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iHiller & Co.*« €J)Utattonal Scrits.
HINTS AND ANSWERS
TO
EXAMINATION PAPERS
IN
ARITHMETIC
BY
J. A. McLELLAN, M.A., LL.D.,
Inspector of High Schools,
AND
THOMAS KIRKLAND, M.A.,
Science Master, Normal School, Toronto,
TORONTO:
ADAM MILLER & CO., 11 WELLINGTON STREET WEST.
1877.
ley
Entered according to Act of the Parliament of Canada, in the
year one thousand eight hundred and seventy-seven, by
Adam Miller & Co., in the office of the Minister of
Agriculture.
OLOBI PRIKTINO COMPANY, TORONTO.
\(y
RESULTS, HINTS, &o..
FOB THE
EXAMINATION PAPERS.
CHAPTER II.
FUNDAMENTAL RULES, VULGAR AND DFXIMAL FRACTIONS, &C.
SIMPLE RULES.
I.— Page 35-
The roferonoea indicated by Art. are to the Canadiau Edition of HambUn
Smith's Arithmetio.
(1.) Art. 17. (3.) Art. 46. (4.) $3945. (5.) Art.
22. (6.) Art. 24. (7.) $2749. (8.) Art. 31. (9.)
10005100. (10.) 289. Remainder, 34.
XL— Page 36.
(1.) 72. (2.) $1049. (3.) 361 59f hours. (4.) In
this question read 83 for 38. 3415956. (5.) 4307.
(6.) 3 ft. 7f I inches. (7.) 166 years. (8.) $111. (9.)
$80. (10.) 171 cattle— gain $26.
III.— Page 37.
(1.) Art. 46. (2.) Art. 47. (4.) Arts. 43. 41. (5.)
67157148372. (6.) 120 lbs. (7.) 392 miles. (8.) B,
$5243; C, $17181; all, $23689. (9.) Art. 60, (10.)
19052.
6
RESULTS AND HINTS FOB
COMPOUND RULES.
IV.— Page 38.
(1.) 36 of each. (2.) 11 ft. (3.) 10.36767 yds. (4.) 9^,.
(5.) 6 women's shares=l 8 men's shares.
8 children's " =16 women's " =48 men's shares
Hence, 4+18+48=70 men's shares.
And ^^D^^=$37.72J, a man's share.
Then, 3X $37.72J=$113.17J, a woman's share.
2X $113.17J=|226.35, a child's share.
(6.) 81 ac. 1 r. 33 p. (7.) 424 lbs. 14 dwts. 6^ grs.
(8.) 89 I^J qra. (9.) Income X $^=$ 6250 .-. In
come= $300000. (10.) A, 60 ac. 3 r. 24 p. B, 89 ac.
3 r. 4| p. 0, 99 ac. 1 r. 25 j^^ p. D, 198 ac. 3 r, lOf?^ p.
v.— Page 39.
(1.) 18662400. (2.) 4 fur. 22 pr. 2 yds. 1ft. 4 in.
(3.) $1.35 per bushel. (4.) 16s. 3|d. "^ (5.) Art. 42.
(6.) $15213.66. (7.) Art. 20. (8.) See^YsVl (=366i
nearly.) (9.) $3327.08. (10.) 271.
VI.— Page 41.
(1.) 67 times; 4 inches. (2.) 1438 acres. (3.)
30303g»^. (4.) $3187.20. (5.) For 8 oz. read 80 02.
240Z.J $3.90. (6.) £782 2s. SJd. (7.) 328 times;
£5 7s. 6d. remd. (8.) 1 oz. 5 drs. 2 sc. 14 J grs. (9.)
258. (10.) $44387.20.
VII— Page 42.
(1.) Art. 46. (2.) The required length must be the
greatest common measure of the three given numbers
=9. (3.) Art. 49. The required number of acres must
evidently be a common multiple of the given numbers.
A*
EXAMINATION PAPERS. 7
The leadfc common multiple of the numbers is 3000.
The required number of acres is 3000, 600, 9000, <kc.
(4.) Arts. 53 and 56. (5.) 360. (6.) Art 38. (7.) The
numbers, when resolved, are 2^. 3. 13. 53., 2^. 3^. 13.
43., 23. 3. 13. 443, and 26. 32. I32 : of which the G. C.
M. is 23. 3. 13, and the L. 0. M. is 2«. 32. I32. 43. 53.
443. (8.) The prime factors of 1680 are 2^. 3. 5. 7. ;
the four numbers are therefore 5, 6, 7 & 8. (9.) A
would go once round the island in G00-i-20=30 days, B
in 600-4-30=20 days, C in 600-^25=24 days, and D
in 600^40=15 days. By finding a common multiple
of these, we shall have the time in which — after each
one had gone several times round the island — all would
be together again at the point from which they started.
The least common multiple of 20, 20, 24 and 15 is 120 ;
hence the travellers would come together i^ 120 days.
(10). 33 in each section— the G. C. M. of 132 and 99.
Vlll.—Page 43.
(1.) 1400490. (2.) 80 ounces ; 1 oz gives 7j^ half
sovereigns, .-. 80 gives 623. (3.) 5554 oz. (=G. C. M. of
the two quantities.) (5.) They stepped together 4440
times. The man took 8800 steps, the woman 13320,
and the boy 17600. (6.) 84 seconds. (7.) The inter-
val will be 62370 seconds. The four points will have
moved over the distance 315, 125, 70, 54 respectively.
(8.) 9 classes of boys and 8 classes '^f girls. (9.)
6 rods. (10.) 7113120 days, when the first will have
made 81760 revolutions in its orbit; the second, 31755;
and the thiid, 19488.
IX.— Fage 45.
(2.) 247. (3.) They will do the same quantity in
8
BSeULTS AND HINTS FOR
27, 28, and 30 days, respectively. (4.) 40 bushels. (6.)
34560 rails, 13 ft. long. (6.) Art. 56. (7.) 649195944494.
(8.) A goes 9 miles, B, 6, C, 4J and D, 4. (9.) 1 400 rods.
(10.) A, 2 ; B, 3 ; C, 4.
FRACTIONS.
I 4a
40 •
(8.)
1.
X.--Page 46.
a.) Art. 64. (3.)U- (4.)imi?;Hli
(6.) il (6-) I- (7.) Art. 72 ; 1.
(9.) m > 2ie- (y^-') i.
XL— Page 47.
(2.) 4§§gjof£100. (3.) 141 ; 36025 min. (4.) 3d.
16h. 6m. 22i^sec. (5). %«-. (6.) 1620 tons. (7.) M 8s.
Ifd. ij^lq. (8.) The unit is 24 cwt., of which 2J4
cwt. is tin, and 21 §| cwt. copper. (9.) The length of the
measuring rod is 28^'^ inches, and is contained 98§|^
times in 77 yards, which is not so near 99 times as by
^^<2^ in defect. The distance, therefore, which approaches
nearest to 77 yards is 99 times the length of the mea-
suring rod. (10.) If the error be in defect j the apparent
length is 502 yards, and 24| inches over. If the error
be in excess, the apparent length is 499 yards, and 3{^
inches over.
XII.--Page48.
(!•) m (2.) A. (3.) mm- (4.) UOJ yds.;
$6.31J. (5.) $29333.33i. (6.) /j ; 1]^||. (7.) Lost
$400. (8.) £27 10s. (9.) 25 men. (10.) If
XIII.— Page 50.
(1.) Art. 71. (2.) If (3.) $6000. (4.) ]^||f J.
(6.) 2800JJ. (6.) tVt of an hour. (7.) $53.10. (8.)
jlj. (9.) 1200 ; Irish, 480; Scotch, 360 ; English, 360.
(10.) $9561.31f
EXAMINATION PAPERS.
XIV.— Page 51.
(1.) Art. 88. (3.) Art. 108; 24.975024; 500.5.
(4.) Are. 99 J 2.2939153408. (5.) Art. 100; 2.1:
210. (6.) Art. 110. (7.) 432; .00857142. (8.) .0108.
(9.) Any finite fraction can only be said to be equal or
equivalent to the infinite repeating decimal, as the limit
of the value which the decimal can never exceed. It
may easily be shown that the more figures of decimal
are taken, the larger the decimal becomes, and will
continue to approach in actual value to the fraction, but
within a difference less than can be assigned by any
fraction whatever. (10.) This fraction having the factor
7 in the denominator, is apparently one which will pro-
duce a repeating decimal, but when the fraction is re-
duced to its lowest terms, the denominator consists of
factors each equal to 2. Repeating 0; Non-repeating 11.
XV.— Page 52.
(1.) .06614; 02027. i2.)^hl>^j^- (3.) lot $412.37^4 ;
house $1187.62|j^. (4.) 3^f §. (5.) 44 bbls. (6.) 5j^|.
(7.) $20. (8.) ^2 ; If. (9.) $65.48. (10.) 906| tons.
XVI.— Page 53.
(1.) .975 ; tVdV (2-) -096. (3.) .0144. (5.) Is. ==
T^TJ ^' i^-} 11 025- 9 <lwts. 2y2j grs. (7.) 3420 grs.
(8.).S '85714; 1.21527. (9.) ^J^^. (10.) .091782407.
(11.) 6.037|j^ which produces a recurring decimal.
XVII.-Page 54.
(1.) 7910000; .0053. (2.) $50. (3.) $6400. (4.)
181 J miles; 8 h. 35 min. (5.) 2.36. (6.) 70^]^ sq. in.
(7.) $9.23y^. (8.) .03. (9.) $18.74. (10.) $30. (11)
10
RESULT8 AND HINTS FOR
XVIII.-Page 55.
(1.) .007916; .0001099989. (2.) 1199.365234375.
(3.) 69.0625. (4.) $14591.602 eldest; $4166.663 two
others. (5.) Read 4.190476 instead of 4.1908476. 2 tons
2cwt. 2qi's. llA*fflbs. (6.) .65706. (7.) m^l
(8.) .0117203. (9.) Examined, 160; average, 250.
(10.) 61.22.
:IIX.-Page 56.
(1.) If the work be denoted by 1. Then A and B do
1 in 20 days, or r^ in 1 day. B does 1 in 60 days, or
3»5 in 1 day. Hence A does ^'^ — s^^ = toO i^ o"® ^^y»
and 1 -i- jg0 = 33] days, in which A could finish the
the work by himself.
And B does 3*5 in 1 day, or in 20 days he does |g or
J of the work.
A does j§^ in 1 day, or in 20 days he does ^^^ or |
of the work.
(2.) A and B do 1 in 6 days, and ^ in 1 day. B does
j^ in 1^ days, and -f^ in 1 day. And A does J — fs =
5«5: and 1 -5- 5*5 = 30 days, 1 -f- ft = 7^.
That is, A does the work in 30 days, and B in 7^
days.
(3.) A does 1 in 15 days, and y^^ in 1 day. B does 1
in 18 days, and j^g in 1 day. Together they do ^^ of the
work. ^§ remains to be dono. Here B leaves, A con-
tinues for 3 days, and in that time does the ft of the
work. When C begins there remains of work ||| — ft ==
I g. Of this A does the ft in 4 days, and C, therefore,
must do the -/^ in 4 days, or the whole in 24 days.
kXAMINATION PAPERS.
