were they correct? 6. In a field in whioh cows and sheep were grazing, I of the total number were cows ; but when 8 cows more were driven in, the later numbered -^^ of the whole. How many sheep were there ? 6. The true discount for one year is to the bank dis- count for one year as ^ to ^' Find the rate per cent. (860 days=l yr.) 7. The total assessed value of a certain township is $2,300,000 ; that of a separate school section within it is $116,000. The county levied for public school pur- poses on said township $920 ; whioh by mistake was collected off the whole township. How much should be refunded said separate school section ? 8. Three lbs. of coffee and 2 lbs. of tea cost $8.00; an increase of 10 per cent, on the former, and a decrease of 10 per cent, on the latter reduo }d the bill six cents. Find the original price of each per lb. 9. How should a man divide $10,788.12^ between his two sons, aged respectively 15 and Id years, so that each on attaining his majority may receive an equal sum, providing that the money at time of division be deposited at 6 per cent, compound interest ? ^0. The distance between the centres of a fore wheel 204 EXAMINATION PAPEB8* w If r i II ■ ■ fl • I I i I' s I ^ r i u f I i ' and hind one of a buggy is 4 ft. 6 in. ; between the nearest points of the oircumferences of the same, 6 in. ; the hind wheel is 4 in. higher than the fore one. Given that 44 radii are equal 7 circumferences, find what dis- tance has iDeen moved over when the fore wheel has made exactly 100 revolutions more than the hind one. xxxvin. G. K. PoWBUi, P. S., TOBONTO. 1. A man bought goods for $750, and sold a certain portion of them at a loss of 4 %. Having increased his selling price 12^ % he gained 4 % on the whole transaction. Find the portion of goods sold at a loss. 2. Two farmers, A and B, together sold 500 sheep, A at $7.25 and B at $7.75. They received altogether $18 more than they would have done had they both rold at the uniform rate of $7.50 a head. Find the number sold by each. 8. A merchant in Ottawa buys sugar in New York at 7 ots. currency per lb., pays an ad valorem duty of 20 % and a specific duty of 2 cts. per lb. Exchange is I % premium and gold 112. At what price must the sugar be sold to yield a profit of 25 % ? (Duties paid in gold.) 4. Find the market value of 6 % bank stock, so that after paying an income tax of 4c{. in the £ it may yield 6 % interest. 6. A merchant buys a quantity cf syrup for $1512. By the use of a false measure and by marking his goods at a piofit of 20 %, his gain is $604.80. Find the size of his gallon. 9, In a German college the professors number 18.2 SECOND CLASS AMD INTERMEDIATE. 206 ^een the e, 6 in. ; I. Given hat dis- leel has id one. I certain ucreased le whole a loss. sheep, together ley both rind the BW York duty of xchange Qust the ies paid so that ay yield $1512. is goods the size er 18.2 % of the whole ; on the admission of 60 more students the professors then number but 12 % of the whole. Find the number of professors. 7. What price must I pay for Montreal Bank stock, three months before the dividend is due, in order to make 9 y* on my money, the bank paying half-yearly dividends of 8 y« ? 8. The cost of carpeting a room whose breadth is two-thirds of its length is £10 14«., the carpet being 27 inches wide, and worth 6s. 6d. per yd. Find the length of the room. 9. The true discount on a note of $946, drawn at months, is $70. Find the rate per cent. ? 10. (a) The sides of a right-angled triangle contain- ing the right angle are 12 and 6. Find the length of the straight line joining the right angle with the middle point of the hypothenuse. {b) The sides of a triangle are 20 and 30, and the base 86. Find the perpendicular on the base from the opposite angle and the segments into which it divides^ the base. XXXIX. I. G. BmoHARD, Esq., P. S., Toronto. 1. Explain the principles employed in finding the^ G. C. M. and L. 0. M, of numbers, and illustrate by applying them to the solution of the following examples : Find the G. C. M. of 2627, 1818, 2780. Find the L. 0. M. of 16, 16, 20, 25, 27, 80, 85. How would you proceed if any of the numbers were fractional ? 206 EXAUIl.ATION PAPEBB. 2. Simplifyl±(21??5!)!±(2!?^!r,a.idfindthe 1 + (-142867) + (-142857)* value of the following to five places of decimals: ^+r+ix2 1x2x8 ' 1x2x3x4 8. Shew that e\wry fraction can be exactly expressed either as a finite or a circulating decimal. How can we determine without trial whether a given fraction when reduced to a decimal will give a finite decimal, a pure circulating decimal, or a mixed circulating deci- mal ? Illustrate by examples. 4. A merchant bought 1295 yards of cloth and marked it at an advance of 20% on the cost price ; in selling the first half of it he gave only 85 inches for a yard, and 87 inches for a yard in selling the remainder. He gained $260.20 ; what did the cloth cost him ? 6. A and B run a race, B has a start of 20 yards, and takes 12 steps while A takes 11 ; but 10 of A's steps are equal to 11 of B's ; how far will B run before A catches him ? 6. A note for $1976, bearing interest at 6%, has run 146 days ; what must be the face of a new note which, discounted by the bank for 78 days, at 6%, will just redeem the former ? 7. A stock broker has $1500 more than -^ of his money in Montreal Bank stock, and the remainder, which is $2500 less than -^ in Toronto Bank stock ; the former pays 7% half-yearly and the latter 10% yearly. Find his net income aft^ paying an income tax of 1^ cents on the dollar. 8. A merchant sendaflour to his agent in Toronto, who sells it at $6 per bbl., and deducts his commission 8B0OND GLASS AND INTERMBDIATB. 207 d find the Lecimals : Bxpressed How can fraction ecimal, a ;ing deci- loth and price ; in hes for a smainder. lim? 20 yards, LO of A's nn before 6%, has new note o. ^^ ^ of his imainder, stock ; ter 10% income Toronto, omission at 2% ; he then reinvests the balance in goods, deduct- ing his commission at 2% ; his whole commission was $28^^. How many bbls. were sent? 9. There were 64^:4682 letters posted at the Toronto Post office in 1876 ; if the average size of each were 8 in. by 6 in., how many miles of King street, 66 feet wide, would they cover? 10. A well 80 feet deep and 6 feet in diameter is curbed with a wall of loose stone 1^ feet thick. (1) How many cords of stone are in the wall ? (2) How many tons of water would it hold if the interstices between the stones occupy i of the volume of the wall. XL. G. B. Spablino, B. a., Uppeb Canada Golleoe. 1. Find the difference between 7i-2f of 2^ and 6f-f(84-i ) 2-6 of 2-27 1186 6f-8f-|-2.08 of £3 188.9 of 1^ guineas. 124(-06 of -8 of 4)-l -f-(.J+^) 2. Two pipes, A and B, fill a cistern in 16 and 20 minutes, respectively, and C empties it in 6 minutes. Suppose the cistern to be empty at first. After A has been open 4 minutes, B is opened, and after 4 minutes more C and D are opened, and the cistern is emptied in 66 minutes. In what time would D empty it if full. 8. How many boys must assist 27 men in order to eai'u f 804.86 in 18 days, if 7 men and 5 boys earn 208 fi m ii EXAMINATION PAPEBS. ).05 in 9 days, and 2 men and 19 boys in 11 days earn $65.45 ? 4. What principal, lent out at Bi" Compound Inter- est for 8 years, will produce the same aihount as $2222.64, lent out at 6% Simple Interest for 4 years 2 months? 5. A person invests the proceeds of a note for $9607.50, due 18 months hence, discounted (truo dis- count) at 4J^%, in 6% stocks at 91, paying brokerage ^7!.. Find his net annual income from this investment after deducting an income tax of 2^ per cent. 6. A garrison is provisioned for 180 days; at the end of 80 days it is found that 25% of the stores then remaining are unfit for use; at the end of 80 days more it is reinforced by 2000 men, and then the stores are made to last 110 days longer by putting the men on half rations. Find the number of the original gai-ri- son. A, B, and engage in business. A puts in $400 at first, and $400 more at the end of 6 months ; B puts in $900 at first, and withdraws one-third of his capital at the end of 6 months ; C puts iu $200 at the end of every '6 months ; at the end of two years they have gained $6700. What share of the profits should G receive iu .addition to 25% of the total profit for managing the business? 8. If there be melted together 80 oz. of copper, of ■specific gravity 8*7, 10 oz. of tin, of specific gravity '7*4, and 4 oz. of lead, of specific gravity 11*4 ; find the specific gravity of the resulting bronze, allowing for contraction in the ratio of 100 : 99. 9. A grocer mixed ^een tea which cost him 28 ctB. per pound with black tea which cost 2 cts., and by sell- SECOND GLASS AMD IMTEBMEDIATE. 200 11 days d Inter- ount as years 2 note for truo dis- erage if, lent after i; at the ores then lays more atores are 3 men on nal garri- $400 at B puts in capital at 4 of every re gained Ireceiv© in [aging the )pper, of io gravity find the |oimg for 28cts. id by sell- ing the mixture at 86 cents he gained 16% on the green tea and 20% on the black. In what ratio were the teas mixed? 10. I sold goods which cost me $4000 so as to gain mi* of the proceedSf and a second lot which cost me $6000 so as to gain 28^% of the proceeds. Find my gain % on thQ entire outlay. 11. (1) If the parallel sides of a garden be 66^ ft. and 49^ ft. respectively, and their perpendicular dis- tance 66f ft., what did it cost at $1627.60 per acre ? (2) It is required to cut off from a triangular field whose sides are 1200, 1000 and 800 links respectively, 1 acre, 2 roods, 16 perches, the dividing line being par- allel to the longest side. Find the sides of the triangu- lar part cut off. XLI. J. W. GoNNOB, M.A., High School, Beblov. 1. Divide 8878 by 16, using factors, and explaining without reference to fractions the method of finding the complete remainder. What would be the remainder if the divisor t^ere 8x6x7? ^"3 2. In Babylonia a capithe of meal was sold for 4 sigli. A siglus was worth 7\ obols, the capithe held 8 qts. Find the price of meal per bushel, taking the obol ata^. 8. Assuming only the fundamental definitions, prove that multiplying both terms of a fraction by the same number does not alter its value. Show clearly what operations depend on this property. 4. Beduoe y^, i^> A> ^ '^ common numerator, and hence find which is greatest and which is least. 210 EXAUINATIOD FAPEBS. -■'-■, ^V: l»! 5. Divide to fiye dooixual places 2*6878 tons by 266' 185 tons. State the denomination of the quotient, and express the remainder in lbs. and oz. 6. A lump of gold 22 carats fine contains 27 oz. of alloy, how many oz. of alloy in a lump of the same weight only 18 carats fine ? 7. A bankrupt's estate was expected to pay only 48 cents on the dollar ; but a claim of $1000 being dis- allowed, it paid 60 cents instead ; find its value, the costs amounting to 20 % thereof. 8. A and B become partners, and invest $15000 and $20000 respectively, B to get 8 % per annum inter- est on the excess of his capital over A's, A being paid $800 a year for his time, balance of profits to be shared equally. At the year's end A has drawn $600 on account, and the net value of the business is $37200 ; how much of this belongs to each partner ? 9. How much better or worse is it to buy 6 per cents at par with $20,000, and also with the half-yearly divi- dend thereon, selling at par at the end of the year, than to use the money in discounting 70 day notes at 6 % per annum, the money being employed the whole time ? 10. A. buys a lot for $800, agreeing to pay every year $75, with interest thereon at 6 % from the date of the purchase. At the end of two years he sells it for $400 to B, who assumes the two payments yet to be made, and pays cash for the balance. Supposing that every year interest was paid on the whole sum due on the lot, out of how much was B cheated, money being worths %? Al. A man in England wishes to buy as much 6 per cents municipal debentures as will give his daughter L?ii!m«i SECOND GLASS AND XNTEBUBDIATB. Ml resident in Canada an inoome of $794 per annum ovei and above income tax at 1^ cents in the dollar, $400 of every one's income being exempt from taxation. Debentures selling in Montreal at 96f , brokerage J, and sterling exchange being there at 8 % premium, whal sum in sterling money must he lay out ? XLIL C. A. Babnes, Esq. — STBAxmiOY, P. S, 1. A man bought 860 bushels of wheat at a certain price per bushel and sold ^ of it at a gain of 10 %, ^ ai a loss of 25 %, and the remainder at a gain of 45 yo, and by so doing realized $594 for the whole lot. What was the cost price per bushel ? 2. A's farm contains 5 acres as ofiien as B's con- tains 8, and G's farm lies betwean them. Now if C should give up f of his farm to A, and ^ of the re- mainder to B, he would have 68 acres left; and A's farm would then be equal to B s in extent. How many acres has each ? 8. A, B and start to walk in the same direction, B being 10 miles ahead of A, and C 5 miles ahead of B. A travels 6, B 5, and G 4 nules per hour. When witi A be midway between B and C ? 4. If a quantity of spirituous liquors is sold before arrival in port under agreement as follows : If 86 % strength above proof, at $5.40 per gallon, if over that strength to be paid in proportion. It arrives and is found to be 88J- above proof. What increase on 1000 gallons ought to be charged as an equivalent of Sf % increase ? 5. Two vessels have part of th^ir cargoes, consists 212 EXAIOMATION PAFEBB. ing of tea and sugar, of the same quality. One carriea 104 owt. of sugar and 26 owt. of tea; tbe other 91 owt* of sugar and 22| owt. of tea. The former pays for duty 5 cwt. of sugar, 1 j^ owt. of tea, and $1061.20 ; the latter pays 5 owt. of sugar, Ij- cwt. of tea, and $915.60 Supposing the duty on tea to be 28 times that on sugar, and the prioe of tea 9 times that of sugar, what is the price of each article per lb. (112 lbs. to 1 cwt.) 6. Three men. A, B, and 0., have $11,700 each ; they wish to invest it in the 8y» consols to pay them 4%, How much must they give per cent.; how much stock will each hold, and how much interest will each receive at the expiration of one year, A taking besides his own ^ of B's interest and ^ of G's interest ? 7. A man buys goods for a cei-tain sum, and m irks } of them at a profit of 24^0, and f of them at a profit of 86% ; but had he marked f of them at 2iX gain, and ^ at 86% gain, he would have realized $240 less than before. Find the cost of the goods. 8. A and B start from the same place and in the same direction. A travels 86 miles a day, and after 10 days turns and goes back as far as B could travel in 6 days, he then turns again, and pursuing his journey overtakes B 26 days after they first set out. At what rate does B travel ? 9. A merchant shipped 1000 barrels of flour from Toronto to his agent in New York, with instructions to seU at $8 per bbl. on a commission of 5^% and invests the proceeds in tea on a commission of 4%, but the price of flour having fallen, he sold at such a price as enabled him to send his employer $6887.50 worth of tea ; at what rate per bbl. did he sell the flour ? and how much did the merchant lose ? 8B00ND GLASS AND INTBBMBDIATS. 218 oarrieB H owt. ays for 0; the ;915.60 hat on X, what 1 owt.) each; bem4%. )h stock 1 receive his own id n irks i a profit 'aiu, and ess than d in the after 10 avel in 5 journey At what )ur from stions to %, and 4%, hut a price I worth of lur? and 10. A B C is a triangle, the side A B 20, A C v/881, and the perpendicular let fall from A on B C is 16. Find B 0, and also the length of the line joining the vertex with the middle of the hase. XLIII. D. McKay, Esq. — Newburo, P. S. 1. A gentleman is owing three notes to A. McLellan, one of $100 due in 4 months, another of $100 due in 8 months, and a third of $200 due in 12 months. Should the three he converted into two for the same amount, the one to run just twice as long as the other, when ought they to he made payable ? 