11
(4.) 2 days woil; of A = 3 fl:ivs work of 0;
and 5
44
B= 4
n
c.
.-. 8
tt
A= 12
it
0;
and 15
U
B = 12
u
0.
llunce 8
(1
A = 15
<(
Bj
and 1
((
A 15
l(
B.
Theiofore 36 days work of A .:^ ' 'b"-? ^'i" 07 A days'
work of B, or B will require 11^ weeks to complete
what A can perform in 6 weeks.
(5.)* Glass A contains 3 parts water -|- 1 part spirits=
4 parts.
Glass B contains 4 parts water -j- 3 parts spirits=
7 parts.
J of water -f- J of spirit=l,
and 4 °^ water -f- f of spirit =1.
thorefoif l/gof water -j- ;Ji o^ spirit=^2.
Or the mixture consists of Ij^'g of water, and ^^
of spirit.
. (6.) The capacity of the cistern may be represented by
1. Pipe A tills ^- in 1 hour. Pipe B tills \ in 1 hour.
A and B fills j^^ in 1 hour, but C empties the cistern in
1 hour. Hence the quantity poured out being greater
than that poured in during the same time, the cistern
will become empty in a certain time. At 3 o'clock, when
C is opened, the cistern contains f -j-^, or ^h. And in
1 hour, 1 — -^.2=2-^{^ in excess of quantity poured out above
that poured in. Hence -}-^-^ y^^=-y-=2^ hours. The
vessel will be empty in 2^ hours after 3 o'clock, or 12
minutes past 5 o'clock.
(7.) yV of a day. (8.) 9 d. 20 h. 15 m.
(9.) There are 11 intervals between 1 and 12 strikes.
The interval of two strikes of the first clock is f f sec.
12
RESULTS AND HINTS FOR
and of the second f f sec, and the seventh strike takes
place on the completion of the sixth interval. The times
are ^y'y^ and W^ seconds ; their difference is f J of 1
second, or -^j of 1 minute.
(10.) In conjunction at XII, and at intervals of 1 h.
5y^,- m. thereafter; in opposition at 32j®|- past XII, and
at intervals of 1 h. 5y\ m. thereafter ; at right angles at
16y\, and at intervals of 32y^y m. thereafter; liable to be
mistaken 5j^^ m. past XII, and at intervals of 5y|3 m.
thereafter.
XX.— Page 58.
For the first five questions see Art. 224. (6.) 113.27
litres. (7.) 25.38 kilogrammes. (8.) Art. 224. (9.)
108 kilogrammes. (10.) 762 mm. (11.) ^ gram;
1.4147 mm. (12.) 12732.406 kilo.
XXL— Paffe 59.
(1.) 200§gg; 3^111^15. (2.) 3 cwt 16 lbs. 4^1 oz.
(3.) £i 16s. lOyW^ d. (4.) 2 h. 57 m. 58§£| sec. (5.)
A ; A- (6.) 3. (7.) 1|^ min. past 6. (8.) 45.5008
metres. (9.) 1 lb. 6 oz. (10.) 307 ac. 3r. bp.
XXII.-Page 60.
(1.) 8086. (2.) 80. (3.) 2 cwt. 1 qr. 8fgibs. ; Icvrt.
2qr. 9i^lbs. (4.) m (5.) 2.411482. (6.) $llf
(7.) 3Jh. (8.) i»g2g«-. (9.) 64 ft. 4| in.
(10.) Instead of 67700421, read 72644830039 ; the
other number is 2521777.
XXIII.-Page 62.
(1.) 7. (2.) $261.2685. (3.) 113g^3grs. (4.) $158.40.
(5.) A, 18J days; B, 22 days. (6.) A, $160; B, 240.
(7.) ^ (8.) £199 19s. 2y,Vud. (9.) 47 lbs. 163^ oe.
(10.) $59.69J. (11.) 1st year, $700; 2nd year, $756.
EXAMINATION PAPE&S.
13
CHAPTER IIL
PAPERS FOR ENTRANCE
INTO
HIGH SCHOOLS AND COLLEGIATE
INSTITUTES.
I.— Autumn, 1873. Page 63.
(1.) 18|8If (2-) $3000. (3.) Art. 71. 15^8 J. (4.)
2^. days. (5.) 23V days. (6.) ^ff f f^. (7.) $266960.
(8.) 26 ft. 3giin. (9.)$26.19i-V (10.) Sum=5387TV3.
diflF. =120iJi
II.— January, 1874. Page 64,
(1.) £4 14s. 12|d. (2.) %^~^^^ bushels. (3.) 146730
minutes; ^V^ of a year. (4.) 2||. (5.) $3000, value
of house J $600, value of lot. (6.) 2417sVo^ sqr. yds.
(8.) 2\. (9). 147 bushels. (10.) 7jt days.
III.— June, 1874. Page 65.
(1.) Instead of forty-eight thousand, read four thousand
eight hundred; the divisor will then be 200563. (2.)
22503744 square inches ; 3 ac. 3 rd. 26 per. 3 yds. ft.
108 sq. inches. {Z.) 163f f||. (4.) 1^ of \, smallest ;
J of 2|, greatest. (5.) l^ff. (6.) f. (7.) $40000. (8.)
jei23 16s. 10|d. (9.) 3. (10.) $7600,
14 RESULTS AND HINTS FOR
IV.— December, 1874. Page 66,
(1.) 476,§|f^. (2.) 44000 ft. (3.) 4750 irs.;26aa
2rd. 30 p. 8yds. 8 ft. 115 in. (4.) 68 yds. 3ft. Sin.
(5.) £1 13s. 7}d. (6.) 4||. (7.) 8^f yds. (8.) 81 gals.
(9.) 9. (10.) 540.32 yds. ; $4786.0352.
v.— June, 1875. Page 67.
(1.) 1. (2.) 800 bbls.; $5.75 (3.) $16200. (4.) 15s.
Of |d. (5.) ej%\%. (6.) 7711-^. (7.) $60000. (8.) Read
32 instead of 23. Divisor is 102. (9.) £51 3s. l|«f.d.
(10.) 144451i|g| acres.
VI.—December, 1875. Page 68.
(1.) $100.78. (2.) 600 ac. 2 r. 1 p. (3.) 5-if J. (4.)
Art. 73. (5.) 400 barrels. (6.) 1st, $2000 ; 2nd, $^500;
3rd, $1200; 4th, $1300. (7.) /g; f. (8.) $555.01t»2»,V
(9.) 420x|f J^ lbs. (10.) $131.55 ; $56.25.
VII.— June, 1876. Page 69.
(l.)$53.88J. (2.) 8.83002. (3.) 4 hrs. 42 min. 15/^ sec.
(4.) 25-fi„V3V (5.) $4.80. (6.) $12.80. (7.) 34J cub. in.
(8.) 14 days. (9). $80. (10.) $45.
VIII.— December, 1876. Page 71.
(1.) 23048771 square inches; 18 tons 17cwt. 3 qrs.
18 lbs. 11 oz. (2.) 5040. (3.) 14789. (4.) %% of 8.2,
greatest; \ of 9^, kast. (5.) 40}^ miles. (6.) 2 ft. 9|in.
(7.) 114 yds. (8.) 82{|. (9.) 37.2748839 ; .0625.
(10.) UJft.
IX.— Page 72.
(1.) 1 ; }. (2.) 16/t minutes past 3. (3.) The dis-
tance is 3.7984 miles; the beat of the pendulum meas-
ures .795872 of a second. (4.) .14; 4.8. (5.) Supply
m
EXAMINATION PAPERS.
15
the word Jialf before property ; $36000. (6.) 1318||.
(7.) 325. (8.) The one is Troy weight, the ofcher Avoir-
dupois. The pound of feathers is 2 oz. lldwts. 16grs.
heavier than a pound of gold ; and aii ounce of gold is
42J grs. heavier than an ounce of feathers. (9.) Read
1872, instead of 1827 ; 31 years. (10.) Read per cwt in-
stead of per ixnt.f $2,143.
X.— Page 73.
(1.) 3759. (2.) 3ac. 2r. 23 p. 10 yds. 8 ft. 10 in.
(3.) AVheat 90 cenvs; Oats 55 cents. (4.) fj. (5.)
62.206 feet. (6.) 40 acres; $6. (7.) Art. 56. (8.) $3.36
per day. (9.) $3915.96. (10.) 3 ft. Sin; 18341^4^ Iba.
XL— Page 74.
(1.) 5d. a pound.
(2.) Before the Strike :
• 52 weeks' wages at $6 per week, - - $312.00
Savings at the end of year, - - - - 10.40
52 weeks' expenses of living, - - - $301.60
After the Strike :
Wages, 52 weeks at $6.80, - . - - $353.60
Expenses of living, &c., increase 10 cts.
in 40 cts., gives an additional increase
of $75.40 to $301.60, and yearly ex-
penses $377 00
Instead of saving— in debt to amount of - $23.40
(3.) 4 revolutions of the larger wheel are equal to 5
of the smaller, which can be made in running 60 feet.
(5.) 99-i-V (6.) 199Jg? yards. (7.) .067 is more nearly
equal. The first is less by forty-eight one hundred-thou-
ll
16
RESULTS AND HINTS FOR
Bandths; the latter is greater by fifty-two one hundred
thousandths. (8.) He gains 5 cents on the pound or
$5 per cwfc. (9.) 12|| days. (10.) 8^f months.
XII— Paf?e 75.
(1.) lOT^^mVffi UMl (3.) 3rd June. (4.)
3cwt. 3qrs. 18. libs. (5.) 39 J miles; 80 miles. (6.)
4 days. (7.) j%. (8.) 40 francs. (9.) 62 yds. 1ft.
(10.) 514 minutes. The man would have rowed in still
water 4^ miles, in the 1 hr. 12m.; hence stream flowed
I miles in that time=| miles an hour. Rower's rate
down the stream would, therefore, be 4§ miles an hour,
hence, &c.
XIII.— Page 77.
(1.) $16.10xV (2.) 261|| lbs.; $313.69if (3.)
37^ cts. (4.) Read " what must be subtracted from " ;
AVh- (5-) .0338235. (6.) 63 pupils. (7.) £15 16s. 3d.
(8.) 55 lbs. 6 oz. 14 dr. (9.) $0.32^%- (10.) A, 10 ;
B, 20.
XIV.— Page 78.
(1.) $4000 average yearly gain in 7 years. (2.) If
the second has 1 share, then the first has 3 and the third
lias 4, and sum of all is 8 shares, and value $4000 ; they
are $500, $1500, and $2000. (3.) 7 workmen at $10 a
week, 14 at $6.30 a weak, and 77 at $2.80 week. (4.)
3600. (6.) 45 gallons. (6.) l^f inches. (7.) .127 lbs.
Troy. (8.) 200? (9.) $159.6875. (10.) IJf hours.
XV.— Page 79.
(1.) 18. (2.) 197 yds. 6 ft. 54 in. 284 yds. 2 ft. 1^ in.
(3.) 371280. (4.) :ililh' (5.) 216000. (6.) 1411141.2.
(7.) 2333. (8.) $15.38-i«^. (9) £27 6s. (10.) A gets
$36; B, $60; C, $67.60.