2. If $4 be allowed as discount off a bill of $40 due 6 months hence, how much should be allowed off a bill of the same amount due 18^ months hence ? 8. A merchant bought 70 yards of cloth If yards wide for $4.50 per yard, but the cloth having been wet shrunk 5 % in length and 6 % in width, for what must it be sold per square yard to gain 12 % ? 4. The flag pole on the University Grounds is 80 ft. high, at what height from the ground must it be broken off, so that the top of it may fall on a point 40 ft. from the bottom, the end where it was broken resting on the stump. 5. A gentleman bought a lot in Little York for $56 who sold it to James Thompson for a certain sum, Thompson sold it to Miles Caton, Caton sold it to Jas. Smith for $12096 each man gaining the same rate per cent. ; find Thompson's buying and selling price. 6. If a certain number of workmen can do a piece of work in 25 days, in what time will If of that number ""I I ill Km 214 BXAMINATION PAPEBS. of men do a piece of work twice as great, supposing that 2 men of the first set can do as much work in an hour as 8 of the second set can in 1| hourb, and that the second set work half as long again as the first set ? 7. A person invests in the 8 per cents so as to ob- tain 8% clear on his investment, when there is an in- come tax of 7 cents in the dollar. What percentage clear does he obtain, if the tax be doubled ? 8. A tradesman, who is ready to allow 6 per cent, per annum, compound interest, for ready money, is asked to give credit for two years. If he charge $27. 56^ in his bill what ought the ready money price to have been ? 9. A room whose length is to its breath as 4 to 8 costs $96 to carpet it with carpet 27 inches wide at $1.50 per yaid. What is the height of the room pro- vided the cost of papering is to the cost of carpeting as 68 to 820, the paper being 2 ft. wide and costing 15 cents a yard ? 10. What is the weight of a hollow spherical iron shell 5 inches in diameter, the thickness of the metal being 1 inch, and a cubic inch of iron weighing ^^ of a pound. XLIV. : ( W. SooTT, B.A. — Model School, Toronto, 1. A can do a piece of work in 12^ days which B can do in 18J days, and C in 12J days. They com- menced to work together, but after working 1*^ days A stops and B and G continue till the entire work is f done, when B stops and C finishes the work. If the whole work is worth $12.12f^, what does each receive? ■EOOND-OLABB AND INTKRIIBDIATB. S16 fi. A oommiHsion merchant received a consignment of flour which he is to sell on a com. of 1^^ % and invest the proceeds in tea after deducting his commission on this new transaction at the rate of 1} %. His total commission being $220, what did he invest in tea ? 8. Two trains 100 feet and 120 feet long re- spectively, are observed to pass each other going in op- posite directions in 8 seconds and going in the same direction in 15 seconds. At what rate were the trains going ? 4. A wheat buyer sold \ of his wheat at a certain gain percent., ^ of it at a gain of twice the former rate per cent, and the remaiiider at a gain per cent, of 8 times the first gain. If the gain on the entire stock was 26 %, what did he gain on each part ? If he gained 6 i» on the first paii;, what was the entire gain per cent? 5. If 70 men in 10 days of 9 hours each can dig a drain 90 yards long, 4 feet wide, and 16 feet deep, what length of a diain 5 feet wide and 18 feet deep can 100 men dig in 14 days of 10 hours each ? 6. B bought 10000 centals of wheat at $1.20 per bushel of 60 lbs. and sold to A at an advance of 10 per cent. A gave his note for 4 months in payment. Money being worth 6 %, what was B's real gain ? 7. A merchant wishes to mark some goods which cost $1.20 per yard, so that after making a reduction of 20 per cent. o£P the marked prices, he may yet gain 10 per cent. At what advance per cent, must he mark the goods, and if A buys without getting the reduction, what does he pay per yard ? 8. How much must be invested in the U.S. 6's 6-20 at 120 currency interest payable in gold, so as to pro- duce a net income of $6232^ in gold after deducting an I I ii ?!ii 216 BXAMIMATION PAPEBB* inoome tax of 1| per cent, payable in ourrency, the pre* mium on }3;old being 40? 0. If 40 oxen can eat up a field of grass in 8 weeks, or 80 oxen can eat up tbe same field in 12 weeks, the grass growing uniformly, how many oxen can do it in 5 weeks ? 10. A invests $760 more than 60 % of his money in the Dominion 6's at 101 ; $9600 more than 88| % of the remainder in bank stock at 116^, which pays a divi- dend of 8 % ; and the remainder which is 26 % of the whole, is invested in building society stock at 179^, which pays a half-yearly dividend of 6 %. Brokerage being ^ % on the first investment and ] % on each of the other, what is the total income for the year? XLV. J. MosBisoN, M. A., M. B. — ^Nbwmabkbt High School. 1. What is the difterence between Bank Discount and True Discount ? The Bank Discount of a certain sum for six months is $188.49 ; what is true discount ? 2. The longitude of Newmarket is 79® SO' west; at a certain time it was as much past noon at Greenwich as it lacked of noon at Newmarket ; what was the time then at the latter place ? 8. A person buys f of a property, which afterwards falls 4% in value. He then sells 20% of his share for $800; what was the whole property worth at first ? 4. The salary of the Principal of a High School was $1100 before the income tax was levied. How much must it now be with an mcome tax oi 1^ cants per dollar, in order that he may still have $11CH) BKCOND 0LAB8 AND INTBRlfEDIATB. 217 weeks, )k8, the I it in 6 oney in H%ot I a divi- ; of the t 179^, okerage each of School. iscoimt onths 3st; at mwich ^e time rards re for ? School How ;iioo per annum ; $400 of his salary being exempted from taxation. 6. How far mnst a person proceed on a sta^e which travels 5^ miles per hour in order that he may walk back at the rate of 2} miles an hour and be 6 hours gone? 6. In the winter term of 1876, the number of boys in the Newmarket High School was to the number of girls in the ratio of 4 to 8. In the spring term the de- crease in the number of boys was 5|- per cent., while the increase in the number of girls was 88^ per cent., and the number of boys was to the number of girls as 8 to 9 ; there being 68 in aU during the spring tenn. How many were there in the winter term ? 7. An express train goes from Toronto to Stratford in the same time that a mail train takes to go from Toronto to Guelph, and that a freight train takes to go from Guelph to Stratford. If the velocities of the freight and mail trains aie as 4 to 6, compare the velocities of an express and a mail train. ^ • i ^ 8. A certain sum amounts to $1488 in 8 months, and $1680 in 16 months, simple interest ; what is the rate per cent. ? S' /o 9. A person sold two watches, one for $60 gaining 4%, and the other for $60 losing 4% ; how much did he gain or lose by the transaction, and how much pei cent. ? 10. A manufacturer exports a certain quantity oJ goods to the United States and after paying freight duty &c., realizes for them only $6440 which was at a loss of 8% on the cost price. If he had sold them at home he would have realized a profit of 8% ; how much were they sold below the trade price at home ? :! ^ : I 218 EXAMINATION PAPERS, XLVI. hK.' ^1? W. E. TiLLET, B. A. ^BOWMANVILLX HlGH ScHOOL. 1. Find the cost of enclosing with a stone wall 10 ft. high, 2^ ft. thick, an acre in the form of a square at $2.25 per perch of 22i cub. ft. 2. A person sold a horse gaining 11J% of the pro- ceeds. Had he received $85 less he would have lost df % of what the horse cost him. Find the cost and selling price of the horse. 8. A merchant marked his tea at a profit of 48f %, but threw off 5 cents per lb. for cash. Had he marked his tea 5 cents per lb. higher, and then thrown off 10% for cash he would have gained 2^% less on his outlay. Find the cost and marked price of tea per lb. 4. B invested $5000 in 8% accumulating stock at 112, on which nothing had been previously paid, secur- ing $8000 stock. Four months afterwards he paid in $2000. Two months after he made the second pay- ment, and just after the dividend had been declared he paid up the balance. Find amount of last payment and liie rate % per annum which B received for his money. 6. I bought $10000 stock through an agent who charged me i% for buying. Had the stock been quoted 5% higher, and had I also bought through an agent at ^%, 1 should have received $688-]r1;- less stock on the same outlay. Find the price of the stock in the first case. 6. My purse and the money in it are worth $128. If I spend 8% of my money and sell the purse for 5 times its value I shall tlien have $150.40. Find the value of my purse. BROOND-OLASS AND INTERMEDIATE. 219 7. A merchant bought a quantity of goods for $4324.80, on which he is allowed 3 months' credit, and immediately sold them for $6300 on a note of 8 mos. He at once had the note discounted at the bank (no days of grace) at 9y» per annum. How much % of his net investment did he gain, money being worth 8 % per annum, and how much would he have saved if the note had been discounted at true discount. 8. If the par of exchange be is. 8d. English for the American dollar, but if an American bill of exchange for $180 be negotiated in London for £86, how much per cent, is the course of exchange below the par of ex- change. 9. A merchant bought 2 bbls. of beer and 8 hhds. of wine. He sold the wine at a profit of 1T^% by which the profit on two gals, of wine is equal to the cost price of one gal. of beer. He sold the beer at a loss of 5%, but on the sale of the whole made a gain of $27.20 Find cost price of wine and beer. 10. At what % advance on cost must a mer- chant mark his goods so that after allowing 12% of his sales for bad debts, an average credit of 4 mos. and 16% of cost of the goods for his expenses, he may make a clear gain of 9% on first cost ot tne goods, money being worth 8% per annum ? XLVn. 1. John D. Ham, of the village of Newburgh, has a farm adjoining the town of Napanee, containing 673^gV acres, which he wishes divided into square lots of the largest size possible. The farm is rectangular, its length being to its breadth as 4| to 1. How many lots will he have, and what the area of each lot in rods ? 220 EXAMINATION PAPEBS. 2. If the simple interest on a sum of money for a given time and date be -^ of the principal, show that the true discount is r-. a-\-o 8. Four men, A, B, and D, start at the same point and in the same direction to travel round a circular island 10 miles in circumference, till they are all toge- ther again. A makes f of a revolution in a day, B ^^t C ^\, and D ^. How many miles does D travel more than B ? 4. The difference between the simple interest and true discount on a certain sum for 3 years 8 mouths 6 days, (=8^!^ years), at 4f %, is $98. What is the sum ? 5. A lady purchased a piece of cloth at 80 cents a yard, and lining for it at 80 cents, the cloth and lining containing 16 yards, and the price of the whole was $7. How many yards were there of each ? 6. A man at the time of his marriage agreed to give his wife f of his estate, if at the time of his death he left only a daughter ; and if he left only a son she should have -^ of his property ; but as it happened he left a son and a daughter, in consequence of which the widow received in equity $2400 less than she would have received if there had been only a daughter. What would have been the wife's dowry if he had left only a son ? 7. A man being asked the time of day, replied that it was between 5 and 6, and that the hour hand wanted as much of being at the point 6 as the minute hand had passed that point ; what was the time ? 8. A alone can finish a piece of work in 12 day ; B and C help him for a certain time, B quitting 5^ and BBOOND CLASS AND INTERMEDIATE. 221 sy for a low that me point circular 1 all toge- ay, B i\, i,vel more Brest and mouths 6 lat is the 50 cents a md lining le was $7. ed to give death he son she )pened he which the }he would er. What left only a plied that nd wanted hand had L2 day ; B 5^andC 2} days before the work is finished. How many days did B and C help A, provided A's efficiency is to B's a? 8:2, and B's to G's as 4 to 8. 9. What must I ask a yard for silk that cost me $1.60, so that I may fall 10% and still make 20%, allow- ing 10% of the sales for bad debts ? 10. A man invests a certain sum in Toronto 6% debentures, selling at 6% discount, and $500 less in Bank of Toronto stock, selling at 5% premium, and pay- ing yearly dividends of 10%. The income from the Bank stock is $100 more than from the debentures ; find the amount of stock held. XLvni. 1. Show that {^S--iiV-i^}x{i^ + |~i}x{^-f 9 I —1 X 1 m '0' 3'«-711 2. The manufacturer of an article makes a profit oi 10 %, the wholesale dealer a profit of 15 %, and the retailer makes a profit of 25 %. What is the cost oi the manufacture of an article which is retailed for 16 shillings? 8. Three merchants contributed J, |^, and i, respect- ively, of the capital for a commercial adventure, on the condition that the gains should be divided at the rates of 7, 6, and 8 per cent, respectively, on the sums each had contributed. If the gains were $1500, what was the share of each ? 4. If pure gold be worth £4 per ounce, and pure silver 5«., what percentage of copper must be mixed with pure gold in order that the value of a given quan- tity of the compound metal may be 15 times that of an equal weight of a mixed metal containing 80 per cent. of pure silver ? If 222 EXAMINATION PAPEBS. 6. If 20 men, 40 women, and 60 children receive among them $1400 for 7 week's work, and 2 men re- ceive as much as 8 women or 6 children, what sum does a man, a woman, and a child receive weekly ? 6. If the atmosphere were of the same density throughout as it is at the level of the sea, its height would he 26258 feet ; find the weight of air which sur- rounds the earth, having given that 876*1 cuhic feet of air weigh as much as •! cuhic foot of mercury ; and 30 cuhic inches of mercury weigh 14*7 lbs. : supposing the earth a sphere of 8,000 miles in diameter, and hav- ing given the content of a sphere equal to two-thirds of its circumscribing cylinder, and the area of a cu*cle equal to 8* 141 5926 times the square of the radius. 7. The estate of a bankrupt worth $84000 is to be divided among four creditors ; the debts due to A and B are as 2 : 8, to B and C as 4 : 5, and and D as 6 : 7 ; what must each receive ? 8. If a manufacturer sell an article of which the first cost is $400, to a wholesale dealer at 10 per cent, profit, the wholesale dealer to the retailer at 15 per cent, profit, and the retailer to the consumer at 80 per cent, profit ; what sum is paid by the consumer as pro- fits in addition to the first cost of the article ? 9. Paper money is at a discount of 20 per cent. A man buys goods marked £6 10«. (paper money), and tenders that sum in gold. How much paper money must he receive in change, 6 per cent being allowed for present payment ? 