EXAMINATION PAPERS.
17
undred
and or
BS. (6.)
in still
xn flowed
rer's rate
an hour,
ed from";
15 16s. 3d.
0.) A, 10 ;
(2.) If
id the third
4000 ; they
n at $10 a
week. {^')
7.) .127 lbs.
^ hours.
XVI.— Page 80.
(1.) 16§pks. (2.) 92. (3.) 252. (4.) 49896 ; 17.
(5.) $1500. (6.) 65.367. (7.) 27.05. (8.) $34^3, loss.
(9.) lib. 11 oz. lOdwt. 20i£fgrs. (10.) Art. 168 :
$82.03.
XVII— Page 8i.
(1.) The gi*eatest weight is 40 grains; the least 175
lbs. Troy, or 144 lbs. Avoirdupois. (2.) 68 weeks
3 J days. (3.) The shorter course is to add J of the sum
to 13 times the sum, £89 6s. l^.Jd. (4.) $100 bequeath-
ed gives $90 to legatee, or he receives $90 'for $100, or
$1 for $Yi/^, and, therefore, $1000 for $^^i^ or $111^
the sum to be bequeathed. (5.) $1.50 on $4 is f of
whole; J is, therefore, lost; whole debt $802.80. (6.)
Meadow and arable land is ^4-|=f o > *^® rest ^3=1 ac.
3r. 26 p. =306 poles ; and ^^,=18 poles .'./^ or i=144
poles, meadow; and \^ or |=270 poles, arable. (7.)
$2.98. (8.) $640. (9.) 203^^. (10.) The $3 hat; $3.28.
XVIII.-Page 83.
i (1.) Art. 66. (2.) $536.32; 16^ cts. per lb. (3.) J.
|(3.) 4 yds. 5 ft. 16 sq. in. (5.) $497.973^g; $435.72^ ;
l$392.633Vg; $293.67^^. (6.) 5 f cents. (7.) 668 ac.
113 p. 14 yds. 2 ft. 72 288 in. (8.) 48 lbs. of each. (9.)
%137.98|. (10.) 14h. 46min.
8. 2 ft. li in.
) 1411141.2.
1
■a
XIX. - Page 84.
(1.) Read 7000 grs. instead of 17000 ; 42500 grs.; 708J.
12.) $30.30. (3.) 1000. (4.) $6187.50. (5.) $6. (6.)
(10.) A gets §815; $12. (7.) 288. (8.) Read 2 in. instead of 3 in.;
^54186 times. (9.) $24000 ; $36000. (10.) 1000 bushels.
B
18
RESULTS AND HINTS FOR
XX.— Page 85.
(1.) To buy one acre from each required
$145; then No. of acres bought is 53215^145=367.
(1.) Each sack must evidently contain a common measure
of 66 and 90 bushels. Hence 2, 3, or 6 bushels. (3.)
Art, 71. (4.) 2|ff§^. (5.) 20| lbs. ; 171flbs. (6.)
1368 yds. (7.) 6^1 days. (8.) g of an hour. (9.) Art.
101. (10.) 1000 acres.
XXL— Page 86.
(1.) 4 days. (2.) A^if (3.) 19ycts.; 1104J yds. ;
$212.08J. C4-) 206/^ fbs. (5.) 1 h". 1 min. (6.) 9187.
(7.) 4.4115; 16.
XXII.-Page 88.
(1.) 198990 inches. (2.) 33x24x72x11X13. (3.)
1619. (4.) 352. (5.)2,\days. (6.) 3 pints. (7.) 1709.
(8.) £1 3 s. 4d. ; 3s. 4d. (9.) $100000. (10.) 840.
XXIII.-Page 89.
(1.) $12.5. (2.) 2 m. 4 fur. 14 r. 5 yds. 2 ft. Sin.
(3.) $12000; $16000; $7000. (4.) Ifggg. (5.) 25
seconds; 75 yards. (6.)/2. (7.) 8.65. (9.) ^1625 7s.
9fd. (10.) 51.
XXIV.-Page 90.
(1.) The factors of the multipliers are 6, 7, 11, 12.
(2.) $30.98. (3.) Man's share, $4; woman's, $2.66J;
child's, $1,331 (4.) 29 yds. (5.) $21.66f (6.) J^.
(7.) Multiply numerator and denominator by L. C. M. of
3, 4, 8, and the fraction becomes |f ; 562.1. (8.) Whole
cost =$440 ; and to make a profit of $150 the whole must
be sold for 440-|-150=$590. There was sold J of
EXAMINATION PAPERS.
19
=367.
leasure
.. (3.)
. (6.)
.) Art.
) 9187.
3. (3.)
.) 1709.
HO.
't. 8 in.
(5.) 25
1625 78.
, 11, 12.
$2.66J;
(6) if
C. M. of
.) Whole
lole must
aid \ of
(34-f46)=20yds., for (5J-f-lJ) X20=$136. The re-
mainder, 60 yards, must bring $455 ; hence it must
bring 455-f-60=$7/3 per yard. (9.) bO cents. (10.)
156lf days.
XXV.— Page 91.
(1.) f. (^.) 1000. (3.) A's, $1500; B's, $4500.
(4.) .00000032; .00081; 3. (5.) $76,495 gain. (6.)
$36,165. (7.) 216. (8.) 15 ft. (9.) A gets 35 cents;
B gets 5 cents. (10.) 6 years.
XXVI.-Page 92.
(1.) $337680. (2.) Oistern filled at rate of 325X2—
100=550 gals, per hour; number of hours in which it
would be filled=15000-t-550=27T\ hours. (3.) The
G. C. M. of the numbers, which is 25 yards. (4.) The
quantity purchased by the first is ^j greater than that
purchased by the second. (5.) S^^y. (6,) 11^^^. (7.)
123|| sq.ft. (8.) Gains $7.50. (9.) $2000. (10.) 46.
XXVII.-Page 94.
(2.) 60 cwt. gunpowder, 9 cwt. charcoal, 6 cwt. sul-
phur. (3.) .056875. (4.) 24000. (5.) 210. (6.) |o ;
.00000292035. (7.) 47^^. (^.) Hf,', ^UUh- W
$2256.964 (10.) 3 days.
XXVIII.~Page 95.
(1.) $1675. (2.) The required number of rods must
be a common multiple of the three given numbers. The
least number of rods is 252. (3.) 2 f. 23 p. 4 yd. 2 ft. 4 in.
(4.) $376. (5.) First, one half-penny is the gain on
three half-pence ; the gain is, therefore, J of capital, and
gain in £100 is £33J, or 33J per cent. Secondly, one-
half-penny is the gain on four half-pence ; the gain is
20
IlESULTS AND HINTS FOR
i of the capital, and the' gain on £100 is £25, or 25 per
cent. The difference is 8J per cent. (6.) Art. 67. 638,
684, 667. (7.) 15. (8.) .0137507f |. (9.) 0. (10.)
13^ days.
XXIX.-Page 96.
(I.) £U 16h. 5j%%\d. (2.) 120 days; the clock that
loses 3 J sec. in 12 hours will show 14 minutes to 2 o'clock,
and the other 16 minutes past 2. (3.) ^\\. (4.) .C0064.
(5.) 633f. (6.) A, in the ratio of 25:24. (7.) }.
(8.) $4.05. (9.) 12300 ; 2^^. (10.) A, $5400; B $4600.
(11.) 33^ cents on the dollar.
XXX.-Page 97.
(!•) lUh' (2-) 6788574 gals. (3.) £6 15s. l-^^%d.
(4.) 16000000 cub. ft. (5.) If. (6.) 13^. (7.) £26
Is. U^d. (8.) 24791 cub. ft. (9.) 30 miles. (10.)
$6.75^.
XXXI.-Page 99.
(2.) ||. (3.) 19/39^ cts. (4.) 64.35J. (5.) 7.757751*8.
(6.) A 12 days; B. 16 days. (7.) $416.70. (8.)
.0820yV7Vo- (9-) 55^3^^. (10.) $395.92^.
XXXI I.- Page 100,
(1.) Art. 225. (2.) 407 rails and 72 lbs. left.
(3.) 1.5416. • (4.) -J^y,V (5.) $430.26f. (6.) 400.
(7.) 868 Jg. (8.) 127f perches. (9.) 14 gals.
(10.) 13s. 9^9d.
XXXIII.— Page loi.
(1.) 3|J§. (2.) $19554.174. (3.) A gets $30.40;
B $18.66§ ; C $14.93J. It will be found that ^ of the
work is done when B and leave ; therefore, | of $56 is
to be divided in the ratio of -^^, Jvj, j^g ; and A gets re-
maining J of the money in addition. (4.) 1.6094 ^^^^^-
EXAMINATION PAPERS.
21
5 per
638,
(10.)
ktliat
'clock,
:0054.
(7.) I
142/1
.) £26
(10.)
577518.
(8.)
)S. left.
;.) 400.
4 gals.
$30.40 ;
I of the
of $56 is
gets re~
9i} kilos.
(5.) $720.51. (6.) $1800. B's savings are seen to b3
$1100, or $550 for a year; annual expenditu>*es are, in-
come — 300, and income — 550, and one of these is | of
the other, .*. <kc. (7.) $1584. It will be seen that the
average per cubic yard is 15 cents. (8.) 500. (9.) 420
miles. (10.) 100.
XXXIV.-Page io2.
(1.) 346. (2. ^J. (3.) Taking 4 for numerator the
fractions are y2g5j.-gy^,.-g3l7.¥??ff.-T5iZ75.-s32'7- (4.) A
19, days; B 18 days; C 36 days. (5.) 25. (6.) 26^/^
(7.) $292.74 nearly. (8.) 18 miles. (9.) 1583^^^^%%%%%'
(10.) 12§.
XXXV.-Page 104.
(1.) 17|. (2.) Iff. (3.) II of a day. (4.) $10140.
(5.) 66j§cts. (6.) 12 hours. (7.) 23^3 days. (8.) A
$1260 ; B. $1120. (9.) Eldest son $2400 ; second $1600;
wife $3200. (10.) 3.22yVg. (H.) $2.18|.
XXXVI.— Page 105.
(1.) I (2.) $14.31JV. (3.) 29 of each. (4.) 281^
inches. (5.) 135535656 sq. inches. (5.) 27 miles 3 fur.
36 per. 2 ft. (7.) -\K (8.) $2250, (9.) $145. (10. U,
hours.
XXXVII.--Page 107.
(1.) }|t>9.33f. (2.) 612304 gals. (3.) 40" 38f". (4.)
$4000.40. (5.) ii 192937 15s. (6.) When the servant
bought at the prices $40, $5, $50, to obey orders he must
spend the L. C. M. of $40, $5, $50, which is $200 on
oxen, the same amount sheep, and the same on horses,
and .'. he must buy 5 oxen, 40 sheep, and 4 horses.
Had he bought at the prices $40, $5, and $60, he would
T
92
RESULTS AND HINTS FOR
only have had to spend $120 on each, and .*. he would
only have had to buy 3 oxen, 24 sheep, and 2 horses ;
he, therefore, buys two oxen, 16 sheep, and 2 horses
more than necessary, and these at the forfeit prices $2,
$1, and $4, cost the servant $28.