10. The sides of a right angled triangle are 8, 4, and 6 ; find the length of the perpendicular from the light angle on the hypothenuse. SECOND CLASS AND INTERMEDIATE. m receive 2 men re- what sum ekly? ae density its height which sur- abic feet of ry ; and 30 supposing ir, and hav- j^ro-thirds of of a circle radius. )00 is to be 3 to AandB iDas6: 7; f which the 10 per cent. ir at 15 per Br at 30 per amer as pro- Le? )er cent. A [money), and laper money allowed for zle are 3, 4, far from the XLIX. 1. A teacher spends f of his salary in board for him- self and family, ^ in clothing himself, his wife's cloth- ing costs -^ as much as his own, his daughters' i as much as his wife's, his son's ^ as much as his daughter's, ar^ he lays by $116. What is his salary ? 2. Three merchants have an interest in a steam vessel ; A puts in $960 for six months ; B, a sum un- known, for 12 months ; C, $640 for a time not known when the accounts were settled ; A received $1200 for his share, stock and profit; B, $2400 for his, and C, $1040 for his. What was B's stock, and C's time ? 8. I wish to line the carpet of a room, 6^ yards long and 5|^ yards wide, with duck i wide. How many yards of lining must I purchase, if it will shrink 4% in length, and 6% in width ? 4. If a merchant wishes to draw $1275 at the bank, for what sum must he give his note at 60 days, dis- counting at 6% ? 5. I received an 8% dividend on bank stock, and in- vested the money in the same stock at 80%. My stock having increased to $18,750; what was the amount of my dividend ? 6. f of T^ of what number, diminished by ^ — leaves \ ^l "^ ^ 7 7. A man purchased a farm for $8000, and agreed to pay principal and interest in 4 equal annual instal- ments. What was the annual payment interest being 6%? 8. At a certain time between one and two o'clock 3 224 EXAMINATION PAPBBS. the minute hand is between 2 and 8, and within an hour the hands will exactly change places. What is the first mentioned time. 9. Four towers — A 126 feet high, B 26 yards high, G 160 feet high, and D 70 feet high — stand upon the same plane ; B directly south, and 40 rods from A ; C east from B ; and B south from C. The distance from A to G plus the distance £rom G to B is ^ a mile, and the distance from D to B is 82^ yards farther than the distat oe from G to D. Bequired the length of a line to connect the tops of A and D. 10. A gentleman wishes to set out a rectangular orcha^rl (,{ 1260 trees, so placed that the number of row J al'^ >i ^« to the number of trees in a row as 6 to 7. If the l.*et>L ^e 8 yards apart, how much ground will the on hp.rd occupy ? -.«»h 1^ CHAPTER VI. EXAMINATION PAPERS FOB FIRST-CLASS CERTIFICATES AND UNIVERSITY HONORS. I. July, 1871. 1. Show how to find the least common multiple of two or mo -e fractions. A, B, and C start at a given place to travel round an island 120 miles in circumfer- ence, A's rate is 5^ miles a day, B's 8^, G's 9f ; in what time will they all be together again ? ^ %^^( (X^ ^ 2. Prove the rule for finding the present worth of a sum of money, payable at a future time, without in- terest. Bought a farm for $5928.24 cash, and sold it for $7880.40, payable in 18 months ; what was thv. cash gain, money being worth 8 per cent. ? c ^ - 1 f^^ 8. Paid 807(> duty on a watch, and sold it at a loss of 5%; but had it been sold for $21.06 more, there would have been a gain of 8^% ; find the cost price. <;' / % 4. Distinguish specific and ad valorem duties. A quantity of raisins invoiced at $877, cost $990.26 in store, after paying duty and $16.12 for freight ; find rate of duty. // " /?y J 6. On what principle is the common rule for e^ua- 226 BXAMINATIOM PAPEB^. tion of payments based ? Bought goods as follows i 1st April, $560 on 8 months ; $600 on 4 months ; $400 on 5 months ; and $1120 on 6 months ; find equated time of payment. Ct^c^^/'^i ^^ 6i Define a logarithm ; state the properties by whi^h they facilitate arithmetical calculations. The log. of 2 is -8010800, and log. of 8 is -47711118; find the log. of i^(v/j X vt-*y# 7. A merchant in N. S. wished to pay $10,000 greenbacks to another in Boston, where gold was 184 « ;(C^,)and N. S. cy. 181 ; how much did he gain or lose, if, ^'instead of remitting N. S. cy., he remitted American gold, purchased in N. S. at a premium of 8 per cent. ? 8. On what condition do the respective shares of profit and loss in partnership depend ? A, B, and invest in business , B puts in his capital for 4 months, ^1 and claims \ of the profits ; C's capital is in 8 months, and D invests $7000 for 6 months, and claims \ of the profits ; how much did B and put in ? Explain your work fully. i3(:b^ -^^ ^ ^^ o'^C % - 7 ,' '' 9. A triangle, altitude 40 yards, is bisected by a line drawn parallel to the base ; find the perpendicular distance between the base and the dividing line. //^ , 10. Find the area of an ellipse, whose axes are 26 chains and 22 chains 40 links. 11. The transverse and conjugate axes of a prolate spheroid are 10 feet and 7 feet ; find the volume. 12. Into a conical glass (full of water), whose height is 7 inches, and diameter across the top 6 inches, a sphere of iron is gently let fall, of such a size that the plane of the glass's edge is tangent to it ; how much water will remain in the glass ? FmST'OLABS AMD UNIYBBSITT HONOBS. 227 )llows t ; $400 equated )g. of 2 tihe log. $10,000 ^as 184 lose, if, jnerican ir cent. ? ihares of 3, and niontbs, months, 4 of the lain your •,ted by a endicnlar \s ore 26 prolate le. Ise height (inches, a that the low mudi X- n. August, 1871. 1. Find G. 0. M. of 8, 4|, 4 J, ,'^, giving reasons foi the work. V6" -.)r 2. Prove that a vulgar fraction will produce a finite decimal, or a pure circ. decimal, or a mixed circ. deci- mal, according as its denominator has only the factors of 10, none of such factors, other factors also ; and that" the number of finite figures will be equal to the greatest number of equal factors, 2 or 5, in the denominator. y 8. State the different cases in percentage. To each of a class of 6 pupils 800 questions were proposed ; the 1st answered 275, the 2nd 260, the 8rd 240, the 4th 200, the 6th 210, the 6th 180; what was the standing of the class ? / i' "^ ^ ^ y~ 4. In building a house, I paid 2^ times as much for material as for labor ; had the latter cost 8% more, and the former 10% more, the whole cost would have been $2872.60 ; find the actual cost. J f ^ o ^ " > 6. A merchant consigns a quantity of flour to an agent in Montreal, who charges 2^% commission for seUing, and 8^% for buying, with instructions to invest the proceeds (after deducting his commission for both transactions), in certain goods ; the agent sells the the flour at $6.26 a bbl., and invests as directed, his entire commission being $482 : how many bbls. flour were consigned ? //■ ,^ ^>^ 6. Define the terms Company, Corporation, Charter, Firm, Joint Stock, Scrip. I had $8000 Bank of Toronto stock ; when at a premium of 96% a new issue of stock was ordered, giving to each stockholder at a 22d EXAMINATION PAPEB8. premium of 6%, half as many shares as he already possessed ; the market value of the stook then declined l^irsYo' How much did.j gain or lose by not soiling out before the new issue Z^ / 7 ^ "^S -^ 7. Define the terms Insurance, Uncferwritei;, Policy, ■•' Premium. For what sum must I insure property at 1|% to cover a loss of $3965 ? ^^ " £,//]/]'() 8. The duty on certain imported goods at 86% was / «$198, an allowance of 16% having been made at the Custom House for damage sustained by the goods after shipment. What was the invoice (cost) of goods ? ^(-/y / 9. " The course of exchange on England is usually given with reference to the old par of exchange." Ex- plain this statement ; shew that when sterling money is quoted at 9|% premium, it is really at par according to present standard. A Bill of Exchange on DubUn for je720, cost $3472 ; find the course of exchange. . r 10. What relative quantities of sugar at 7 cents, 8 cents, 11 cents, and 14 cents, must be sold to reaUze an average price of 10 cents ? Give reasons for your solu- tion. A, ^^/i3 ; i)/,^,f ; i^;/? ,ife j; s/ 11, The three sides of a triangle are 80, 40, 48 ; find the segments into which the base is divided by a per- pendicular upon it from the vertical angle, ^-i ^ ^'"l^ y 12. If it cost $76 to inclose a circular pond contain- mg 8 A. 2 E. 6 P., how mucl;L will it cost to inclose one of 85 A. 1 E. and 20 P. ? , tkl t / J m. Deoember, 1871. 1. Six men start together to travel in the same di- rection round an island, 60 miles in drcumference ; PIBST-OLASS AND UNIVEB8ITY HONOSa. 22£ '»-t^ their respective rates per day are 5, 6^, 7 J, 8|, 9 J, and 10^ miles. In how many days will they all be togethei again ? ?%(j '> ^ 2. A Note of $2,000, drawn at 60 days, payable a1 the Bank of Toronto, is discounted by a broker, at 2 /^ a month ; what rate of interest does he make on Iuf money ? Explain the analysis. ^ s' yo 8. Show how to find the amount of a sum of mone^ fat compound interest, for a given time and rate. ffM f) 4. City of Toronto 6 7^ debentures having six yeare to run, are offered for sale ; what price shall I pay in order to reaUze 10 'f> on my investment. 6. Define a logarithm ; what is the log. of 2187 to base 8 ? Given log. 2= -801080, and log. 7 =846098, find log. of -0086. 7 ; " ^^ ''^t^Oht 6. A man bought a farm for $5,000, and agreed to pay principal and interest in four equal annual pay-r*7^/*'/^'^S ments ; find the annual payment, interest being at 6 i^. y 7. A, B, and C, form a partnership with a joint stock of $12,600; A's stock continues in trade six months, B's eight months, and C's twelve months. A's gain is $1,800, B's $1,600, and C's $1,800 ; what stock did each put in ? ^^/^l" 3/ ' //'/ ^:^ w'V .' :^(/A),^'^ 8. At what advance on cost must a merchant mark his goods so that after allowing 6 % of his sales for bad debts, 7 % of the cost for expenses, and an average credit of 6 months (money being worth 6 %), he may ^ j^ make a dear gain of 16 % on the first cost of the goods ? ""' X*7 9. Find the present worth of $520. 12|, due nine months hence, supposing 4 per cent, stock to be at 92. 10. A society collected among themselves a fund of ig418 8«. 9 of the estimated value of a ship and cargo, and 4^%, and immediately re-insured 50% of the risk in another company at 8^%. During the voyage the ship was wrecked, and the second company lost $900 more than the original insurer ; what did the owners lose ? 8. The expense of constructing a railway is $10,000,000, of which 40^0 is borrowed on mortgage at 6%, and the remainder is held in shares ; what must be the average weekly receipts so as to pay the sharehold- ers 6%, the working expenses being 65% of the gross receipts ? 9. Three persons. A, B and C, form a partnership, contributing to the common capital $8500, $2200, and $2600 respectively ; at settlement, A's gain is $1120, B's $880, and O's $1200 : giyan that B's stock was in the business two months longer than A's, find the time the money of each continued in trade. 10. If gold can be beaten out so thin that a grain will form a leaf of 66 square inches, ho .v many square inches of such gold-leaf will be required to make a cubic inch, the weight of a cubic foot oi gold being supposed to be 1200 lbs. Avoirdupois ? 11. The sides of a triangle, ABC, are 26, 80 and 85 feet respectively ; on these sides external squares are described, A C D E, A B K H, B G F : find the ag- gregate area of the squares described on the lines G H, KD.EF. 286 EXAMINAnON PAPEBS. 12. The sides of n rectangle have to each other the ratio of 1 : ,/S ; and a perpendicular is let fall from one of the angles upon the diagonal : find in what ratio the diagonal is divided. vn. December, 1873. 1. A person asked for a lot of land 40 per cent, more than it cost him, but finally reduced his price 16 per cent., gaining on the whole $1000 ; for how much did he sell the land ? 2. A Washington despatch to the Gbbe, September 14, says: "Explanation is made to the Treasury De- partment that the Coinage Act of 1873, by which the value of the pound sterUng was altered from $4.84 to $4.8665, will increase the protective duties upon the imports from Great Britain to the United States by a little more than one-half of one per cent." Explain this statement, and find exactly the increase per cent, referred to. 8. The difference between the true and the bank discount of a note of $6300, payable in 9 mouths, is $18. Find the rate per cent. 4. A speculator gained 26 per cent, on three-fourths of his investment, and lost 10 per cent, on the remain- der, and his net profits were $1000 ; what would have been the result had he lost 10 per cent, on three-fourths of his investment, and gained 26 per cent, on the re- mainder ? 6. A banker in Toronto remits $10,000 to Liver- pool as follows : First to Paris, at 6 francs 40 centimes per $1 ; thence to Hamburg, at 186 francs per 100 JIBST-CLASS AMD UNIVEBSITT H0N0B8. 237 I other the II from one at ratio the per cent, lis price 15 : how much September :easury De- r which the m $4.84 to ps upon the States by a Explain le per cent. id the bank months, is iree-fourths )he remain- would have iree-fourths on the re- to Liver- 10 centimes cs per 100 marcs ; .thence to Amsterdam, at 17^ stivers per marc; tlience to Liverpool, at 220 stivers per pound sterling ; how much sterling money will he have in bank at Liverpool, and what will be his gain over direct ex- change at 10 per cent premium ? 6. A merchant buys on January 1st a quantity of coffee at 25 cents a pound, and another quantity at 20 cents, and chicory at 8 cents a pound. On April 1st he mixes them together in the proportion of two parts of the better coffee to three parts of the poorer and five parts of chicory, and immediately sells half the mixture at 18 cents a pound. On 1st July he finds half the re- maining stock damaged in consequence of a leak in his warehouse, and sells out the damaged part (12,700 lbs.) at 7 cents, and at the end of the year he sells the re- mainuer, money being worth 7 per cent, during the year, and rent of warehouse being $200, payable at the end of the year ; what must he get per pound for the portion last sold in order to make 6 per cent, on the whole cost at the end of the year ? 7. Three men form a partnership : A's money was in 8 months, and he received $500 of the profits ; B's was in 9 months, and he received $860 of the profits ; and G's was in 10 months, and he received $800 of the profits ; find the capital each put in. 8. A mortgage, dated Ist January, 1872, payable in three equal annual payments of $200 each, witii in* terest, payable half-yearly at 6 per cent., is sold on the 1st July, 1872; what sum must the purchaser pay so that the investment may be worth 8 per cent. ? 9. Two circles of given radii touch externally, and ft common tangent is drawn intersecting the line join- ing their centres in P. II the tangent touch the circles 288 EXAIOMATIOM PAPBBS. in Q, B, respectively, iind the area of the rectangle contained by PQ, PR. 10. Find— (1) The area of a quadrant whose radins is 4 rods. (2) The soHdity of a cone whose altitude is 6 feet and circumference of base 7 feet. (8) The surface of a sphere 5 feet in diameter. (4) The length of the side of a cubical vessel that shall contain three times as much as one whose side is 2 feet 6x6» 1 vm. JuNB, 1874. 1. Express 16 x |-L__r_ . &C.A in decimals accurately to five places. 2. A person annually increases his capital 20%, less a yearly expenditure of $500. At the end of four years his capital amounts to $18,052 ; find his original capi- tal 8. Having sold a quantity of flour on a commission of 8 %, and invested the proceeds in tea on a commis- sion of 2 % on the price paid for the tea, I find my whole commission is $260. Find (1) the amount received for the flour ; (2) the sum invested in tea. 4. The present worth of a debt due at a future ..ime, as found by the common method (bank discount), will not amount to the debt if invested for the given time and rate. Show that the error varies exactly as the square of the time. hbst-olass and univebsity honobs. 289' rectangle 4 rods, is 6 feet ter. tssel that }e side is 1 7x6'"*" BS. 20%, less our years iual oapi- imiHsion commis- ly whole iiyed for re iiime, ^nt), wiU Ten time as the 6. If the increase in the number of male and female criminals be 1*8 per cent., while the decrease in the number of males alone is 4*6 per cent., and the increase in the number of females is 9*8 per cent. Compare the number of male and female criminals respectively. 6. An insolvent compounds with his creditors for 65 cents in the doUar, and has $2,000 left. If he had made an assignment and surrendered all his assets to his creditors, they would have reahzed 69 cents in the doUar, after paying the expenses of the insolvency, amounting to 8 % of the whole estate. Find the assets and UabiUties of the insolvent. 7. A loan of $1,000 is to be repaid in 8 years, in half-yearly payments ; interest being 10 % per annum. Find the amount of each instalment. 8. A man invests $10,000 equally in shares of two banks. The shares of the one are at 8 % discount, and of the other at 5 )(> premium ; the price of stock in the former suddenly rises 7 ^, and that in the latter falls 6 % lower than when the purchase was made ; if the man now sells out what will he gain or lose ? 9. Examine the following solution of question 8, giving a proof of its vaUdity or fallacy : 250-i-*05 = 5000 : 5000-4-2 per cent, of it=5100-amt. received for the flour ; 6000-8 per cent, of it » 4860 =amt. paid for the tea. 10. In a certain lake the tip of a lotus bud was seen 9 inches above the surface of the water ; forced by the •■ wind it gradually advanced, and was submerged at the •■ distance of 86 inches. Compute the depth of the water. 11. (a) A field (rectangular) contains 27a. 8r. 8p., and ratio of its length and breadth is 21 : 18. How- many rods of fence will be required to enclose it ? 240 EXAMINATION PAPEBS. (h) A stone 20 in. long, 15 in. broad, and 8 in. thick, weighs 217 lbs. ; find the dimensions of a similar stone weighing 1,125 lbs, IX. July, 1874. 1. A merchant sold f of a lot of tea, at a loss of 12^ per cent., ^ the remainder, at a loss of 15 per cent., but realized a profit of 40 per cent, on what he had left : if he had received $25 more on this last sale, he would have gained 8^ per cent, on the whole. Find the prime loyed to hoe a field of com for $60.60; A could hoe 4^ rows per hour, B 8f rows per hour, and C 2^ rows per hour; it so happened that when all first came to tlie end of a row at the same instant, the work was completed. How long were they at work, and how much in equity ought each to receive ? 9. A consignor sends 1000 bbls. of flour to a com- mission merchant, with instructions to sell it and remit the net proceeds by draft. The consignee pays freight and expenses, $240.80; sells the flour at $8.60 per barrel ; charges 2^ % commission, and pays -f % pre- mium for draft ; how much does the consignor receive ? 10. A's money is 76 % of B's ; if A's money together with 80 % of B's be put on interest for 4 years at 10 % per annum compound interest, the amount will be $14641. How much has each ? 11. (a) A field in the form of a trapezoid has an area of 8 roods ; the perpendicular distance between the parallel sides is 8 rods, and one of these sides is 18 rods ; find the other parallel side. fb) If a spherical shell when formed into a solid sphere be equal in volume to its own cavity ; what must be the thickness of the shell ? 240 SXAUIMATION PAPPUS. xn. July, 1876. 1. On May the 1st, 1876, a banker discounts a note of $600 at 8 per cent., and by so doing receives 8| per cent, on his money. Find when the note was payable. 2. In an election of a member of Parliament 10 per cent, of the constituency refused to vote ; of two candi- dates, one received 47 per cent, of the votes of the whole constituency, and was elected by a majority of 80 ; find the number of votes cast for each. 8. A and B are employed upon a job for which they are to receive $4. A begins work in the morning half an hour before B ; and at noon the amount of work he has accomplished is greater than that of B by ^ of the whole work to be done. They rest at noon for an hour. On resuming theii* labor, B works with diminished energy, while A goes on with the same efOioiency as be- fore. A stops working at 6 p.m.; and B, continuing to work alone, finishes the work at 7 p.m. If paid in pro- portion to the quantity of work each has done, find the ratio of the amounts they receive. 4. Bought in London 2000 yards of broadcloth at 16«. 9d. sterling a yard, and paid for it by bill of ex- change. After pa3ring 60 per cent, ad valorem duty, at what price per yard ui currency must it be sold in New York to make 26 per cent, currency on the purchase, exchange on London being 9| per cent., and gold at a premium of 36 per cent. 6. A person invests $200 at the end of each year, and at the end of tlie third year finds he is worth $800 ; find the rate per cent, compound interest. \ FIB8T-CXiA8B AND UNIVEB8ITY HONOBB. 247 fear, ioO; 6. A person sells $12,000 Canadian bank stock which pays half-yearly dividends at 4 per cent., at 112, and invests in Ameiican railway stock at 98f currency. Gold being quoted at 112}, (and Canadian currency considered equal to gold) what yearly dividend should the latter stock pay in order that the person's income may be unchanged ? 7. A Canadian retail dealer buys from a Toronto wholesale merchant at an advance of 85 per cent, on the latter' s sterling cost, the English currency, after such advance, being converted into Canadian at 20 cents to the shilling. The retail dealer pays $4.44 for a certain article : determine the whole merchant's gain per cent., allowing 75 cents for insurauce, freight and customs, and taking exchange at 109^, brokerage | per cent. 8. A and 6 invest a oertain sum of money in a busi- nezB, A invests 66} of what B invests. At the end of seven months A withdraws 26 per cent, of his capi- tal, and at the end of nine months B withdraws 25 per cont. of his. The profits at the end of the year are $668 : how should this sum be divided ? 9. A railway train 44 yards long passes a man (A) travelling (in the same direction) at the rate of 6 miles an hour in 8 seconds. Half an hour after (A) it meets another traveller (B) and passes him in 2^^^ seconds. Determine the distance from the point where the train leaves A at which A and B will meet. 10. Fencing is worth 20 cents a yard, and the greatest amount of laud that can be enclosed in rect- angular form for e« certain sum of money ia 62 ac. 178, 166 yds. Find the cost of the fenoiue:. 24B EXAMINATION PAPBB8. xin. July, 1876. 1. Prove the rules for pointing in Multiplication and Division of Decimals. Beduce to its simplest form, (•076)«-t-(-05)'' (•076)* -(•076)3 (•025)» + (-06)* 2. The owner of some city property allows his agent 6% for collecting his rents ; the amount which he annually pays for insurance and repairs (and on which he pays no income tax) is 8^% of his net income ; his income tax at 2 cents 7^ mills on the dollar, is $198.25. Find the gross rents from his city property. 8. Beckoning commercial discount at 8 %, how many years would a hill have to run so that the holder would he willing to pay something to take it off his hands ? Shew that the error in computing commercial discount, instead of true discount, varies nearly as the square of the time, when the time is small, and where the dis- count is small compared with the deht. The interest on a sum of money for 2 years is $7141^, and the discount for the same is $68^ ; find the rate % and the sum of money. 4. A Building Society wishes to realize 10 % on its loans ; the instalments paid to it can be reinvested at 8j% per half year ; extending the foimula A=PB° to include the case of n being fractional, shew that the quarterly instalment on a loan of $1000, payable in 6 years, is 1.000(1.1)« x ^^JJ® i~~. rntST-oLASs and ttntversitt honors. 249 5. A retail dealer bought a quantity of broadcloth, and marked it for sale at an advance of 20 % on cost ; in measnring it off to the customers he used a false measure, by which he gained on the entire sale an ad- ditional sum of $89, making on the whole a profit of $879.20. Find the cost price of the cloth and the length of his yard stick. 6. By the construction of the Canada Pacific Bail- way, 80 i» is added to the debt of the Dominion ; for the next fourteen years after the completion of the road $6,000,000 of the principal, in addition to the in- terest, is annually paid off, and at the end of that time the rate of interest on the national debt is reduced 10 % ; if, in spite of these reductions, it be found that the in- terest on the public debt is still 20 % more than before the increased debt, find the cost of the Pacific Eailway. 7. Examine the merits of the following definition : " Four quantities are said to be proportional when a part of the first is contained in the second as often as a like part of the third is contained in the fo'irth." Give examples of its failure. Where do you consider that the notion of ratio is first introduced in works on arithmetic ? Given that the distance through which a body draws another in one second varies as the force of attraction ; that the force of attraction is directly proportional to the mass of the first body, and inversely to the square of the distance from the centre ; that the mass is pro- portional to the product of the density and volume ; and that when the earth's voinme and density are each unity, those of Jupiter are 1887.481 and .22 respect- ively. Find how far a body will fall from rest in one 260 BXAIONATION PAP£B8. second at the surface of Jupiter, if at the surface of the earth it fall through 16.08 feet in the same time. 8. A person has an estate which yields a net income of £1620, after paying expenses to the extent of 10^. He sells it and invests the proceeds in the 4^ per cents at 96v the income now being subject to charges at 5 %, and his net income is £16 lis. 6d, less than before. Find for how many years' purchase on the gross income he sold his property. 9. EngUsh standard gold is -f^ alloy, and 44} guin- eas weigh one pound troy ; the weight of a shilling is 87^ grains troy, and pure silver is 14 |g|g heavier than an equal value of pure gold. If silver were to fall one per cent, in value, find what change would have to be made in the alloy in a shilling in order that 20 shillings might still be equal to £1, the alloy being supposed of the same specific gravity as silver, and the weight of the shilling unchanged. 10. (a) The three sides of a triangle are 20, 80, and 25 respectively. Find the position of the point which is equally distant from the three angles. (b) Two sides of a triangle are 8 and 12)- respective- ly, and the line bisecting the angle they contain is 6* Find the third side. XIV. 1. At what per cent, in advance of cost must a mer- chant mark his goods s t that after allowing 8% of his sales for bad debts, an average credit of 6 months and 6 per cent, of the cost of the goods for expenses, he may make a dear gain of 15% on the first cost, mouoy being worth 8% ? FIB8T-0LA8S AND UNIYBBSITT HONOBB. 251 2. A merchant barters 60 yards of silk, which cost him $1.50 a yard, but which he sells at $2.50, .giving 9 months' credit, for cloth which another merchant sell? for $2, giving 6 months' credit. How much cloth ought the first merchant to receive f 8. Three merchants enter into partnership; the first (A) puts in $400 for 6 months ; the second (B) $550, for a time not known ; the third (C) an unknown sum for 12 months. At aettling, A received for his stock and profit $424, B $605 for his, and G $120 for his. Find B's time and G's stock. 4. The Toronto Trust and Loan Company advance $2400 upon a mortgage on a farm on the following con- ditions : The principal to be repaid in 20 years by equal annual instalments, anil interest at the rate of 6% to be charged on the part unpaid. If the sum due in any particular year be $177.60, how many previous annual payments have been made ? 5. At a certain time between 2 and 8 o'clock, the minute hand was between 8 and 4. Within an hour after, the hour hand and minute hand had exactly changed places with each other. What was the precise time when the hands were in the first position ? 6. If $10 be allowed as 6 months' discount oiT $60, and at the same rate of interest $3 be allowed off a bill of $88, for how long a period had the latter to run ? 7. A merchant in London remits to Amsterdam £1000, at the rate of 18d. per guilder, directing his cor- respondent at Amsterdam to remit the same to Paris, at 2 francs 10 centimes per guilder, less ^ per cent, lor his commission ; but the exchange between Amsterdam and Paris happened to be, at the time the order was re- ceived, at 2 &auo8 20 centimes per guilder. The mer« 252 EXAMINATION PAPEB8. chant at London, not apprised of this, drew npon Paris at 25 francs per pound sterling. Did he gain or lose, and how much per cent. ? 8. A gentleman has an estate that brings him in $8000 a year, but this gross income is liable tor rates and repairs to the extent of 12 per cent. He sells it at 24 years' purchase on the gross income, and invests the proceeds of the sale in 8 per cents at 07^. What dif- ference is caused in his income ? 9. I have a board whose surface contains 49| square feet ; the board is 1^ inches thick, and I wish to make a cubical box of it. Required the length of its side. 10. A man standing 40 feet from a building, which is 24 feet wide, observed that when he closed one eye, the width of the building just hid from view 90 rods of fence, inclined at an angle of 45^ to the side of the building ; what must be the distance between the eye of the observer and the remoter point of the fence ? XV. 1. Find an approximation which shall differ from \/866 by less than ^^yVir* Find the numerical value of (2+y8)MJ2-,/8)^ ?6 2. A borrows a onm of money from B at 8^%, B borrows the money from G at 8^% for 7 months in or- der to lend it to A ; A repays B the sum with interest before the 7 months have expired ; and when B repays C, he finds he has neither gained nor lost anything. Foi how long did A require the money ? FIBST-OLASB AND UNIVBBSITY BONOBS. 258 8. Prove that if from any number be subtracted the sum of its digits, the remainder will be divisible by 9 ; and hence show that a number will be divisible by 8 or by 9 if the sum of its digits is so divisible. 4. A builder signs a contract estimating } of the whole cost for materials, and ^ for labour. When } of the time has elapsed, 80% of the material rises 10% ; and on the expiration of half the time, 60% of the labor obtains a rise from 16 cents to 18 cents per hour. Sup- posing a profit of 6% to have been charged originally, what is the ultimate gain or loss per cent. ? 5. Desiring to remit ^^1480 to Portugal, will it be better for my Portuguese correspondent to have a direct remittance from London to Lisbon at 6Qd. per milree, or to have the money transmitted through Amsterdam and Paris, the exchange between London and Amster- dam being at 378. 3d. Flemish per £ Sterling ; and be- tween Amsterdam and Paris at 66 pence Flemish for 8 francs, while between Paiis and Lisbon the exchange is 460 rees for 8 francs, and expense of 1^% being incurred in the circuitous course ? How many milrees will be saved by taking the more profitable course? (1000 rees=l milree.) 