(7.) A 10.15 a. m. A has evidently gone 10 miles,
and B gains 2 miles an hour on A, and .'. will overtake
A in 5 hours, or at 3.15 p.m., and will have travelled
50 miles. C must, .'. travel 49 miles or 4J hours, and
/, must start 4 hours 6 minutes he/ore 3.15 j>.ii». or
at 11.10 a.m. (8.) $340.40. (9.) 6J lbs. (10.) 26 ft.
^jj inches.
XXXVIII.— Page io8.
(1.) Divisor 25, dividend 541, remainder 16. From
the problem the dividend=33 times the remainder-fl3;
but the dividend always=divisorXqwotient-j- remainder,
and since quotient is 21, and divisor=rem.-j-9, .*. 33 times
rem.+13=2lXrem.-|-21X9+rena., from which rem.=
16.'.divisor==16-J-9=25, and since quotient— 21, the
dividend=2l'x 25+16=541.
. (i-f-4) (4-i)X9999^^T7-_. .
G^2i4-4)X2iXl000.
4iX3|X(10000-,,^,) .
■" 3} X 2^X1000.
=? (12??9— till)-
1000. "
=20 ^-y-fVoo'
=19+(1-,,Vtoo).
(3.) Bead two games instead of ten games. The three
games are the same as if A should lose one game, and then
A's money diminished by 10 shillings=| (B's money -f
(2.) Fraction:
EXAMINATION PAPERS.
SB
10 shillings) .'.A's money= J B's money +-'3<i shillings4-
10 shillings. But A's money=4 times B's money, .'.4
times B's money = J times B's money-f^a" shilIings-{-10
shillings.
Or I B's money =J-p shillings.
Or B's money =20 shillings.
.'.A's money =80 shillings.
(4.) The G. C. M. of 119 and 153 is 17 which is the
number in ea'^h class, and .*. there will be 9 classes in the
lower form, and 7 in the upper form, or total number of
classes is 16.
(6.) y'j. (6.) Cost of wine is $200, and as he clears
$25, he must sell it for $225. But he sells it for $2.25
a gal. .♦. he sells 100 gals., but each gal. by using a false
measure, contains 3|| quarts .*. 100 gals.=99 true gals.
Hence he keeps one gallon for his own use.
(7.) It is evident that the number of cents is equal to
the number of boys X70-|- 16X30; again the number
of cents is equal to (No. of boys-|-34) 20 ;
.*. No. of boysX70+480=No. of boys X 20 -j- 680,
or No of boysX70=No. of boys X 20+ 200,
or No. of boysX»''0=200;
.*. original No, jf boys=4. (8.) $4653.11.
(9.) Let the value of the estate be the unit; ^
then the first son has J+^,
" • " second " " i— ^,
" " third « - I (Hi),
,•, the three sons together liave —
(i+i)+(i-^)+S(i+^)=i§
•*• if 4~$300=1, value of estate.
;. .', = 300,
or value of estate = $8100,
(10.) $741.25.
mmm
mmmmm
24
BESULrS AMD HINTS FOR
XXXIX-Page 109.
(1.) 207192591. (4.) No. Multiplier cannot bea c -
Crete number. (5.) 34yy^. (6.) $12.54J. (7.) A, 64}j
B, 33i. (8.) I$3840. (9.) 3J days. (10.) 100 gala.
XL.— Page III.
(1.) 31 per. 14 yds. 7 ft. 91 inches, (2.) Read find
dividend 944. (3.) $9.20. (4.) .1159|^. (6.) 64^..
(6.) 3^ ft. (7.) A, 75 ; B, 50 ; C, 25. (8.)
(9.) $2880. (10.) $1250.
EXAMINATION PAPERS.
26
CHAPTER IV.
THIRD-CLASS PAPERS.
I.—Page 112.
(1.) 701014000120014009. (2.) 8 years U
months 13 days 19 hours 6 minutes. (3.) G C M =51
(4.) L. C. M. = 297J. (5.) 21§igg. (6.)' Diff. = 3 r.*
9 per. 27J yds. (7.) 630 acres. (8.) SUi, :^ 28
HUUh' (9.) 6.152625, 16.21065625, 17.8654: (10)
!!^l-2l2% cost per C. (11.) $2794.93 + . (12.) |4316|j;
1952*y.
II.— Page 113.
(1.) £16 17s. G^Vod. ; £621 13s. 7d. (3.) U. a )
$11056.10. (6.) By the Unitary Method we get
(216 X 30 X 7i X 9,^) - (25 X 228 X 12 X 4) = ej ft
(6.) 4i| yards. (7.) 80H. (8.) $8.76. (9.) 105
gives 6 com. 5250 - 21 = 250. (10.) $412 32J.
III.— Page 115.
(1) 11^. (2.),V (3.)$293.12j-V (4.) A $1875.
B $2475, C $3150, D $3000. (5.) $332.03J. (6 )
$24.32i. (7.) 6i|. (8.) 150 gallons. (9.) $16,681
(10.) $231.48^^ ^ ^ '
IV.— Page 116.
(^•) T%V (2.) $9/g. (3.) 2.4635355427434;
.47100370. (4.) 7880^^2 ft,
26
RESULTS AND HINTS FOB
I
•»'
r,
?-:
(5.) True discount $42.41.
Bank " $45.20.
difference $2.79.
(6.) $150.46§. (7.) 20000 men. (8.) 276 shares.
(9.) 117j|, 882/,. (10.) 384 shares. (11.) $28350.
(12.) $4000.
v.— Page 117.
(1.) £3 17s. lO^d. (2.) $11.80, $17.70. (3.) j%\,
(4.) 58 cents. (5.) $5.06^. (6.) A's $3^, B's $2,
C's66f cents. (7.) $310.08. (8.) $1535. (9.) $175.50.
(10.) l.;?.^. (11.) $1267.93^.
VI.— Page 118.
(1.) 3}. (2.) 2997 H; 24003
(3.) A child $14.40 ;
A man, $33.00 ;
A woman, $33.60.
(4.) $16800. (5.) 16 ft. 6 in. (6.) 22^ days. (7.)
$39.46^. (8.) $60000. (9.) $108. (10.) 58J4, %.
VII.— Page 120.
(1.) Expresssion=-V- X i^ X JSI^^eflf (2.) 12
dozen of each ; $2.39/., $4.79 1, $9.58^.
(3.) $lX($240--$.96775)=$247.998.
(4.) A'ssLare=H5V«=;h'5; lfa=B'« and C's, &c.
A's share=$16700. (5.) Pres. worth of 600 ($1.30) for
6 mos. at 8%==625, and 625 - 20=605 cash value, .*. loss
$5. (G.) 17s. 9yVd. (7.) 300 barrels. (8.) $7.50. (9.)
3Uil yds. (10.) $1426.17f.
VIII.— Page 121.
(1.) 5s; .0853333357619047. (2.) .^9.84^, IJ must
pay A. (3.) Amount earned by 1 man, ij women and 3
EXAMINATION PAPERS.
27
«7
Ten-
children in 6 days = $20.66§. .M24-^20§=6 men, 18
children, 12 women. (4.) 40%. (5.) 3692/^. (6.)
Work done by A, B, and C respectively will be in pro-
portion of i§, i|, i|, &c. A 26J days, B 35|, C 28?.
(7.) 20 head more at original price would have cost
800+200=--$1000 .*. 1000-4-20=150 original cost, &c.;
and 2000h-50=40=No. cattle. (8.) |97.9-f-. (9.)
j19^ miles distance, .*. Iff yds. (10.) P. W. of credit
price=|| of credit price=cash price .*. ratio is 50 : 53.
IX.— Page 122.
10
(1.) 1st expression=5^ ®^
"3"
85
I o 1027
71
T(50S«
12 ' 15
2ndexpression=|^ .'.
(.2) .0253 is a factor of numerator, and .025^ of the
denominator, and the expression = 4 x .025 = .!;
2.72637. (3.) /gV,,. (4.) §g of cost price=^g of mark-
ed [.rice, «*rc., $4.60. (5.) 360. See solution 6, page
12, "Ex. papers." (6.) We have altogether 345 ft. of
pathway 5 ft. wide and 62^ x 345 x 5 -^ 9 = $119. 79+
(7.) Expenses=$560 .-. net profit $2260, A's gain=JLj'-
of B's=$1250 ; B's=$750 ; .-. $260 for managing. (8.)
6^% ; 15 years. (Sols. 4 and 6, page 8, "Ex. papers.")
(9.) $2480. (10.) $1732.50. (See Sol. 8, page 8,
" Ex. papers.")
X.— Page 124.
(1.) 5W (2.) 12 days. (3.) $3106.521+. (4.)
526J gulden. (6.) S^fg seconds. (6.) $1278J. ir)| fi?
(page 17 "Ex. papers"). (7.) $5949.69^3. (8.)
A^ per cent. (9.) $.5.49. (10.) UOlUm. j^^/^S/^^^^ ^^
XL— Page 125.
(1.) .025. (2.) He will save $80,47i by purchasiu;^
28
RESULTS AND HINTS FOR
demand h\\l (3.) 3 inches thick. (I.) 1000 Iba. (5.)
$455.57.+ (6.) 131. (7.) 80 %. (8.) 60. (9.)
10i3i yards. (10.) $750 per ton.
/ XII.— Page 126.
(1.) A 504, B 252, C 168, D 126. (2.) 8.145 -f
(3.) 11349.89 tV (4.) $48.45. (5.) $l.ll.t«3 por lb.
(6.) 51 oz; XUOs. 6d. (7.) 12^^. (8.) $667.33J;
33 cows, 10 oxen, 13 horses. (9.) Neglecting value of
alloy, an ounce of gold is found to be wortli ^^3*^* wnd
an ounce of copper to be worth skVAii J ^"*' *^^ ^^* A- voir. :
oz. Troy : : 175 : 192. We have then required ratio=
vsp^^'ir^^ni-'fir. im a $4ooo, b$6ioo,
C $7000.
XIII.-Pa«:e 128,
(1.) 9 : 31. (2.) $«i600 stock (see 24, page 33 Ex-
amination papers). (3.) $20. (4.) $118.08, $134.40.
(5) $744. (6.) 3149/,, 1^;(7.) 6j%. i^-) ^^ cents a
stone. (9.) $a«^^(lt)0 Amount of alloy in 100
8OVS. = 1027.058.?. grs. at 5s. 2d. an oz. Amount of
silver =11297.641... grs. at £3 17s. 9d. £100— the sum
of these values = £7.948+.
XlV—Page 129.
(1.) ^|. (2.) .004. (3.) ,V (4.) 1209.50. (5.)
$108. (6.) 96 bushels. (7.) 10 days. (8.) 80 lbs.
tea, 10 lbs. coftee. (9.) 62^ cents. (10.) 1^.
XV. -Page 130.
(1.) 1.93959183673409387; .0581877+ton8. (2.)
£65 15s. 9/gd. (3.) True worth=:£216 14s. 6i|;}Jfd.
Mercantile value=£216 14s. lid. (4.) $3078 stock.
(5.) $50000. (6.) $4166:1. (7.) 4%, 5%. In
railway stock his income is J^ of his stock ; in 2nd case
income is ^XM-^X ,'„=-,?„ ,^c. (8.) 50 cents. (9.)