6. A boatman rows 6 miles with the tido in the time he would take to row 8 miles against it; but if the hourly velocity of the current were ^ a mile more, ho would move twice as rapidly with the tide as against it. Find his power of rowing in still water. 7. A man owes a debt to be paid in four equal in- stalments at the end of 4, 9, 12, and 20 months re- spectively; and he finds that true discount being al- lowed at 6% per annum, $8000 paid at present will discharge the whole debt. How much did ha owe ? 254 EXAMINATION PAPEB8. 8. A tradosman buys a quantity of sweets at 60 cents per pound Avoirdupois, and retails it at 5 cents per oz. Troy. Another buys at 60 cents per lb. Troy, and retails it at 6 cents per oz. Avoirdupois. Find the ratio of their profits per cent. 9. A dock that gains 24 seconds per hour is set to right time at a quarter to 5 p.m. What will be the right time between 8 and 9 o'clock the same evening, when the hour and minute hands point in exactly op- posite directions ? 10. The perimeter of a right an£^led tiiangle is 25. and the radius of the inscribed circle is 2 ; determine the sides of the triangle. XVI. 1. Taking the ordinary definitions for the numerator and denominator of a fraction, what is the meaning of } X f and I -^ |. 2. A, B, and start from the same point to move round a course of 6 miles, at rates of 8^, 4^, and 5^ miles per hour, respectively, O's direction being opposite to that of A and B. Find when first they will be to- gether it a point 8 miles from the starting place. Show that ^jhey will never be together at a point 1^ miles from the starting place. 8. (1.) What is the least number which being a cube is also divisible by 4, 5, 9, and 12. (2.) On a railway are two parallel tracks ; on one of these trains pass a certain point every 49i minutes ; on the other, the same point every 52| minutes : a train on the former track has just passed this point, and in 27| minutes one on the latter will do so. Will trains FIB8T-CLASB AND UNIYBBBITT H0N0B8. 265 on these tracks ever pass this point at the same instant? If so in what time from the passage just mentioned ? 4. A person has a certain amount of bank stock which he sells at 110| and invests the proceeds in 6 per cents at 79|. When this has risen 5^ per cent., he purchases the same amount of the original stock as he held at first at 109^, — which now pays 8 per cent. — and finds that, while $110 remain in cash, his income has fallen $8. Find the percentage originally paid by the bank stock, aUowing | per cent, brokerage on each transaction. 5. Shew that the difference between two numbers having the same digits is divisible by 9 whatever be the order of the digits in the second number. 6. A and B are moving round a circle 10 miles in circumference at rates of 8^ and 5^ miles per hour, respectively. A passes a certain point one hour ahead of B. Find the point which first A shall pass 1^ hours ahead of B, and determine in what time this wiU take place. 7. Shew how to find the present worth of an annuity reckoning compound interest. 8. A, B, and C join in a business to which they are to contribute in the proportion 1 J, H, 1^4^ respectively. A pays down $1102*60, B $1026, and G $1068*76 ; what must each pay to the others or receive from them to make the proportion of capital according to agree- ment? 9. Suppose that a tank receives a uniform and con- tinual supply of water, and that when it contains a certain quantity, 12 equal taps being set open would empty it in 7^ minutes, or 7 of the same taps would 256 HXAMINATION PAPKB8. empty it in 16 minutes ; how many of the taps would empty it in 50 minutes ? 10. The radius of a oirole being 10 feet, find the side of a square inscribed in a oircular segment which is contained by a chord and one-third part of the whole circumference. xvn. D. MoKat, Esq., Newbubo, P. S. 1. A Toronto wine merchant buys three kinds of wine and mixes them together in this proportion : 1 cask of the first, the price of which is $80 a cask ; 8 casks of the second, the price of which is $90 a cask ; and 2 of the third kind. He keeps this mixture for 12 months, and then it sells for $104.50 a cask, clearing 10%, after allowing ^% for interest of capital. What was the original price of the third kind of wine ? 2. If $10 be allowed as discount off $250, due a cer- tain time hence, what would be the discount if it had twice as long to run ? Suppose compound interest what then would be the answer to the above question ? 8. A tradesman marks his goods with two prices, one for ready money and the other for 12 months* credit, allowing, as he says, discount. Now if the credit price of a yard of silk be $1.80, and the cash price $1.20, and if the credit price be marked 28|^% above what he gave for it; how many yards must he sell at cash price to gain $60. 4. The present value of a freehold estate of $100 per annum, subject to the payment of a certain sum at fIBST-OLABB AKD UNIVBBSITT HONOBS. 267 the 120, he [00 At the end of every two years, is $1000, allowing 6% com- pound interest. Find the sum. 6. Suppose a olook to have an hour hand, a minute hand and a second hand, all turning on the same centre. At 12 o'clock all the hands are together. How long will it he hefore the hour hand will he equally distant hetween the other two ? 6. A carpenter has a plank 1 foot wide, 22f^ feet long, and 2^ inches thick ; and he wishes to make a hox whose width shall he twice its height, and whose length shall be twice its width. Required the dimen- sions of the hox. 7. A and B engage to reap a field for 4/. 10a.; and as A could reap it in 9 days they promise to complete it in 6 days. They found, however, that they were obliged to call in 0, an inferior workman, to assist them for the last two days, in consequence of which B received Ss. 9d. less than he otherwise would have done. In what time could B and reap the field ? 8. A, B and bought a grindstone for which they paid $10.60. B paid 20% more than A, and 10% less than C. The diameter of the stone was 65 inches, and the diameter of the place for the shaft 8 inches. What sum did each pay, and how much must each grind ofiF from the semi-diameter to obtain his proper share of the stone ? 9. There is a conical glass 6 inches high, 5 inches wide at the top, and ^ of which is filled witl'i water. What must be the diameter of a ball let fall into the water that shall be immersed by it ? m BXiOnNATION PAPBB8. xvm. W. B. Harvby, Esq. — Oollinowood High School. 1. There are htro bars of metal ; the first contains 16 oz. of silver and 8 oz. of tin, the second contains 27 oz. of silver and 6 oz. of tin, how many oz. must be taken from each bar to form a bar that shall contain 19 oz. of silver and 6 oz. of tin ? 2. There are two armies — | of the first are killed in battle and } of second ; then \ of the remainder of first army desert to the second and \ of remainder of second desert to the first ; each army now contains 24,000 men; how many in each army at first ? 8. A and £ engage in trade, B's capital is f of A's. A loses $200 and B gains so that his capital is now f of A's. Should A now give to B j^ of his present capi- tal, and B give to A ^ of his, they would each have equal sums ; find original capital of each. 4. A farmer mixes com and wheat in the ratio of 8 to 9 ; had he taken 12 bushels more corn and 9 bushels more wheat the ratio would have been as 12 to 18 ; how many bushels of each did he take ? 5. A owes B $1000 ; but is able to raise only $600, with this sum he proposes to pay part of the debt and the interest in advance on the remainder on his note for 2 years at 10 %. For what sum ought the note to be drawn ? 6. A merchant sends to his agent, pork, wheat, and cash, to the value of $18800, with instructions to sell the pork and wheat and invest the whole proceeds and the cash in buying goods. The agent charges 6 % for selling pork, 4 % for selling wheat, and 4 % for buying FIR8T-OLAB8 AND UNIYKBglTT HONOBS. 269 ;600, and note Ite to and seU and for goods, his whole oommission amounted to £1100; find amount of cash and value of pork and wheat Heut hy the merchant. 7. How long will it take $4000 to amount to $6000 at 6 % compound interest ? 8. A merchant deducts from his prices at 6 months 6 -fo for cash and 4 % for 8 mouths' credit. At his 6 months' prices he makes a profit of 80 -fo. Find the cash price of an article that he sells, on three months' credit, at an advance of 95-^^ cents on cost. 0. U' 8 acres of grass, with the growth thereon, keep 18 oxen 9 weeks, and 4 acres keep 20 oxen 6 weeks, for how many weeks can 86 oxen graze on 6 acres ? 10. A field is 80 rods long, 40 rods hroad at one end 60 rods at the other. How far from the smaller end should the field he divided crosswise ao that the parts may he equal in area, and what will he the hreadth where out ? XIX. D. A. Maxwell, Esq., Stbathbot High School. A and B engaged to work foi a certain numher oi days. A was ahsent 2 days, and received $81 ; B was ahsent 12 days, and received $86. If the days of ab- sence had been reversed, they would have received equal amounts. For how many days were they engaged and at what rate ? 2. Two lots are assessed for a drain in the sums of $76 and $79, the principal to be paid in five equal an- nual instalments, with interest at 6 % per annum on the unpaid principal. Debentures were issued June Ist, ■ 260 BXAMXMATIOlf FAPBBS. I payable Jan. 6th. Three year's rates have been levied, when it is found that tlic clerk has inadvertently charged the lots at |79 and 176. What payments must eaoh lot make during the next two years so that the mistake may be rectified. (Ontario Twch&r,) 8. If a sum of money is borrowed for n yean at a given rate r on one dollar per annum, the interest being paid q times per year. Show that the compound inter- est : simple interest :: 2q-i-(qn — 1) r : 2q, nearly. 4. What is the value of the U. S. gold eagle (282 grains fine gold) at the French mint, a kilogramme of standard gold ( |^ fine) beicg worth 8100 francs, and a mintage of 6f. 70c. being charged ? 6. Id eaoh of two chests there are two kinds of tea, tixe proportions of good tea to the poor kind in the first chest being as 8 to 7. If equal quantities be taken from each chest and mixed, the good tea in the mixture is 81^ % of the poor kind ; but if four times as much be taken from the first as from \h.Q second, the difference between the quantities of good and poor tea is 140 % of the quantity taken from the second. Find the propor- tions in which the teas are mixed m the second chest. 6. I borrow $1,000 on condition that I rjpay $10 at the end of every month for 10 years. Find an equa- tion which will determine the rate of interest I pay. 7. Prove that a number will be divisible by 11 if the sum of the digits in the even places differs from that in the odd places by a multiple of 11. 8. A giocer wishes to mix together teas at 60, 70, anv! 90o. per lb., with 40 lbs. at 66 j., 60 lbs. at 60c., 80 lbs. at 65o., and 100 lbs. at 90o., that he may hav« 1280 Ibo. which h*,^ can suU at $1.0U|^\ per lb., uaing a riBST-OLABB AND UNIYB&SITT BONOBB. 961 in kve ft Iff oz. weight for a pound, giving a credit of 4 mouUia when moaey is worth 12 ^ per annum, making a pre« sent gain of 20 %, allowing 10 % for bad debts, and add- ing $10.60 to the cost price of the tea to cover inciden- tals. How many pounds at each of the given prices may he take ? 9. A certain piece of goods is marked with two prices, one for ready money, the other credit. If the credit price be $2.60, and the cash price 00 % of it ; and if the credit price is 80 % above cost ; how much is the cash price above cost ? 10. Four places. A, B, 0, D, are so situated that the distance AD is ffO miles, and from D to the middle of AO is equal to tlie half of AG. The angles BAD, BDC. are equal, and BDC is double of BDA. Find tlie dis- tances AB, BC, CD and BD. XX. Jims Bbucb, Esq. — WatxbiX)wn High School. 1. The simple interest on a sum of money for one year is $45 and the compound interest on tlie name sum at the same rate for the 6th year is $54 097781 26. Find the sum and the rate por cent. 8. What sum invested at 5 y« per annum, simple interest, would secure an annual income of $400 f'^r 8 years. 8. Required the present worth of a pension '>f $160 to continue 4 years, supposing money worth 4 % per annum compound intiirost. 4. What must the porpendicuki depth of a cisterr. in the form of an iuvortod cone having the angle at tb<' ♦inox' 00, to contain 400 callona of water f 262 EXA^HNATIOM PAPBBB. ''I hi i I \ 5. A merchant boufj^ht some goods for $620 with 8 months credit, and sold them forthwith on 8 months credit, gaining thereby 10 %. If he had sold the goods for $10 more, giving 6 months credit, what would have been the gain per cent, taking money worth 6 i» per annum ? 6. / grocer had three kinds of tea worth 60c., 70c., and $1 per lb. respectively. How much of the $1 tea must he mix with 20 lbs. of the 60g. and 70 lbs. of the 70c. tea, so that by selling the mixture at $1 a pound, he may clear 10 % on the cost after allowing a discount of 10 % to the purchaser ? 7. A merchant in Toronto remits to his agent in Manchester $2000 directing him to deduct his commis- sion at 2% on the purchase, and invest the remainder in cotton goods at 4d. sterling per yard. The goods ar- rive in 8 months after sending the money. When the goods arrive he pays $180 for freight, insurance, etc., and an ad valorem duty of 4 %. Three months after the goods arrived they were sold at 12 cents a yard, giving 6 months credit. Money being worth 8 )(., find tlie merchant's gain y» on investment. 8. The ratio of two sides of a triangle is 6:6, and the segments of the base made 4)y a perpendicular fall- ing from the vertical angle on the base are 10 and 14. Find the sides of the triangle. 9. The radius of the base of a cone is 4 feet and the surface of the cone is 118)^ square feet. Find its altitude. 10. A farm was bought for 20 years purchase for $800, four-fifths of the purchase money remahiing on mortgage at 4%. Tlie purchaser had to erect some nBBT-OLABB AND UNIVBB8ITT H0N0B8. fences which cost him $860. This sum he paid in three equal annual instalments (the first instalment on taking possession of the faim). The other annual expenses of the farm were $60. Assuming money worth 8^ per annum, what annual percentage did he make on his in- vestment ? XXI. Edgar Fbisbt, M.A., Naval Observatort, Wabhinoton. 1. Two men, A and B, agree to perform equal pieces of work. A begins one piece, and B the other, and after working 6 days they exchange places. A finishes his piece in 12 days from the time they exchange places, and then returns and helps B ; and after work- ing together 2 days they finish his piece. How long would each alone be in finishing either piece ? 2. What will be the true interest on $1000 for 6 months, it being supposed that if this interest is Invest- ed for the next 6 months that the whole interest for the year shall be exactly 6 per cent. ? 8. A railroad train travels for i of the distance at the rate of 80 miles per hour, the next jr of the listanoe at the rate of 85 milos per hoiu', and tlie remaining distance at the rate of 40 miles per houjr. What is the average rate in miles per hour ? L A person has a note for $100, payable at the end of two years, and another of |60, payable at the end oi three years ; he is willing to take $185 for them ; when should this money \e paid so as to allow 6 per cent, compound interest for the money, and what is the pre* sent value of the notes ? 264 XXAJflNATION PAPEBB. I 11 I " ( u • 6. What is the least number of weights, and what are they that will weigh any number of lbs. from 1 up to 9841 ; and how can 7961 lbs. be weighed with these weights ? 