12 days. (10.) Will lose 8.81 per cent.
EXAMINATION PA I' K 119.
20
XVI. -Page 132.
(1.) J. (2.) 158. 10' 0(1. (3.) A $11.50, B $5.75, <0
$9.20. (4.) A $500, 11 $100,0 $1000. (5.) 15 nip.n,
20 women, 24 clnUlron. (0.) ^ milo an hour (hoo 11,
page 26 "Ex. PapoiH"). (7.) 42«%. (8.) 0.;^./,%.
(9.) 1G974.5U3 cubic t(M)t (10.) 150, 100 at oacli into.
XVI I. -Page 133.
(1.) J. (2.) $90. (3.) $()fiO. (4.) 402 apples.
(6.) 8', Icot. (<;.) 1:10. (7.) 10 ininutos. (8.) 5 tiincH.
(9.) ,V,. (10.) 3,^%
XVIII Page 135.
(1.) 1097.00,^,^. (2.) 1 (lay 3 lir.s. 52 minutes. (3.)
5.0420108. (l.)$r)0O. (5.) -pi f^ of furlong. (0.) 33J1%.
(7.) $19,512. (8.) $217,344-. (9.) 188 oz. (io.)
$6.30.
XIX. Page 136.
(1.) 0. (2.) 2584. (3.) 8.95-fHliillinga. (4.) .3
sliillings. (5.) 720.i^J^|8. (0.) $400. (7.) 4 fur-
longs 16 p. 4 yds. (8.) $8; $16. (9.) 27^\J^^%%.
(10.) 23885^ (lays.
XX. -Page 137.
(!•) ooWogJ U\l' (2.) 130.8G-|-imperial gallons.
(3.) y^.' (4.) -fVa of months' price-r.$4.70,.-.that
price is $5, and $4.80 is 3 months' price ; $4.80 - .95/3
--.$3.8l,8j=cnsh price .•.gain%=:-30. (5.) 180 years,
95%. (6.) 08 yds. 1 ft. 4 in. (7.) -f;^^, .-^^ j stock 96.
(8.) $96.3. (9.) 5|% (=j'^) lost .*. selling price of 1st
=$18. 31|% (=3 /,) gained .'. selling price— $35, and total
=53 against cost $43,-.gain%=23]i. (10.) 2;^g lbs. '■"^.
lead, 7|§jof tin.
1
i
30
RESULTS AND HINTS FOR
XXI. -Page 139.
(1.) «,V (2.) $205.51^. (3.) $4.50, $5.50. (4.)
$2G77.72^«fJ. (5.) !),•„ milos. (6.) « inoi.t,li«.
(7.) $4.20, $3, $180. (8.) ^Jj^oo gminH-=l sov.. or
7G800 grs.-=023 sovs.i.e. 13.\ llw. -:023.-.4O lb8. = l80U;
Ans. 46. (9.) 16 bushels. (10.) 15 a.
XXI I. -Page 140.
(1.) 70 gallons. (2.) $1.20. (3.) $500, $750,$G25.
(4.) D's $1200. (5.) $7400. (G.) 6 liours. (7.)
$34.6G§; $50. (8.) A $G75, B $G00, $500.
(9.) No. ■/24-|/3<|/10. (10.) By tlio common way
of reckoning there is neither gain nor loss. In reality A
gains, for pres. worth of 100 clue 3 months h(uico-[-P. W.
of 100 due 9 mo:=». honco is greater than the P. W. of 200
duo 6 months hence.
EXAMINATION PAPIM.
li\
ClIAPTIOU V.
SECOND CLASS AND INTERMEDIATE.
I.— Page 142.
(I.) I60/. «iv08 loHH Ol' lj"fl.*. I givOH loHH of ^\^ff,
and ^Y« of 173.92 :*7«^2. (2.) $14 1105 1^|. (3.) Ex-
inrHHion = |6-f-, ''„-}-« r^ 7.307U285. (4.) A 15g^;
B 12?g; C 2i:f '. (5.) Tlnwotical. (0.) \i--,% of j|{
=A'o .'. ^o«R=^tL J ^^%- (7.) PrftH. wortli of credit
price---=!|0.11);;|]'j .'. loss on oach l)bl.=10j,7!y centH : he
will gain $263.16.{}J^. (8.) $7480 »«. (U.) Decreme^
72.9. IncimK0.=9().G. A^«< increaHe~23.7 from 2600;
andlOOgiveH.968%. (10.) $94G0«. (11.) Hyp.--:50,
and line joining rt. anglo with middle pt. of hyp.=lialf
the hyp.==25. (12.) 3XHquaro of breadth==11346.76.'.
breadth=61.6, lengtli=184.6.
Il—Page 144.
(1.) Theoretical. (2.) ExpresHion = (/j+^i — ^g)
-^-1^8=14. (3.)41f%. (4.) 14Ji months, (6.) does
t'^^o in one day. A $9.37}; B $7.60; 0$8.12J. (6.)
$593.70. (7.) 6 oxen, 15 cowh, 75 sheep. (8.) $39.94^.
(9.) $7500=cost of goods ; then /COO (1.10) (1.20) (1.25)
=$12375. (10.) 16^ acres. (11.) 216 and 162. (12.)
3.1416 (1152—00^).
32
RESULTS AND HINTS FOR
III —Page 145.
(1.) Tlieoretical. (2.) 100— 89|^=10|§ %. (3.) $900.
(i.) $1250. (5.) ^§|. (6.) 72, 48, 24. (7.) $5141.
See "Ex. Papers" — page 47, q. 7. (8.) $29.04.
(9.) $6.01f. (10.) A right-angled triangle ; line joining
middle points is parallel to base, and=lialf the base,
«fec., 150.
IV.— Page 146.
(1.) Find G. C. M.; 7 yds. 2 ft. 2 in. (2.) Time loat
in 1 yr.=5 h. 48 min. 49.7 sec. Hence 4th year, leap
year, gives <7am= 44 min. 41.2 se^. (in four years). And
.*. time gained in 100 yrs.=18 h. 37 min. 10 sec, which
lacks 5 h. 22 min. 50 sec. of 1 day ; hence time lost in
ICO yrs.=5 h. 22 min. 50 sec. in 400 yrs.=21 h. 31 min.
20 sec, which lacks 2 h. 28 min. 40 sec. of 1 day; .*. time
gained in 4000 yrs.=24 h. 46 min. 40 sec ; or in 4000
yrs. there will be 970 leap yrs.; (5 h. 48 min. 49.7 sec.)
X 4000=968 d. 23 h. ?3J sec, and 970 d.— 968 d. 23 h.
13J sec =as before. (3.) 2000. (4.) 1 oz. alloy will be
found=y3g guinea, <fcc ; 2|| guineas. (5.) 2.2360679774 ;
l/5-f 1^6+2^/5^ 2.618033987. (6.) $1320; $1452.
]/6 — 1 5 — 1
(7.) 4744.186. (8.) 777857142 tons. (9.) 75 cents.
(10.) $2000 cost of wheat; $3000 do. of barley; $4000
do. of oats. (11.) 272. (12.) 50.
v.— Page 148.
(2.) 1 oz. Troy = 480 grs. 1 oz. Avoir. = 437 J L. C. M.
- 84000 grs. (4.) 42, 1042. (6.) (|ii)"=:3. n(log 81
— iog80)=log 3. i.e. nj. 477121 X4-(.301030X3-|-1) [-
---.477121..-. n = 88yV5. (7.) (1) $1400; (2) 7500;
(3) 12; (4) $4480. (8.) 1275 bbls. (10.) 78f
KX A M 1 NATION I'A PKIIS.
33
VI.— Page 150.
(1.) 120. (2.) Theoietical. (3.) 15 tons. (.5.) 6400
— 213i^6186i| ; P. W. int. on (HSG-; for 8 months
@ 5 % == 206^ ; 213i — 20^ ^ .$7'. (6.) G1)U3.75.
(7.) Selling price to gain 20 % = !)(> .-. J»^ ol
asked price=96 ifee. l.OGlf. (8.) .ill.73-{-. (9.) A's
$1714|; B's 22851'. (10.) 250. See Kx. papeis in
Arith. q. 7, page 17. (U.) .$13^. (12.) It may bo
shewn that the triangle B D C (D being intersection ot
bisectors)=^ triangle A, B, C, tfec. 75|/3.
VII.— Page 151.
(1.) 3-T-yi|=:^yjjOt* invest.=gross income 3'^ of this
income tax. .v^i^^g of 8063=253 income. (2.) §48682.40
rec'd. for the apples $3.25 a bbl. giving 14975^|. See
"Ex. Papers" page 17, q. 7. (3.) $6200.64. (4.)
They make revolutions in 11|, 10, lOJ, 8^ days respec-
tively, L. C. M.=:1050. (5.) Disct. at 8%— No days
of grace— disct. =5*5 of note /. |^=7600=$7755-/g. (6.)
Disct. =5»^ of principal ; then (see Can. Ed. H. Smith's
Arith.) Int.=3';j : for twice time int.=2X;iV=Ti ^^^^^
disct.=T'5.-.^3Xl25=9/^. (7.) Money worth 7%,
stock in B. C. is U^, &c. 1st income=|2000 ; new in-
come 1660.06+. (8.) 20 lbs. at 50c., 20 at 70c. (9.)
"^•^-^^1138. (10.) Difi'erence in favor of circ. exchange=
£2 17s. lUnearlv.
Vlll.-Page 153.
(1.) Theoretical. (2.) =£.6583=13d. 2d. (3.) 945
Xl2X23iX2JXl| divided by 33fX2|X2|X217Xll,
=2 hrs. per day. (4.) (1.02)4— 1—08243216. '.rate %
=8.243216. (5.) 14400. (6.) 4§| ; 5^. (7.) j^ix
l|?ii=$1.31ff. (8.) G. C. M. of 88f9 and 119§|=G.
u
RESULTS AND HINTS FOR
C. M. of nnm'is divided by G. C. M. of denom8.=3f ^
yds. (9.) |99|f. (10.) 160 time8*(7M«re of thickne8s=
2500.-.thickness=2^; height 10, length 100. (11.)
3-S5.58S24 sq. rods=2.4lU ac.
IX.— Page 154.
(1.) Expression --=^ (34.3_|_J^)-21f = j^^. (2.)
For every unit of No. wo get (1.20) (1.16^)=1.40, &c. ;
200. (3.) 100 men. (4.) 4 % loss on the whole ; 10 cts.
alb. on ^=^ on whole .'.4 % =3^ cts., &c. ; 83^ cts.
(5.) Multiply both terms by 8+|/7 gives lO-{-i/5G—
17.483+. (6.) Goods cost $360; B $384 ; A $400.
(7.) A's stock=3iX5 + lf X7=29f ; B's=4X5+l^X
7=29|, &c. ; A's gain 3570; B's 3520. (8.) Creditoi-s
lose 35 cents on | .-. , io+8000=2''^ ; liabilities=|266C6|.
(9.) $16.92y4g. (10.) 300. (11.) P. W. of £1664=1664
Xl00-T-103| which will buy 1676— U.IOjV&t ^^ ^6.
(12.) 24Xcube of length =3000,. -.length 20 ; breadth
15 ; thickness 10.
X.— Page 156.
(1.) $5000; $8750; $11250. (2.) li(6-5-1.07J)=
6|f; {7—ll)-^M=6j%. (3.) 60 at $6; 90 at $5.
(4.) Reckoning from Nov. 1st, 100x0=0, 225X5=1125
&c.; 13^^g days; Nov. 14th. (5.) $100 bought $96;
$500 must bring 540, .-. 100, $108 which is gain 12^ %.
(6.) ^ x4J=4.-. cost would be the same. (7.) Cost
= 10006 ($2.15 4- .3 X -J^ X If X 4^) = 28375 ; returns
= 10000 X -?ji X .30 = $33750;.-. gain = 5375. (8.) 48
men ; length of day same in each case. (9.) 9^^ shillings.
(10.) [a] 6 |/69 ; [b] 73J5 inches.
EXAMINATION PAPERS.
35
XI. -Page 158.
(1.) 2 X 6 X 8 X 10 X 14 >; 135 divided by3x5x7x9x
16=64. (2.) SOj%%%. See " Ex. Papers," page 25, q. 9.
(3.) $100 invoice value costs $125, wb. sells at $112.50
or 10 % loss .-. 10 % +2 %==600; $5000. (4.) 2000 f.=
$377.35 direct exchange; cir. exchange gives -yfy- v V
X .{.O9^!i^369.80 ; $7.55. (5.) Amt. paid on 2nd contract
end of the time=$20520 ; .-. 20520— 20000=:$520 at end
of the time. (6.) $14560 = A's; $12320 =:B's. (7.)
£4953 128. (8.) Sell, price of 1st lot=$700; of 2nd=
$600; 1400—1300=100 loss=74 %. (9.) $99000 new
stock gives income $2475 ; Amt. consols=97826|, wh.
gives income £2934^f ; diff. in iftcome=$459Af. (10.)
(1.) 6 X square of side=2300 ; side=39.15-f- ; lengths
58.73. (2.) Area of second field is 5| times that of
1st .*. circumferences are as 1 ; ]/5^, &c. ; $469.04-j-.
XII.— Page 160.
(!•) 7||f§ %. (2.) £150 15s. (3.) 594| seconds.
See " Ex. papers," page 25, q. 9. (4.) After his 3rd pay-
ment he will still owe $10508.12^. (5.) End of 2nd yr.
his cap. is |§ of original ca]>. ; of this he loses |, leaving
j%%-'.$600=j^ji-\-g\ of original cap., which=20000.
(6.) $861.84+ ; See " Ex. Papers," page 31, q. 20.
(7.) Allowing no days of grace 77^3 X 3^0 ^^ principal=
38.70|f .-. principal=$5221 .85^. (8.) $415 very nearly.
(9.) $l00 ; 105 J buys $100 bond.-. $40000 bonds. (10.)
(1.) Cost of first = 436.36 -f- ; of second $354.55 -j- •
diflFerence=$81.81. (2.) v'450=15v/2.
XIII.— Pa^e 161,
(1.) 1st expression=(5-2)X.£l 10s. 6d. 2nd ex-
pression=(2-|-0) of XI 5s. 6d.; diff.=£2 Os. 6d. (2.)
Reckoning days of grace disc't is for 73 daya=^ year; true
36
RESULTS AND HINTS FOR
5
diso't.==|242% ; int. on t]nH=fjain=:^2i.;^^^ cents. (3.)
$461.20. See "Ex. Papers," page 27, Ex.*^l3'. (4.) $9500 ;
$16200. See "Ex. Papers," page 19, Ex. 13. (5.) $1.87^
=B's; $1.56^=C's; $2.50=A's. (G.) $2190. Seo "Ex.
Papers," page 14, Ex. 11. (7.) 116 lbs. @ 5i, 136 lbs. @
7^. (8.) By 1st method he would pay $1610.51; by tho
2nd, the same sum. (9.) Buying pi-ices 12^c., 75e.;
selling prices lOc, $1.00. (10.) [«] 50-— 40-«=9*'oO=ditr.
of squares of segments, into which required point
divides dist.=120Xdiffce. of segs. .'.diff.=7^, sum=120:
63f : 56|. [6] Sum of sqs. of parallelogram=sura of
squares on diagonals &c., 50.
XlV.-Page 164.
(1.) Expression=£(4 x f i)+(|:^ x -^^^ x f )s.+700d.
=£6 16s. 5d. (2.) A JJyi ; B J.y^ ; C ^ . (3.) 60 acres.
(4.) $380 gain on direct exchange. (5.) $1276=semi-
annual income. (6.) 223% %. (7.) P. W.=$29600 ;
then this ~- by '^'^ and x by 6 ^ 93| gives $896
-^ Too -^ TOO TOO *
net income. (8.) Ratio 1st 6 mos. = 4:5 ; do. 2nd 6
mos.=6:5 .•. = A $60 for 1 month, B do. .-. profit to be
6^M«% divided. (10.) Side=]/2"x~4T40T 30| V9 k 144
=1584|/5.
XV.— Page 165.
(1.) 75^256000=.00029296875. (2.) 4s. 7^ (3.)
(1.05)3—1.15 &c., sum $4899.67 gV (4.) Actual rate
=30—18=12 miles; supposed rate = 30+18=48 .-. {^
of 1 minute=15 seconds. (5.) 2 yds. blue+1 black cost
$-V\&, then $168-T-V,8-=77 yds. black; 164yds. blue; cloth
sells for $184 and $184.07-$158=| J of usual profit which
.-.=$23.70 which is gained on $158=15 %. (6.) £3 16s.
=value
629
6d. (7.) $998.40. (8.) 1^ days. (9-) $5 x ^^^^^^
of gold ; $6X J^==do. of silver etc.; Ans. gSS"*^^. (10.)
1.0044- ; 2ac. 0V26^|/>.
EXAMINATION PAPERS.
87
XVI.-Page 167.
(1.) $1750. (2.) $'1 cost, |1| .second selling price;
37^-^U=30. (3.) A's$28;B's|22.50. (4.) $35. (5.)
(7-5)X No. lbs.=r70-t-30.-.50 1bs.==$5.60 cost. (6.)
127^ miles. (7.) 25 miles per hour. (8.) 50: 51.
(9.) $24.24i-f-i|jx3j^ig=5100, of which 5%=:$255.
(10.) A lost ' ^fB 2 X ''^^, of which each had .-. 50.25
-i-TVo=75.
XVII.-Page 169.
(1.) ToW J 4§2. (2.) /a- (3.) $3.20 a yard. (4.)
$1.30; 52 cents; 19J cents. (5.) 35^ifd. (6.) 16;
L.C.M. of 20 and 50 is 100; then 1600-^-100=16.
(7.) 240. (8.) $2778.30; lOj-^g. (9.) $2222|;
$3333J ; $10000. (10.) $469.33J.
4 .
XVIII.-Page 170.
(1.) £2 Is. 3d. (2.) .£188 6s. 3,»fd. (3.) 127.07
ounces. (4.) C will win hy -^^^ of a yard. (5.) $6.25
a barrel; 8125 lbs. of tea. (6.) — | (7.) 7 minutes in
6 miles. (8.) 5^ per cent. gain. (9.) In Ig^ years.
(8.) 51^ per cent. gain.
(10.) 60 cents a lb.
XlX.—Page 171.
(1.) J. (2.) 405 guns ; 5 rounds in 8 minutes=|
round in 1 min. (3.) Lost $16.80 - $12.48=$4.32, which
divided by 24 cfcs.-(-60 cts.=54 days. (4.) £59 6s. ll^d.
or $286.62. (5.) $5. (6.) 9J %. (7.)$547.50 ; face—
tV ^ 3V5 <^^f«^ce = $538.05 ; i.e. |||7- efface = &c. (8.) 12
per cent. (9.) At first I pay Tj'g of the whole, afterwards
5'^ of the whole minus $8, (int. on $200) and this=| of
former interest, ike. (10.) 3000 days=L. C. M. of the
given periods.
38
RESULTS AND HINTS FOB
XX.— Page 173.
(1.) 2.6583. (2.) $158400 increase. (3.) 58.8 days.
(4.) 1 franc=|.181 : 10000 francs=$1810. (6.) 72
ounces of gold, 24 do. silver. (6.) $2400 ; $3900. See
"Ex. Papers," page 19, Ex. 13. (7.) $1.57 J per. tt).
and$1.33jdo- (8.) 20.39. (9.) $48.45|i. (10.) $450;
$270.
XXI.— Page 174.
(1.) S; f (2.) If; 3ft; hi (3.) ^696 lis. 2d.
Gain=£82 18s. 5d. (4.) 12| months. (5.) $1.53f gfi^.
(6.) .24. (7.) 70 cents a pound. (8.) $431.52. (9.)
($4800 -f $14400) in gold. See Solutions, Sec. IV., prob.
13. (10.) 860.
XXII.— Page 176.
(1.) .2375 : observe that (.0125)'* is a factor of the
numerator, and (.0125)^ is a factor rf the denominator.
(2.) .7U710G5; 7.071065; 42.42639 ; .1414213; 4f. (3.)
A $540; B 1200; C $300; D$180. (4.) 156 yards. (5.)
^^fls' (<5.) 8 minutes. (7.) $18y2_. For 1 year-
(8.) $2 J, and $2 per day. See " Ex. Papers/' page
23, Ex. 4. (9.) $33350. (10.) 3570. In the question
read horses j'g per cent. &c.
XXIII— Page 177.
(1.) f . (2.) 8, 10, and 12 months respectively. (3.)
$1190.70-1-. (4.) Difference in annual income=$37.
(5.) A 10.10 ; P $9.09 ; C 6.06 ; L. C. M. of given frac-
tions =Y, then time is 10, 9, 6, &c. (6.) $744.12.
See Solutions, Sec. V., question 23. (7.) $1997. (8.)
4001bs., SOOlbs., 428^1bs. (9.) .4422. (10.) 55 minutes.
Tec " Ex. Papers," pages 26, 27.
I
EXAMINATION PAPRnS.
do
2d.
XXIV.-Page 179.
(1.) See "Ex. Papers," page 23, q. 4.
It is found
that Id. = 5^1? oz. = ^f grs. /. 1 oz. = 237y'i qra.
(2.) The first says he owns ^ and second ^ of entire
quantity ; the second farmer says he owns |, his neigh-
bour f, .-. |— f (or ^—\)=^\ = 574 acres, .-. total —
1600; .-.1100; 500. (3.) .0047 cub. inches. (4.) 2 hrs.
37 min. (5.) £1222222 48. n^jd ; $23504 6s. 5^|d. (6.)
6% ; $720. See Appendix Canadian Edition of Hamblin
Smith's Arithmetic. (7.) 104 hours per day. (8). ^^
days. (9.) $5375.90. (10.) 15 months.
XXV.— Page 181.
(1). 160-J-1.04— 150 divide by 150^-.5i,=22|%. (2.)
For 1st half he earns 90c. per day and requires ^ of
whole time, and there is | of time left, .*. f x 90-j-g x
110=98| ; loss is .'. 1^ cts. per day or $1 in 90 ; also | x
112J = 50. (3.) (l.00|) (3x98 + 105) =399.975, which
buys 30 five per cents, and 10 six per cents. (4.) 50 per
cent. (5.) $110. (6.) A 16, B llf, C 26f. (7.) Sum
of rates = 80 miles an hour, diflforence of do. = 20 . *.