6. What is a $1000 6 per cent, bond worth, having 20 years to run, that pays interest 8 per cent, semi- annually, allowing the compound interest on all these semi-annual payments to accumulate until maturity, so that I may realize 5 per cent, per annum on my in- vestment, interest being compounded annually. , 7. I buy goods at 25 per cent, below their regular retail selling price ; I calculate all the expenses of the establishment, including freight, help, rent, and all in* ddental expenses, to amount to 25 per cent, on my out- lay, and still sell 5 per cent, below the regular retail price, and gain $100 clear profit. How much did ] pay for the goods, and how much per cent, did I deai on the whole expenditure f 8. A sold goods which cost $4000 to B at a certaio loss per cent., and B sold them to at the same gain* ing rate per cent, which was $25 lebD than A paid. How much did A lose and B gain per cent. ? 9. Gt)ld in New York is quoted at 105. How much shall I pay in Toronto for $100 United States Qovern* ment bond which is quoted in New York at 116, allow- ^ per cent, brokerage ? 10. I bought goods at 26 per cent, below their real value, wliich becoming damaged, I sold at 20 per cent. less than they cost me, which was $80 below their real value. What did the goods cost me f 11. How long must I borrow $120, at 8| per cent, pimple interest, so that if I pay it back in instalments PIRBT-OLASB AND UNI\'EB8ITY UONOBS. 265 of $2, monthly, I o&n pay it off, including interest, these payments a^30 being oaloulated at 8,^ per cent, simple interest, and the first payment made half a moutL after I borrowed the lk ncy f xxn. Jambs Brown, M. A. — U. 0. Collboe. 1. Show that the duodenary scale §|='788; and find the corresponding vulgar and decimal fractions. What terminating decimals will terminate when ex- pressed in the duodenary scale.? 2. Express 629| in the duodenary scale ; and em- ploy that scale to find what length of squared timber^ whose cross section is 4 ft. 7 iu. by 8 ft. 8 in., will con* tain 529) cubic feet. 8. What price per lb. avoird., in English money, is equivalent to 6.48 france per kilogramme, if 1 frpaic= 9}(i., and 1 gramme^s 15.482 grains 9 4. The pendulums of two clocks beat quarter sec- ondfl and are in unison every 5 minutes by the faster one, ^hinh gains 6 minutes a week ? What is the rate of the other ? 5. If a cubic foot of water weighs 1000 o«. avoird., and the imperial gallon contains 277*274 cubic inches, how much will 1 lb. of water measure in pints ? 6. Taking the weight of the sovereign to be 128 grains, and its value to be |4.86|, U. S. gold, and neglecting the value of the alloy, which in Englinh coin id in U. S. coin is -^ of the weight, an Wtii^ht oi the half eagle^ iflT' the 266 ■XAMINATION PAPBB8. I' i I II 7. A dealer, who cheats in weight to the extent of one ounce in the pound, gains 12% by selling an article A*i a certain price, how much would he gain if he gave fair weight ? 8. The gross annual rental of a property is $1800 : at what price should it be bought, so that, allowing $226 per annum for repairs and an insurance on f of its cost @ 1^%, the purchaser may receive interest @ 10% per annum on his investment ? 0. If a dozen oranges be worth 20 peaiis and weigh as much as 16, and a bushel of oranges weigh as much as 7 gallons of pears, compare the values of equal measures of the two fruits. 10. A and B, starting from opposite ends, walk over a course a mile long and retorn without stopping. They meet at 820 yards from B's end and, on theii' return, at 160 yards from A's starting point. If B stai-ted 11 minutes after A, how much later wiU he get home ? xxm. A. SwcLAiB, M. A. — Windsor High Sohool. 1. r ifine Discount^ Present Worthy Inieresit and prove L.Dat at Simple Interest the Diui;otmt is equal to tlie present worth of the Interest. 2. The intoreet on v sum of money for a given rate aad time is equal to | of the sum. shew that the dis- count on the same sum for ^e given rate and time is ^ of the sum. 8. Simple interest at 6 % being allowed ; the dis^^cunt on A's money for 4 years is equal to four times the interest on B's money for I year, and t)ie discount for FIBST-OLABB AND UNIVEB8ITT HOMOIIS. 267 4 years on A's money and B's money ie $220. Find A*s money and B's money. 4. A man by walking 10 hours a day walks from M to N in two days. In coming back he decreases his usual rate by ^ of itself for the first ten miles of his journey, and for the last ten miles he increases his usual rate of walking by ^ of itself, and arrives at M half an hour sooner than he would have done had he travelled at his usual rate. Find the distance between M and N. 5. A cask is partly filled with a mixture of wine and water, the water being 14^ % of the mixture, and the wine is 75 % of the number of gallons which the cask holds. Ten gallons of water are added to the mixture and it is found that the cask is |f full. Find the num- ber of gallons of wine and of water and the number of gallons which the cask holds. 6. A wholesale merchant buys cloth, paying 10 % duty, and sells it to a retail merchant, gaining 10 % on his money, and the retail merchant sells it gaining lO^^j % on his money. But the duty on cloth being abolished and the original price falling 10 %, how should the retail merchant sell cloth which he formerly sold at $1*84, both merchants making their usual profits. 7. A man has a certain sum of money. He spends 11000 and then gains $400, afterwards he spends | of what he has and then gains $800, and after spending ^ of the money then on hand he has $700 remaining. What had he at first. 8. A man has 400 shares in the Union Trust Com- pany and 800 in the Union Saving Company paying yearly dividends of 4 % and 8 % respectively. Wishing to increase his income he sells out 200 shares in the Union Trust Company and 100 sii^-os in tlie Union 1S68 KXAUINATIOlf FAPBBl. i i I I I Saving Company at 60 and 110 respeotively, and in- vests I of the money realized in stook, of which the $60 share paying a yearly dividend at the rate of 10 )k was at a premium of |16 and the rest in the Merchants Bank at 90 ; what should be the half-yearly dividend from the Bank Stock in order that he may inorea^° his income $400. 9. A man receives a certain sum of money of which he spends $6 a day. Ten days after receiving the money he made a bet of ^ of his money and lost, after which he spent $4 a day. Ten days after making his first bet he made a bet of ^ of the money on hand and gained, and after this spending $5 a day, his money l&dted him 44 days ; what sum had ho at first ? 10. A man buys three casks of wine A, B, C, each containing 64 gallons. His seUing price of the wine in A is 10 % above cost, of that in B 20 % above cost, and of that in 10 % below cost. From each cask 82 gal- lons are taken out ; that from A is poured half into B and half into ; that from B is poured half into and half into A, and that from is poured half into A and half in B. From tlie mixtures in the casks 24 gallons are taken out and the operation repeated. He sells the mixture in each cask and receives for that in A $18^-60, for that in B $188-20 and for that in C $102*40. Find the cost price per gallon of the diiff * • ent kinds of wine. xxrv. Wm. 0'C^»nnos, M a. — ^London High School. 1. Prove the rulS tor reducing a circulating de<'imftl \o an equivalent vulrnr frRction. fXBBT'OLASS AMD UNIYKRUTT B0M0B8. tm Find the vftlae of 19.5881240-5.172 3t eaoh wine in st, and 2 gal- [' into intoO to A ks 24 He r tliat at in diffr- ion 7.892+4.1+2.856 2. As A can run 11 yards while B ntns 10, the former gives the latter a fair start in a ooorse of one mile. After mnning at their usual rates for 2 minutes, B falls. A heing 180 feet behind. How many yarda per minute oan each run f 8. The compound interest on $567 for two years i& 1119.07. Find the rate per cent, per annum. 4. A merchant having bought grain at the rate of S bushels for $7, loses 455 bushels, and sells the remain- der at the rate of 8 bushels for $5. The expenses be- ing $847, and the merchant's net loss $122, find the number of bushels purchased. 5. A bookseller bought a number of books for $180. If he had bought ^ less for the same money, each book would have cost 50 cents more. He marks them at an advance on cost, but he sells them at 22| cents less for eaoh book, losing 5 per cent, on cost. Find the num- ber of books and the marked price. 6. A draper bought 240 yards of doth, five-eighths of which he sold at $25 below, and the remainder at 25 per cent, above cost, gaining $9.25 less than 5 per cent, on the whole transaction. Find the cost per yard. 7. I make 20 per cent, by selling 8 parts of greon: tea with 2 of black, the cost of 6 lbs. of the former be» ing equal to that of 7 lbs. of the latter. In what ratio must I mix them in order that I may gain 80 per cent, without raising the selling price ? 8. I invested my capital in mining company stock. at 150, and afterwards exchanged one-half the stock at- 270 BXAUINATION PAPBBI. par for railway stock, paying 6 per cent, annual divi- dends. The mining company became bankrupt, and I found that my income was $60 less than if I had in- vested my original capital at 8 per cent. Find the amount of my capital. 9. I lent a sum of money at 4 per cent., and an- other sum at 6 per cent., the total interest being $68. If I had lent the first sum at 5 per cent., and the second at 4 per cent., the total interest would have been $67. Find the sum lent at each rate. 10. One side of a rectangular field is half as long again as the other, and its area is equal to that of a circle, the circumference of which is 120v^6(8.1416) yards. Find the cost of fencing the field at 20 rents per foot. XXV. W. J. BoBERTSON, M. A. — St. Cathabines Colleoiai Imstitutb. 1. A trains leaves Toronto for Hamilton, at the rate of 80 miles an hour. During the ^ part of the journey the speed continues undiminished, after which it stops for 15 minutes, and then continues at f of its former speed. It is found that it takes 2 hours to accomphsh the journey. Find the distance between Toronto and Hamilton. 2. A and B engage in business. B manages the Insness and receives 10% of the profits for so doing. F, on entering puts in 60% more tlian A ; but 6 months after takes out f of what he puts in. At the end of the year A finds that his share of the profit amounts to $1000 ; giving the total rate of profit to be 80% of the I1B8T-0LA8B AND UmYEBBITY HONOBB. 271 is the loing. lonths )fthe ^ts to f the sum inyested. Find B'b share of the profit, and the sum invested hy each. 8. A merchant commences business with a certain capital. His rate of profit is 20% ; but his household expenses are 5% of the sum originally invested. At the end of 8 years he finds himself worth $16,000. How much did he invest ? 4. A vessel is insured at ^ of its value, and its cargo at its full value. The rate of insurance for the vessel is 8%, and for the cargo 4%. The value of the cargo is 50% that of the vessel. After paying one premium the vessel is lost, and the insurance company loses $16000. How much was the vessel and cargo, respectively, worth? 6. A buys flour to the amount of 600 bbls. He sells ( at 20% advance on cost for cash, and the remainder at 10% advance, giving a credit of 6 months. Given money to be worth 10%, and his cash gain to be $250 ; find the price of flour per barreL 6. A banker discounts a note due 6 months hence, charging 8% for accommodation, and finds that at the end of the 6 months, he has made a clear profit of $60. Neglecting days of grace, find the amount on the face of the note. 7. A has stock in the Merchant's Bank to the amount of $200. He finds that after receiving 8 years' dividends at the rate of 8% (payable half-yearly), and selling out at 90, that he has less money by $6 than what he invested. Money being worth 8%, find the price he paid for his stock. 8. An English capitalist sells out of the 8% at 90, and invests the proceeds in Canadian securities at 25% premium, giving a dividend of 8%. He finds that he IMAGE EVALUATION TEST TARGET (MT-3) 1.0 i.l 1= 1.8 1.25 1.4 1 A •< 6" ► Photographic Sciences Corporation 23 WEST MAIN STREET ^ WEBSTER, N.Y. 14580 (716) 872-4503 ^ iO* iV ^^ :\ \ ^ .w <* *\ ;\ '^ .^ . '^^ A 6^ ?> 272 EXAMINATION PAPEBS. has increased his annual income by $10,000. Supposing brokerage to be ^% on each transaction, find in Jg's sterling the amount of stock he held in the 8% — exchange on London being at a premium of 9f %. 9. A mortgage of $1000 bearing 6% interest is sold out after one payment of $200 has been made, and after one year's interest is due. The buyer wishes to secure 8% for his money, find how much he must give for the mortgage, the debt still due to be paid off in 4 equal annual instalments. 10. A farmer borrows $5000 from a Loan Company at the nominal rate of 8%. He repays the sum in 5 equal annual instalments of $1400 each. Given money to be worth 10%, find the actual rate the company charges. XXVI. Alexandeb Mubbay, ,M.A. — Galt Coll. Inst. 1. The L. C. M. of two numbers is 100798 ; the G. C. M. is 17 ; the difference of the numbers is 1224 ; find the numbers. 2. A man has $6000 stock in the 4 per cents, which he sells, and invests the proceeds in the 4^ per cents at 88. If the increase in his income be $48, what is the price of the 4 per cents, allowing brokerage in each transaction at i% ? 8. An article is sold at a loss of as much per cent, as it is worth in pounds ; shew that it cannot be sold for more than £25. 4. A and B engage to do each half of a certain worL A began in the morning half an hour before B. They .nested an hour at noon, when half the whole work WM FmST-CLASS AND X7NIYEBSITT HONORS. 273 iposing in £'8 ) 3%— • is sold id after secure for the 4 equal )inpany tm in 6 money jmpany JT. theG. I 1224; J, which 3ents at \,t is the n each er cent, sold for n worL They >rk was done. B finished his work at 7 p.m., and A his at a quai*ler to 10 p.m. At what time did A begin ? 6. The present income of a railway company would justify a dividend of 6^0 if there were no preference shares ; but as £400,000 of the stock consists of such shares which are guaranteed 7i% per annum, the ordi- nary shareholders receive only 6%. Find the amount of the ordinary stock. 6. A cistern is kept constantly supplied with water. Supposing that it is full at first, it is found that 28 equal taps opened together will empty it in 4^ minutes, and that 21 of the same taps will empty it in 12 minutes ; how many taps will be required to empty it in 25^^ minutes ? 7. Two articles, of which the united cost is $90, are sold each at a gain of as much per cent, as it is worth in $ ; shew that the sum of the selling prices cannot be less than $180.50. 8. Two clocks strike the hour, and are heard to strike nineteen times ; they differ two seconds in time, and the one strikes every 8 seconds, and the other every 4 seconds. When they strike together it cannot be distinguished whether one or both are striking ; and this is the case with the last stroke of the faster. What hour do they strike ? 9. The population of a county increases in 4 years from 10,000 to 14,641. What is the rate of increase ? 10. A field of the form of an equilateral triangle contains just half an acre. What must be the length of a tether fixed at one of its angles, and the other end to the nose of a horse, so as to allow him to graze e;^- actly one-half of it ? 274 EXAMINATION PAPERS. 11. A note for $860 is payable on 1st November ; $200 are paid on Isfc September ; what additional pay- ment ought to be made on 1st October, so as to extend the time for payment of the balance till 1st January ? 