30, 60 are the rates. (8.) 8000 x 3 = 24000 = whole
stock, of which A pays 9000 B 15000, or 1000, and 7000
more than their shares. (9.) 14 x 2250—15 x 1960-=
2100, which is geometric mean between 2250 and 1960;
ratio = 4 = 14f %. (10.) Amount = f § x 4000.
XXVI.~Page 183.
(1.) $98.80. $100 received for goods gives $3 com., and
on $97, $1.94 com. is received, .•. whole com. = $4.94 ;
and 100— 4.94=: $95.06 .-. $4.49 x (1901.20 -j- 95.06)
= &c. (2.) $7145. See " Examination Papers," page
17, q. 4. (3.) A $304.41 ; B $333.33. (4.) A 8|f ;
B 13J; C 14?f. (5.) £44 lis. 5d. (6.) 4 hrs. 17 min ;
in
40
RESULTS AND HINTS FOR
8 hrs. 34f niin
(7.) $2.97; $1.65 ; $1.35. (8.) $8000.
(9.) 58 @ 60c.; 58 @ .$1.08 ; 29 @ 72c.; and 29 @ 96c.
(10.) Area p/77T44 x~2l x 12 = i/ll'^ x 7" x 4 ^TS*
= 924; perpendieiilav =:^ '-8j|?.
XXVII.— Page 184.
A J sec, B I, C I, D I, E ,«,, F jA , G j| ; L. C. M.
of denoms.i=:23. 3. 5. 7 ; the L. 0. M. cf the first four
of the resulting fr8.=22. 32. 52. 7-.-^ 2K 3. 6. 7=52J
sec. ; it will be seen that the L. C. M. of any other four
of the fractions will he greater than 52^. (2.) He travels
2 miles in 12 minutes; he and the tmin approach
at rate of 2 miles in 4 minutes, or 30 miles an
hour — train 30 — 10=20 miles per hour ; length of train
30 X 5280 X 10-^3600=440 ft. ; 2nd train 15 miles an
hour, length ='*^| §^^=440. Now iind point where
trains meet=:l| miles from tunnel ; 17,^ seconds. (3.)
Gold being 111^; 3375 Xl^ divided by 50000 x 1.2.5=
6 cts. cy. (outlay will be found = $4025). (4.) Row once
each way in 22| min. &c. ; stream will be found to carry
boat l course in 10 min. .*. 1:3. (6.) $169. Honest
gain=:^ per unit, <fec. See "Ex. Papers," page 27, q. 13.
(6.) In sixth line read morti^agee for raortg agor ; P. W.
of mortgage=$3486.85^«f-, ; P. W. of Deb.=$2047.
27j\ .-. balance=$1439.57|0|f (7.) Cost of dry goods
=$7486.36/-; Broker's sell, price of wheat =$7725 .-.
total com. $238.63y'V ; com.=on sales = 14.04/, = t"t%
(8.) $3*332. (9.) 451 x 9 divided In- .2 x 1.25 x 40 x 1.1
=£369.
4.4., /o »
(10.) — ^^ . ^^=10.84+.
XXVIII.— Page 186.
(1.) $120. (2.) B's $80; A's $60. (3.) 6-^3 times
rate of stream -\- d -i- rate do. =2^ hrs. ; rate of stream
EXAMINATION PAPEBS,
41
I
3 miles, crew 6 miles. (4.) For investing the cash rate
= 2V' P®'"^ A> gi^i"** Vi °^* every $1 of pork ; all cash would
bring, com. 21 1| instead of 280 — difF. made up by com.
on pork .-. 68^-j-21 =|i440 ; $3000 cash. (5.) 400 men.
(6.) $960. (7.) 5154.63|f. (8.) Moriey worth 6 %.
P. W. = $1000, and $2000 ; equated time = 6].§| months,
and P. W. of $3100 for this = very nearly 53 cts. less
than $3000. (9.) $9.60. (10.) Walk being outside plot,
dimensions are 81|, 116^.
XXIX.— Page 188.
(1.) Of the 80 gallons 52 are water, 28 wine, hence 42
w. at first, i^^o.. : 2:3. (2.) 1008-j-(l -f ^§^_5§^)=$1000.
Days of grace. (3. ) (1000 x 4—800 x 2) -^ 200 = 12
months back. (4.) 4i miles per hour. (5.) £201.61 -|-.
(6.) The selling prices would be 66c., 84c.; then how mixed
to get 76c.?— 4@60; 5@75. (7.) $26.01 dec. (8.) Through
Paris $223214.28 ; direct 242222.22-f ; through Amster-
dam $281250. (9.) 12 hr. + (120 -^ 40) + 75 min.=:
4 hr. 15 min. time special arrived- in London; 120 -f-
(4 hr. 15 min — 1 hr. 51 min)=50 miles per hr. special
between S. Bridge and London; |^X30=17 distance
from Belle River to Windsor, 26 — 17^=9 = distance
from Stoney Point to Belle River (|gX40— 9) -^(60—
40)=!^ hrs.=time of special from London to Stoney
Point, yx 60=83 miles from London to Stoney Point,
120-f 83+26=229. (10.) $5250.
XXX.— Page 190.
(1.) A $780; B $801^ ; C $426|i ; D $!)91>^|. (2.) 4:3.
(3.). One mile to an inch. (4.) 12, 8, 16 ; 9600 gallons.
Similar solids are as the cubes of their like dimensions.
4-2
RESULTS AND HINTS FOB
(5.) $914.36. See Solutions, Sec. V. problem 20. (6.) 1.
Note that (x- + x y -f y^ ) (x- — x y + y^) = x^ -j-
X 2 y2 _j- y 4, (7.| 23 months. See Solutions, Section II.
problem 8. (8.) 4 lbs. sold for 12c., gain 10%, and li
ttiken off leaves 9y25C.,=cost of flour for 4 lb. loaf when
wheat is $1.10 ; but when it is $1 a bus. the cost will be
ifiX9j\=8|j|c. ; 8ff + l^=9|i, total cost of loaf with
2nd condition: 11 — 9||=: 1/3= gain on 11 cents.*.
100+1523-7-11=9111 ans. (9.) Segments are 4Jft., 7J
ft. ; lengths of lines, 5.57+, 3.307, 4.09. (10.) 19Jy
XXXI. -Page 192.
degrees.
(1.) $3200, $2800. (2.) In the alloy there will be
I oz. silver worth 3X75=^ oz. gold, and there will be -'3**-
oz. gold.-.J/-+^=$51.66f, &c., $15 gold per oz., $1
silver per oz. (3.) 120 days, B earns $4 per day. (4.)
Article costs $100; is to gain $110.*. | selling price X
iSi+i selling prico=110, ori§i selling price=110, (fee.
=$113yyy. (5.) To realize $2000 he must discount note
of $2105/g.-. his profit of 20% will be diminished by
$105/^/. $500+$105-i-Sp=$605Y\ = 20% of amt.; .-.
amount=:$3026. (6.) $50000. (7.) Taxes $32.-. house
assessed at $1600, is worth $2000, and repairs will be
$400 ; .*. his rent, leaving out repaii^s, will be $132 ; if A
be the rent due to taxes, it will be T/rH"(T.T)2 "hd t)3 "I"
(T.TK +(T.T)5 =400, A=±^o,Li^l':>^JL ; j. rent will be this
result+$13:2. (8.) 50 gallons. (9.) 50000. (1^)^—1
=32604—2000, &c. (10.) 50 stumps. 1st year's pro-
duce=22 bushels x$l =$22; 2nd year's=24, &c., total
value of produce=$ 130 — 90=S40, cost of stumjung; 1
stump costs, 1st year, $1 ; 2nd, 90 cts. ; 3rd, 80 cts ; 4th,
70 cts. ; 6th, 60 cts. .-. 5 cost $4, and y- x 5=60.
s
EXAMINATION PAPERS.
43
1^
M-1
s pro-
, total
; 4th,
XXXII.- Page 194.
(1.) A; jh> A; Wso or .000505. (2.) 9 hr. 58jL
min. (3.) 40 at 80c. ; 40 @ 75c. ; 44 water. (4.)
£2yVp (less). (5.) P. W. =450 ~ (1.06)«, do.=360-v-
(1.06)« .-. required bill = (.-^ J|,« - ^j%%\, ) (1.06)^ =
$72.50|. (6.) $1 of 1st costs 1.09 ; $1 of 2iid costs 87 J,
diff.=21J cts..-. amt, of lst--=|82-:-.21J, purchased by
^\''5^i; to which add $22. (7.) 39||| above cost.
(8.) ]J^ after 12; at 12 p.m. (9.) 460- (150-}-yJ^Xl50) =
308.50 to be paid 1 month after due with interest at 6 %
amounting to .$1.54^. Equivalent for prepayment is
made by reducing per-centage of interest. There remains
.f310 principal and 310--(308.50-f 1.541) of interest=
.04^ interest which for 1 month=|.51 per year=^Yu pei'
cent. (10.) .3874259; 2ch. 95.77 links. (11.) P.-j-Prt.
=280; 2 P.+Prt.=300.-.P.=20.
XXXIII. - Page 196.
(1.) i't)%. (2.) [a] $1185.92. [h] $1158.125.
(3.) 7^;/ .f ~ 1 7^=deU should be given. (4.) [a] $2500;
[b] $20; [0] $750. (5.) $30000. (6.) At S.I. none;
at C. I. .243216. (7.) 1 franc=19||c. (8.) $30.46.
(9.) $1.02. (10.) 72.
XXXIV. -Page 197.
(2.) £960. (3.) See Canadian Edition of Hamblin
Smith's Arithmetic, page 179. See also, Appendix. (3.)
$315. (4.) $13.15. (5.) 214 hours. (6.) A recurring
decimal. (7.) £200. (8.) "Ex. Papers," page 26. (9.)
M per cwt. (10.) [a] 30.594 inches, [b] 137254^
=(13725Xl0+4)-=137252xl02-i- 2X4X10X13725
-1-16=18838660516.
Il
44
RESULTS AND HINTS FOR
XXXV.-Page 199.
(1.) Multiplying numr. and denr. of first fraction by
54—40+61 705—32*8
1 3, and of second by 60, we got
4336
i)0^52+133 705+328
(2.) 164.3904. (3.) 45000 Xf^ 8 = amount
68881
of G. T. K. stock he would have received, 45000 XJoBX
-j.^^= 1237.50 income therefrom. Again, 45000 Xi}3=
1467.39283 =income from B. stock. .'. 1467.3923^—1237.50
=-1229.892^3 g^i"- C"^) If «old at a uniform gain of
12| %, he would have gained 2|% less on the 50 yards
than he did gain, and 2^% more on the 75 yards.
.-.Net gain=2^ % on 25 yards=y?/jy of 25=1 yd. :.§
yd. = $2.26y9g ; hence 1 yd. = $3.62^. (5.) 7\ miles.