12. One side of a rectangular figure is 60 feet longer than the other, and its area is equal to that of a square of which the side is 40 ft.; find sides of rectangle. XXVII. John Cameron, B. A. — Winnipeg P. Schools. 1. A capitalist holding 6"/o bonds in a Transporta- tion Co. exchanged them at 64^% for capital stock in the same Co., bearing 7%, at 86%, the int. on bonds and stock having just been paid; his cash gain was $258.33^. What amount of bonds did he originally hold, money being worth 6% to him ? 2. Suppose that from the time of its capture the rate of increase in value of the marten skins has been uniform find the original cost of 12 bales of these furs, for which at the end of 8 months after being first taken $120 was paid — it being known that the value of 4 bales at the end of six months will support a lodge oi 12 Indians for 9 weeks, and the proceeds of 5 bales at the end ot 2 months will support a lodge of 86 Indians for 8 weeks. 8. A Hudson Bay trader purchases on commission furs for the storage of which he pays $250 ; he charges commission at the rate of 2% on 6% advance on total cost of furs, storage, duty, and commission ; and duty is paid at 4% on the total cost of furs, storage, and commission. His commission was $84 ; find the orig- inal cost of the furs. FIBST-OLASS AND UNIVTSBSITT H0N0B8. 276 ember ; al pay- extend Quaiy ? 60 feet aat of a :taugle. isporta- itock in L bonds lin was iginally are the IS been e furs, It taken e of 4 odge oi ales at dians 4. A father leaves his 8 sons, aged respectively 18, 16, and 17 years, $16,000, to be so divided that the shares of the eldest and the youngest placed at com- pound int. at 6^0 per annum, will amount to equal sums when they come of age, and be together equal to the share of the other son similarly invested. What rate % is realized by a person who pays $2*^,561 for the eldest son's share ? 6. A Hamilton merchant receives May 21st an ac. sales (due July 6/8) from Winnipeg. He instructs his agent to get the debt cashed at one of the banks and invest the proceeds in a 9-day bill on Toronto. This bill the agent buys on the 27th May at 1^^% discount and remits it to Hamilton. It is received there June 2nd and is sold June 8th at |% premium; he finds that by doing this he has made $66.28 more than if he had drawn June 8th a draft on Winnipeg, payable July 6th, and sold it at f^o premium. Supposing the bank discount to be 7%, what was the net procewde of tUa ao. sales? 6. A Montana whiskey trader is caught by the Mounted Police, and $2400 worth of furs in his posses- sion, which he had received from the Indians in ex- change for " fire water," is confiscated ; he is also fined $400, which, however, is just the amount out of which he had cheated the Indians by using a can in the form of a frustum of a cone, one foot in depth, and contain- ing, as he said, 14 imperial gallons, one of the end diameters of the ocn being } of the other. Find the diameters. 7. In the Winnipeg Public Schools every time a pupil passes the head of his class he is credited with a ** round." Three new pupils A, £, and C, equal in 276 EXAMINATION PAPEBS. ability and superior to the rest of the class, take their positions at the foot of the class ; A had been at three recitations before B entered the class, and when entered A was 4 times as far as B from the foot towards the head ; and when A completed his first " round" he had " got above" as many pupils as the other two, and G had passed one pupil less than four-fifths as many as B. How many pupils were there in the class during this time who did not get a round ? 8. Investigate the formula for compound interest, and interpret when n is negative. What is the present worth of an annuity of $1200 in reversion 7 years, and continuing 18 years, at 6% ? 9. A farmer wishes to build a rectangular sheep- fold which will contain a quarter of an acre, and which will have an old ^7all for one side. Find the length and breadth so that it may be built with the smallest possible number of boards. • xxvin. E. TiLLEY, B.A. ^BOWMANVILLE HiGH ScHOOL. t- Discuss the correctness of the following state- ment: In order that the denominator ot a fraction may be indicated it is necessary and sufficient that the denominator be one of the powers of ten or the differ- ence between two powers of ten. W^^*^ AVoVo ^*^ *^® denominator indicated. 2. A was indebted to B. A failed, and B agreed to take a certain fraction of the debt. The fraction was written as a mixed decimal of two figuies, the right hand figure being the larger. The accountant, in making out the bill, by an oversight treated the fraction FIBST-GLASS AND UMIVERSITV HONOBS. 277 le their it three vhen towards ind" he wo, and nany as during nterest, 1200 in sheep- d which igth and imallest OOL. state- raction lat the differ- reed to )n was right knt, in faction as a finite decimal, and hence made an error in the bill of 4«. Id. Had the fraction been treated as a pure repe- tend the error would have been but 2*. 6d. Find the decimal and the sum B agreed to take from A. 8. A person invested $5746 in bank stock, and shortly after sold it out for $6984. Had he bought and sold through an agent at i % on each transaction, he would have received but $5915 on the same outlay. Find the price of the stock, and tlie quantity bought and sold. 4. The price of pure gold is $4.29| per oz., the price of a mixture of gold and silver weighing 24 lbs. is $849.75. If the weight of gold and silver in the mix- ture be interchanged, the value will be $444. Find the weight and value of silver in the mixture. 6. Find the present value of a mortgage for $7200, to be paid in nine equal annual instalments, that the purchaser may realize 8 % per annum on his invest- ment ; assuming that the first payment is made at the end of the first year, and that the mortgage bears inter- est at the rate of 6 y« per annum. 6. Two trains started at the same time, one from Toronto and the other from Bowman ville. They met at 9 o'clock a.m. One train reached BowmanviQe at 87i min. after nine, and the other arrived in Toronto at half-past eleven a.m. Supposing the rate of each train to be uniform, and that the distance from Toronto to Bowmanville is 42 miles, fijid the time of starting and the distance travelled by each train before they met. 7. January 4th, 1876, B had his note for $600 at 8 moB. cashed by a broker at a discount of 1^ % per mo. 278 EXAMINATION PAPEBS. April 4th the note was renewed for a further term of 8 mos. upon the maker paying sundry charges, which amounted to $2.00, and interest at the rate of 2 % per mo. July 4th, B borrowed $600 at 10 % per annum, and redeemed the note. January 4th, 1877, B settled with A in full. Find the rate per cent, per annum that B paid for the use of the money. 8. A sold 1264 yds. of cloth on a note at 9 mos., and immediately discounted the note at the bank at 8 % per annum, and found that the proceeds gave him a net gain of 25 % on his outlay. The banker's gain, not counting days of grace, was $28.44. Find tho cost per yard of the cloth. 9. B paid $1,000 to A for some mdse., A realizing « a certain rate of gain on the transaction. B sold to 0, his rate of gain being t^' )e as great as A's. sold to D for $1207.50, at a rate of gain three times as large as B's. Find A's and C's buying prices, and the rate per cent, of gain made by each. 10. A person having to pay $2040 two years hence, invested a certain sum in the 7i % stocks to accumulate interest until the debt be paid, and an equal sum the next year. Supposing the investments to be made when the stock is at 112^, and the price of the stock to remain the same, what must be the sum invested on each occasion, that there may be just sufficient to pay the debt at the end of the time ? XXIX. J. MoBBisoN, M.B., M.A. — Newmabeet High School. 1. The difference between the interest and the dia- PIRST-OLASS AND UNIVERSITY H0N0R8. 279 lence, lulate the made )Gk to 3d on pay tOOL* dig. count on a certain sum for 8 months at 6 % is $0.01)^. What is the sum ? 2. A person invests in the Grand Trunk Eailway 8 per cents, so as to obtain 8^ per cent, clear on his investment when there is an income tax of 2^ cents in the dollar, the brokerage being J per cent. At what price must he buy ? 8. A person sells out $4600 stock in the 4 per cents at 92 ; and invests in the 8^ per cents, gaining thereby $40 per annum by the change of income. At what price did he purchase the latter stock ? 4. A and B together earn as much in 80 days as A does alone in 42 days. In what time would B alone earn the same sum ? 6. A person invests f of his capital in the Toronto Bank stock, f in Great Western Eailway stock, and tne remainder in Newmarket debentures. He sella the bank atock at a profit of 6 per cent, the Bailway stock at a profit of 4 %, and the debentures at a loss of 2 per cent, and realizes $5180- What was the amount of his property originally ? 6. A person sells out $5000 stock of the 8 per cents at 96 and invests the proceeds in bank stock at 75, which pays an annual dividend of 2^ per cent. What is his increase of income ? 7. The Earth, Venus, and the Sun were observed to occupy the same relative positions after an interval of 688'921 mean solar days. The Earth performs one absolute revolution round the Sun in 865*256 days. Find the periodic time of Venus. 8. The Moon's mean sidcrial peiiod is 27 davs 7 280 EXAMINATION PAFEBg. hours 48 minutes 11 seconds. Find her mean synodi- oal period, or the mean duration of the interval from new moon to new moon. 9. A solar spot was observed to pass from the east- em to the western limb of the Sun in 18f days. De- termine the time of the Sun's rotation on his axis, supposing, of course, that the spot has no proper motion of its own, and that the Earth performs one revolution round him in the same direction in 865*256 days. 10. The intensity of gravity varies directly as the mass or quantity of matter and inversely as the square of the distance from the centre ot attraction. The Sun's mass is 814760, the Earth's being 1 ; and his diameter 852584 miles, that of the Earth being 7920 miles. Find what a pound of terrestrial matter would weight at the Sun's surface. XXX. C A. Babnes, Esq., Stbathbot, P. S« • 1. A farm is rated at 60 cents per acre, and the tenant on receiving back 10% of his rent found the sum returned amounted to $24 more than the whole rate. The next year the rate was doubled, and he received back 15% of his rent, but found that the sum returned only just paid for the whole rate. Required the rent, rate and number of acres. 2. A and B with despatches between two towns start at the same time, and meet when A has travelled 80 miles more than B, and they afterwards reach their FIBBT-OIiASB AND UNIYBBBITY HONORS. 281 destination in 4 and 9 hours respectively. What was their rate of traveUing and distance between the towns ? 8. Two clocks are striking the hour together, and they are heard to strike 19 times. There is a differ- ence of 2 seconds in their time, and the faster strikes every three, and the other every four seconds. What is the hour they strike, it being observed tliat when the clocks strike in the same second the sounds cannot be distinguished so as to determine whether one or both strike in that second, and that is the case with the last stroke of the faster clock ? 4. An agent in Cuba vidshes to remit $4,000 to his employer in France. Which will be more advantageous, after deducting the expenses of exchange, to remit indirectly through New York or directly by a biU on Paris, provided one dollar Cuba currency be equal to 5 francs, and the exchange of Cuba on Paris be 1% pre- mium, of Cuba on New York 4% premium, and of New York on Paris 5^ francs per dollar. The agents in Cuba and New York each receive |% commission for doing the business. 6. A, B and C enter partnership ; A contributes $12,000 for 6 months, B a certain sum for 9 months, and C ^9000 for a certain time. The gain is $5,400, of which A takes ^ and B $500 more than 80°/> of a sum which is greater than A's and C's by $50, and C the re- mainder. Find £'s stock and C's time. 6. Find what A, B, C, D are worth, by knowing — 1st. That A's money, together with ^ of B, 0, D, is equal to $187. 2nd. That B's money, together with ^ of A, C, D is equal to $187. 8rd. That C's money, to- gether with I of A, B, D is equal to $187. 4th. That 282 EXAMINATION PAPKRfl. D's money, together with ^ of A, B, C, is equal to ^$187. 7k Supposing the elastic power of a ball which falls from^ a height of 100 feet to be such as to cause it to rise 60 feet, or one-half the height from which it fell^ and to ooutinue in this way diminishing the height to which it will rise in geometrical progression till it come to a state of rest, how far will it have moved and in what time from starting ? 8. If several partners advance respectively capitals Cj, Ca, C3, C4, &c., during the time tj, tg, tg, t^, &c., respectively, show that their gain or loss are propor- tional to the products C, t^, C, tg, C3 tg, C4 t^, &c. 9. A man owes a sum of money, which it is agreed he shall pay in 6 instalments equal in their time and amount ; and with each instalment lie is also to pay in- terest at 5 per cent, on the amount then owing. The last payment at the expiration of 12 months being (\idth interest) $28, it is required to know the original amount of debt, and the time and amount of each pay- ment. 10. Three circles whose radii are as the numbers 6, 7, 6, are inscribed in a circle whose diameter is 880 feet. Eequked the radii of the inscribed ciicle. XXXI. I. J. BmcHABD, Esq., Toeonto, P. S. 1. In reducing to a decimal the proper fraction , , b being prime to ten, shew that when the remain- der b—a occurs half the circulating period has been ob- tained, and how the remaining figures may be foundi. Shew also that the peiiod itself is divisible by 9. riBUT -CLASS AMD UNIVERSITY HONOBS. 288 2. Wliat is meant by " Scales of Notation" ? When a fraction is reduced to a decimal in any particular scale, how can you i iou&ly determine the nature oi the resulting decimal v In a certain scale, radix lesH than ten, the fractions ^^ and ^ give respectively two and three finite places of decimals ; in the same scale would ^^ give any finite places ? Shew that the fraction m' cannot give more than places which repeat. (m-l)« 8. Shew that the difference between the amount of the present worth of a note discounted by the Bank and the face of the note is proportional to the square of the product of the time and rate. The difference between the true and the bank discount of a note for $815, payable in one year, is 75 cents. Find the rate. 4. The number of teachers and pupils in the Toronto Public Schools in 1877 were respectively 83^% and 10% more than in 1876, and the number of teachers and pupils together 10-^^%°/^ more ih&n in 1876. Had 10 fewer teachers been engaged, there would have been 9 less pupils per teacher than in 1876. How many new teachers were engaged ? 6. A grocer uses to his advantage a false balance in both buying and selling, and gains altogether 46yV(y%- Had he used the scales to his disadvantage in both buy- ing and selling he would have neither gained nor lost. How many oz. did he give for a pound, and what was his gain per cent. ? 6. A young man enters upon a situation at a salary of $100 per quarter, which is increased $10 every pay- 284 EXAMINATION PAPERS. ment. His expenses are $76 for the first quarter, and increase 6% each suoceeding quarter. After each pay- ment he deposits his spare money in the hank, for which he receives 6% per annum interest ; what will he be worth in 10 years ? Give the result in surd form and approximate its value, taking (1.06)*° =7*04, (1.06)»«=:1.79085, (1.06)^=1.014674. At the above rate would his expenses ever equal his salary? Why? 7. A merchant invests $12,000, which yields 26% annually. At the end of the first year he withdraws $1000 for expenses, and each succeeding year 83^% more than the preceding year. When will he be ruined? When had he better close his business? What will he then be worth ? Log. 2 =.8010800. Log. 8=-4771218. 8. A boatman can begin to row at the rate of 6 miles per hour in still water, but his speed uniformly diminishes one-half mile per hour ; he can row down stream to a certain point in an hour, and return in two hours ; find the rate of the stream. 9. A B is a semicircle. C a point on the circum- ference, such that A G is 8 feet and B C 4 feet. On A C and B C semicircles are described so as to fall with- out A C B ; find precisely the sum of the areas of the two lunes thus formed. Gould you thus find the exact area of a circle? 10. Squares are described on the sides of a triangle 80 as to fall without it, and the exterior angles of the squares are joined so as to form a polygon without any re-entrant angles ; shew that the sum of the squares on these three lines is equal to three times the sum oi the squares on the sides of the triangle. Show also rrBST-OLASS AND UNIVBBBITY HONOBB. 285 that the sum of the three triangles formed by joining the exterior angles of the squares is equal to three times the original triangle. xxxn. Miss Corneb, Tobonto. 1. A and can do a piece of work in 8 days, which B and C can do in 5, and A and B in 4 days. They work 2f| days. Had B working alone been able to fin- ish it 4^ of a day sooner, he would have received $2 more than he did. Find the sum of money required to pay A, B and C their wages. 2. I remit my agent in New York $64960, with in- structions to deduct his commission at 1^ %, and invest balance in sugar. In addition, I have to pay freight $1740, insurance $900, and an ad. valorem of 2^ % on the invoice price of the sugar. He sells the sugar at a profit of 1-|^^ yo on the whole outlay, but instead of re- ceiving cash he receives a note @ 70 days, which on being discounted at the bank at 5 % exactly settles the claim. Bequired face of note and amount invested in sugar. 8. A started in business. 16 mos. after he com- menced, B entered as a partner with a capital equal to *142867 of A's. 2 mos. later entered, and his capital was to B's as B's time was to A's time. At the end of four years from time of starting they agreed to wind up affairs ; D assumed charge, and settled the claims of the partners by making over to them a mortgage for 10 years on the full value of an estate worth annually $9700. What is the P. W. of B's claim, supposing compound interest be allowed at 5 % ; the partners sharing according to their stocks and time in trade ? 286 EXAMINATION PAPEBS. 4. Interest and discount may both be considered as interest on a certain sum. Explain. A merchant being asked his original capital, replied that three years after starting he had been worth $4d74'616, and that he had added annually to his busi- ness a sum equal to his original capital, increased by compound interest at the same rate that he had had a note of $1,120 for 2 years discounted at, receiving $120 as discount. What was the merchant's original cap- ital? 6. A bought 100 lbs. of each of two kinds of tea, the price of the dearer being to the price of the cheaper as 11 : 9. He mixed 15 lbs. of the dearer with a cer- tain amount of the cheaper, and sold it without loss at 95c. per lb. The remainder of the dearer tea he marked at $1.54 per lb., thereby clearing f of the cost price, but sold it 2c per lb. dearer. Bequired gain % in the latter case, and the number of lbs. of the cheaper that he mixed with the 16 lbs. of the dearer. 6. A man in England owns £400 in Bank of Eng- land 4 % selling at 104^. He sells through a broker, who charges ^ % commission for each transaction, when exchange is at 110 and invests, in Dom. 6 %. How much can he afford to pay for latter, in order that his income may neitlier be increased nor diminished ? 7. A man finds by his watch that he can row a cer- tain distance down a stream, running ordinarily at the rate j^ of a mile an hour, in 56^ and upinl hour. He discovers, however, that his watch gains 2' daily. Find the difference between tlie real distance that he rowed, and the distance ascertained from his watch time, sup- posing the watch to show correct time at star^mer. PCRST-CLASS AND UNIVBBSITY HONOBS. 287 8. Deduce a method for finding the time when prin- cipal, amount, and rate % are given compound interest. A farm annually increases in value 20 %, in what time will it be worth 3 times its original value ? Log. 2= -801030. Log. 3= -477121. 9. A merchant* buys 100 yds. of cotton at 10c per yd., and 80 yds. at 7^c per yd., on 6 mos. credit, choos- ing to purchase in that way rather than to receive a certain discount for cash. He sold the former at a profit of 12 % on the cash buying price, and the latter at a profit of 20 % ; had he reversed the proceeding he would have gained 30c more than he did. Required the rate % of discount which the merchant might have received by purchasing for cash. 10. A field in the form of a parallelogram has a tree planted in the centre. Adjacent sides 14 and 9 per. respectively. Shortest distance from corner to comer across field 8 per. Bequired distance from tree to fai*- thest comer of field. xxxm. d, f C. Moses, Esq., P. S. I., Halmmand. 1. Two lbs. of tea and 6 lbs. of sugar cost $2.40, but if sugar were to rise 50% and tea 10% they would cost $2.80 ; find the price per lb. of tea and sugar. 2. My agent in Montreal sold a consignment of fionr on a commission of 3%, and invested the proceeds in U. S. 6's 5-20 at 95 on a commission of 2^ on the amount invested, his whole commission is $530 ; what is my income on said investment ? 3. A goldsmith has two defaced ornaments, the first containing 1§ ozs. of gold and ^ of an oz. of alloy, the 288 EXAMINATION PAPEBS. second containing | of an oz. of gold and IJ ozs. alloy; how much must he take from each to fonu a new orna- ment weighing 2 ozs., containing equal parts of gold and alloy ? 4. A mortgage of $1000, repayable in 5 years at $200 a year with interest at G^o on the unpaid principal, is sold ; what is its value allowing the purchaser 8% for his money. 6. A dishonest broker, having a certain number of old sovereigns, reduced each by ^ of its value and passed i of them thus gaining £1^8. 9d. In attempt- ing to pass the remainder, he was arrested and the sovereigns taken from him with the exception of one which he managed to conceal. How many sovereigns were there and what was the value of each, it being known that the man gained 4«. lO^d. on the whole iiransaction ? 6. A owes B $1200 due in 4 months which £ offers to discount at 12% per annum. Now A finds that for 2% he can get the use of D's name with which he can get the note discounted at the bank for 8% ; which will be the better way and by how much ? 7. An express train leaves Fort Erie for Caledonia at 1 o'clock p. m., at the rate of 80 miles per hour, and 15 minutes after is followed by a freight train at the rate of 20 miles per hour. A mixed train leaves Caledonia for Fort Erie at the rate of 26 miles an hour, and after travelling 1 hour meets the express and in 20 minutes afterwards meets the freight train. At what time did the mixed train leave Caledonia ? 8. A merchant in Montreal imported from England a quantity of goods for which he had to pay a duty of 16%. On account of the depression in trade he is forced FIBST-CLASS AND UNIVEB8ITT HONOBS. 289 to sell at a loss of 6-^% ; had he sold them a month earlier he would have made $496.80 more than he did and then would have cleared 2^^% on the transaction; what price did he pay for the goods ? 9. A statue 80 feet high stands on a pedestal 60 feet high, and to a spectator on a horizontal plane, they subtend equal angles; required the distance of the observer from the base, the height of the eye being 6 feet. 10. The sides of a triangle are 8, 10 and 12 re- spectively ; find the difference between the diameters oi the inscribed and circumscribed circle. XXXIV. James Oablylb, M.D. — Nobmal School, Tobonto. 1. The annual income from an estate is the rent and the income tax which is levied on the rent after it is re- duced 20%. If the annual income be $8175, and the income tax 2 cents on the $, what is the taxable income ? 2. A broker receives instructions to purchase Mon- treal Bank stock, that pays 7% half-yearly dividends, so that 4% may be realized on the investment. What may he pay for the stock if bought two months before the dividend is payable. 8. On January Ist, 1877, B purchased a farm for which he gave a bond securing the payment of $6000, in 10 annual instalments of $600. B paid nothing tmtil January, 1879, when he took up the bond, paying 7% interest on overdue instalments, and being allowed 7% discount for all not due. Required the amount B paid. 4. A owes B $620, due in 6 mos., $648 in 12 mos., $4704 in 18 mos., and $1200 in 2i years. If money \r 91 290 EXAMINATION PAPEBS. be worth 8% simple interest, find when it would be fair to both parties for A to pay his whole indebtedness. 5. If 5 men, 4 boys and 8 girls, can clear a meadow of stones in 9 days, or 8 men, 8 boys and 6 girls can do it in 8 days, or 4 men, 10 boys and 9 girls can do it in 6 days, how long -^ ill it take 8 men, 6 boys and 4 girls to clear it ? 6. If the population of Canada is now 8,750,000, and the increase from all sources annually is ^ of the population at the beginning of the year, and the decrease -j^, find how long it will be before the popula- tion is 10,000,000. Given log. 2 =-801080 and log. 8 = -477121. 7. A person has the offer of $1600 a year for 15 years, or by waiting 15 years, to enjoy the annuity "as a perpetuity. Determine the conditions that will render one better than the other. 8. A owns a mortgage securing the payment of $1200 in three annual instalments of $400, with inter- est at 8%. He exchanges it for bank stock that pays 16% dividends, at 177^-. Find the amount of stock he received. * 9. A dealer bought wheat at $1.75, $1.80 and $2. In what proportions may they be mixed so as to sell the mixture at $2.16^ on 8 mos. credit, when money is worth 10%, and make a present gain of 12% ? 10. A speculator in Toronto purchased $100,000 Bank stock in New Orleans at 80, and sent a draft to his broker in New York, with instructions to settle for the stock. Exchange between Toronto and New York li% premium, between N. Y. and N. 0. }% discount. Brokers charge ^% on amount transmitted to N. 0. Find what the stock cost the speculator. ANALYSIS — Of — THE ENGLISH LANGUAGE, By I. PLANT FLEMINa. HJL, B.0 J.. With a Sbliotioh or Examimatioii Papies rsoit oue Cakaoux Umitkiuitiis, BT W. HODSTOP, M.A., EXAMOmR Ul EneLUH, TOBOHTO UlUTUUIITT. FOR USE IN PUBLIC HIGH SCHOOLS AND COLLEGIATE INSTITUTEa PRICE, $1.00. Okorob DiOKSoa, B.A., Heati Master, Colbgiate Instttutt^ HmtmiltoH. " Flemiiigr's Enfliah Anolytis has been UMd in the Hamilton Collegiate Insti- tute since 1873. " I know of no better text book in English Onmnuur for the Intermediate Fonns in our High Schools and Collegiate Institutes." J. SlATii, 6 A., HsaJ MomUt^ CalUgiaU ItuHtutty St. Caiharitus. " Fleming's Analysis has been in use here for about two years ; tt is the best 'vanual 1 know of for advanced pupils— particularly in etymology.** GhMROK Wallaci, B. a., ffcad Mas/tr, H. S., Weston. ** We have used Fleniiug tor nearly one year. It Is the best book I have ever taught on the subject during an experience of two yesn in Canada and eight In English Qrammar Schools." T. MoIrttrB, M.A^ Head Master, H. S., Iti£erseil. " Fleming's Analysis has not been introduced into the High S'chool, Inger8<^, as a Text Book, but much of its contents has been brought before the notice of the students in the form of lectures. ** I have carefully examined the work, and I have no hesitation in pronounc- ing it 8up<>rior to anything yet presented on the subject of English It is espacially adapted to Uii;h School work. I shall be gratified to learn that It is placed on the list of auttiorised Text Books.*' FLXMIXO'S ANALYSIS OF THE ENOUSH LANOUAOE. W. W. Tambi.tr, M.A., HtadMasUr^ Mifk Schoot, Othatva. '* I think that Fleminfc*8 Analysis Is a very excellent work.*' A. P. KNianr, M.A., Rtctor K. C. /., KingtioH. " Accept thanks. It is in my opinion the best School Text Book on the sub- ject that has ever been placed before the publie, and supplies a want felt by erery teacher in the Dominion." N. J. Wbllwood, B.A., HtadMasttrH. S., Stre*tsvilU. " I consider that it contains much valuable information, and that it is en- titled tu a place on the list of Authorized School Books." O. Stracohon, Head Master, H. S^ Woodstock. " I use ' Fleming's Analysis ' to a considerable extent in the higher classes of the school." A. MlLLBR, Head Masttr^ H. S„ IVatkerton. *' I am ncr,- using ' Fleming's Analysis ' in my senior class in English Oram- mar, and must say that I consider it a most excellent text book, and hope to see it put on the authorised list for High Schools.*' Andrbw MoCdlIiOOH, M.A., Head Master, H.S., DrummondvilU. " I have used Fleming's Analysis for several years, and from its brevity, clear- ness and comprehension, consider it especially adaptea for the use of senior classes in our high schools." L. G, MoROAX, B. A., Head Master, H. S., Vienna. " I am much pleased with it, and hope it will be authorized for use in the Elgh Schools, as it contains much valuable information not found in any of our text books. It is a work long needed. The examination questions at the end will prove very valuable to both teacher and pupil." A. PuRSIiOW, LL.B., Head Master, H. S., Pert Hope. " I have used it extensively in my teaching for two years or more. It has so many excellencies that I would like to see \% permissively authorized, but not pre- scribed to the exclusion of others." W. C. MiDDLBTON, B.A., Head Mastery H. S.^ Amprior. *' I consider ' Fleming's Analysis ' admirably adapted for the upper forms in our High Schools." R. W. YOUNQ, B.A., Head Mastery H. S., DunvilU. ' I think that this work could be used in the Schools with much advanCage.' Robert Mathbson, B.A., Head Master, H. S., Napanee. ' I am very happy to add my testimony to the value of ' Fleming's Ahalysis of the English Liinguage' as a text book for High Schools." OAiuDUir oomucrBT rnnom. HAMBLIN SMITH'S STATICS^ WUk Apfutdim »tf TftM. KMtUmi, M.A., a$lmm MatUr Jf0rtMa Sekooi, T$mi$$>, PriMMotntiL Hud>lln Smlth'a nydioftalka. 7S oantiL *'ThM« are ftw booki in «l«m«ntary mMhwiHitiol ■d«nce thst I ma aora eonildently rMommand. Hm •miiff«nient of Um *< book work* to adminblo, Ito trwtmtnt dmr, and tiM nibjMl ■uuU M alementoiy m U oan be, oonditent with a identUte ttmk moat of it In raeli a itudy, tbe worUng of probloma will ocuMo tho aamo ploararo and impart to tho lubjooi the nmo intomt that tho oondnotinff of ezperimonta dooa in ohemlitnr. Hie «>• amploi at the end ol eaeh oh^tter are well ideoted- unple at tlie and endinf with problem* of raflldent lendf an additi AlifftID BAEn, &A., "Math. Tutor, Unir. OoUcgc^. Vatonto." ampiei a< me ena oi eaon < bMnnning, proftTemlveh ai dlnralif . The appenolz 1 OAVADiAM oomioBT Binnoini BUBUN SMITH'S aZOMSTBT (Sohod ad.) With JtaamifMtim Pap0n fty 3%oil Mirklamdt M.A, PrlMWotnti. 8mlth'ia■ ELEMENTARY STATICS linxml Sclunl, IVronJo. Tk.fciL_. 'RICE n. 00.