(6.) 16 days. (7.) SG -34.20 =1.80 :. ^s^ = ^'^^
5% discount off. .'. 34.20 = 90% or -^^,§^=1%. :.^^,'*
X 100 = 38, price required. (8.) From first condi-
tion we find 12 men and 16 boys will work 1 day for
$29.40 ; 12 men and 15 boys will work 1 day for |28.50;
.M boy for 1 day $ .90; and 1 man, 1 djiy=$1.25.
• |165^60 j2 days. (9.) 20 ft. long and lOi
}|1.25x6+.yOx7 J' V ^ 8 2
ft. high. (10.) By this investment I make 50% on my
money. If I invest in the Consols I make 5% per annum,
i. e. 20% in 4 years ; .-. gain, 50—20=30 %.
XXXVL— Page 200.
(1.) The gain on the good boxes must include 10%
of gain on the whole cost, and the 5% of loss on the
damaged boxei^. $^^^-0^i5=|500=tcost ; and the gain on
the whole is $50. $^fi ft X ? X j^ = $8^ = loss on the
damaged boxes. Therefore 850+$8J=$58J; and if
$d8Jis the gain on $^o»^l the g.xin%will be $17.50.
i f
EXAMINATION PAPERS.
45
(2.) 70 cents, the selling price, must include the cost
price, 10% of gain, and the price of ^'tj of every lb. There-
fore, if the tea is mixed at 70 cts. ^ ^ X j ? "^^ ^1 ii cents per
lb., it would simply clear cost. And clearing cost at
61||| cts., if sold at 70 cents would meet all the condi-
tions of the question.
80_61^||=18|g!i loss on every lb. of the dear tea.
61f 1^ — 60=l5|| gain on every lb. at 60 cents.
61§||— 40=215 § J gain on every lb. at 40 cents.
.'.Total loss on every lb. of dear tea=18]gf . Total gain
on 2 lbs. of each kind of the cheap tea=l3g|+21§^| =
Therefore 1089 lbs. will be divided in the ratio
; 2 J 860 : 664x2 j 425 : 664 ; .-.425 : 332 : 332.
of
mm
That is, 425@ 80 cents ; 332@ 60 cents ; 332@ 40 cents.
(3.) $5.eox5 —the amount paid by the men, ^ajY~=
amount paid by the women ; $^-<yy^=amount paid by
the children. Then if we take the number of men as unity,
if the number of women were equal to that of the men,
the sum paid by them would be --W~X§, but it is
Mfi^JL-j therefore the number of women = -^-*y*g^^X
Bo'ifx3X2^^f ^^^^ ^^ *^^® ^^^^^ J ^^^^ ^^ ^^^^ manner the
number of children would be %'- that of the men ; .•. the
whole number would be I -{-'^-{-^.^-=^^-=7 times the
number of men. But 120 — 15=105, went on the party ;
.*. 7 times the number of men=105 ; and the number of
men = 15; and number of women ^-^^'^^=27. (4.)
|-§=the tax on each gallon of crude oil ; §§ X f
=the tax as it leaves the producer ; |-§ X f X | ==
the tax as it leaves the refiner. if X f X f X -|f
X||=the tax on one gallon of the crude oil as it reaches
the consumer, but it now measures only i; .'.I^XfXl
XifXifXf=3.36 cents. (5.) If
gives
$6, $1
m
.ill
i
46
EESULTS AND HINTS FOR
it
■]
\
would give $,-gft, und $105 would give $fi^jyofl_|6 3.^
and this is the dividend paid by the stock. Then if the
stock is bought at 10% discount, $90 will give ^^'^±=
$«g ; and $100 at the same rate will give ^-^yVxg'o""—
7% ; but what was bought at $90 sells for $100 ; .-. $90
gains $10 on the sale ; and $100 would gain 11^ at the
same rate; .-.the whole gain is (T-f-llJ) %=18,'j%. (6.)
The lines joining the centres of the circles form an equi-
lateral triangle ; and inasmuch as all the angles at the
centre of a circle=360'', the equilateral triangle will in-
clude ^ of each flower bed, and taken together=| of one
of the flower beds ; .'.h of the area of one of the flower beds
subtracted from the area of the triangle will equal the
area of the portion between the flower beds. But area
of the triangle=5529.2184 * iches ; and | the area of one
of the flower beds (using |^| as the ratio of the circum-
ference to the diameter) =50 14. 375 inches ; therefore the
area of the portion between the flower beds=(5529.218r|-)
— 5014.375=514.843+square inches. (7.) $^0jQ^-9
=$18000; and $18000+$1000=$19000 capital at the
end of the fourth year. $i^Yo--=^17100 ; and $17100
-|-$1000=$18100 capital at the end of the third year,
and so on for the other years=$15, 904.90 at first. (8.)
In this question, the mortgage is supposed to be bartered
for its value at the end of the fourth year. $-^-i«-Oo^iio>il
,=$500, the amount paid down ; and ($1.08)5 X2000=
$2938.6561536, value of the mortgage at the end of the
fifth year. $39^8.j-5fJ|-3-6JUoi)=$2671.505941,the value
of the mortgage at the end of the fourth year. $1 -j-
$l.l+$(l.l)^+$(l.l)3=$4.641,theamountof one dollar
at the end of the fourth year ; that is, the amount of one
dollar of annual payment. .-.afil^ ;|^f£i.i-=575.6315.
(9.) 60+10-1-20=90% ; .-.the profit is -J^ of the whole
EXAMINATION PAPERS.
47
)'eceipts. But after the fall in the price of the flour, and
rise in the price of delivery, ^X^=i'i cost of flour ; j-'„X
«=J'g the cost of delivery. .-.The whole cost=A| + 5''o4"
^g=10=| ; but if the profit is the same as before this
must=: j% of his receipts ; since i, = j% of receipts, .*. the
whole of his receipts must be I ^ of what they formerly
were. 10X|9=r8| cents. (10.) (a) If $20 be the dis-
count of $200, the same sum will be the interest of $180
for the same time and rate ; and at double the rate, and
double the time, the interest will be $80. Then by the
ordinary rule for discount, ^-%%''-^=$Qlj\. (6) So for
half the time and half the rate of interest, -jg5-=5||.
Xi:XVII.-Page 202.
(1.) jU- (2.) The gain is H of 25 on 95, i.e. 26^^^%%.
(3.) What is paid for 175 is received for 96; /.gain % is
82/^. (4.) The rate of No. 1 is .9995 ; of No. 2,
1.009495. Therefore the rate of gain of No. 2 is .009495
minute in 1 minute; hence No. 2 has been gaining
.g|§;j"j5 minute. 5 p.ii- Tuesday, Ans. (5.) At first
as often as there are 18 sheep there are 3 cows; after 3
cows are driven in, as often as 18 sheep there are 4 cows;
the increase has been 1 cow for every 18 sheep. 54 sheep.
(6.) Deduct discount for 3 days' grace, iffl of i§i = i|^;
bank discount for 360 days, -'-|^ - J-^^ = interest on J-§*
for 1 year. Rate is 5 per cent, (7.) The money must
be paid back out of the common funds of the township.
I^^utjVuWtsuuo oi $920.00 = $48.42tV (8.) Tea,
90 cents per lb.; cofiee, 40 cents. (9.) Divide in the
proportionofl to (1.05)3. $5000 and $5788.1 2|. (10)
Circumferences are ^.s^jj. inches and 3.5.^14 inches re-
spectively. 2 miles 4499^1 feet.
i,H|
III
43
RESULTS AND HINTS FOR
II
XXXVIII.- Page 204.
112s
(1 .) j^ X 96=108%,cost price=selling price of goods
gained on ; then 8 % goods lost on = 4 % goods gained on;
goods lost on = ^ goods gained on - ^ whole. (2.) A
sold 224; B276. (3.) (Tlj"oXf?3X7)+(|S^XjfSX7)
-f 2 = 9.55 cents = whole cost ; j§0X9.55 = 11.9375 cents
= selling price. (4.) £81i|. (5.) TiHTli^^-So = ^fiii8
= 4 gallon = size of his gallon. (6.) {\%^ - -VV/-) = j§£ X
professors = 50 ; 7^5 X 50 = 66 = number of professors.
(7.) $100X-/-= 177| = price of stock, not considering
dividend; $4x^g§ = $3,912 = present worth of $4 of
dividend, to which buyer is not entitled ; $17754-^3.912
= 181.689 = price of stock three months before dividend
is due. (8.) 18.257 feet. (9.) 10§ %. (10.) (a) 6| ;
(6) let p, s, and s' be perpendicular and segments of base,
302 _ 202 = s'2 - s* = (s' + s) (s' -s) = 35(s'- s)^3<yj - 14f =
s'-s; 35-s' + s, from which 8 = 10/^, s' = 24,Sj, p =
17.11.
XXXIX.-Page 205.
(1.) 7; 76600. (2.) Reduce the deciir.o.is to frac-
tions, and divide the numerator by the denominator; the
result is l—|4-(4)2=4f... 2.71828.-. (4.) Resells two
yards for (|f +|4) yds.; .'. the buying price multiplied by
tIISXtuS 8^^®^ *^® selling price; or the gain divided
by Iff f Xto^ — 1> gives the buying price ; hence we find
the cloth cost $1.00 per yard. (5.) 2400 yards. (6.)
$2048.00. (7.) $3132.30. (8.) Total commission —
$1.00 = 1 - j%% = 3\ ; 100 bbls. (9.) ^ i /o. f: \-. 'f.'
(6+3) (6-3) X30X.7854^^^y^^^^^.^
^ ^ 128
tons.
EXAMINATION PAPERS.
49
XL.— Page 207.
(l.)10s.9d. (2.)24min. (3.) 29 boys. (4.) $2400. (5.)
$576.98||. (6.) I consumed, | left, of which ^ is spoiled,
leaving |; ^ more is consimied, leaving f — 5=3^ y ^^If
rations for 110 days consume \l^X^=ih •'' i? — lh^^\i
left=1000 rations for 110 days, .-. 72000 rations at first;
and 720000^180=4000 (men). (7.) A's whole profit
=16754-900==$2575. (8.) (30+10H-4)-^(g»^4-^»f +
4^) =8.65. (9.) See "Solutions," Sec. III. pr. 13.
35 ] 42s<i2oZ502 ••• Joss of 1 cent on j\ at 28 cents, and
gain of 1 cent on ^^^ at 42 ; j% ; ,y\=ll : 2. (10.) In
first case, 11^ %=^.'. | of proceeds=4000 ; proceeds=
4500. In second case, 28^ %=§ . •. f of proceeds=5000 ;
proceeds=7000. .-.whole gain on 9000 is 2500=27^%.
(11.) (1) $121j|i. (2) 927, 772J, 618 (linl-s).
XLL— Page 209.
(1.) Depends on the principle that the remainder is of
same denomination as dividend, 53. (2.) $11.62. (4.)
Multiply numerator and denominator of fractions by a
number that will make numerators 24, and we get ^j\,
V5?> ^vi> ®^ which last is greatest, and second least. (5.)
Quotient is abstract ; remainder .00217085 tons, or 4 lbs.
5.4672 oz. (6.) 81 oz. (7.) Difierence between J/gO
and Yir of sum to be distributed=1000. Ans. $2880.
(8.) $16000 to A ; $31200 to B. (9.) The first way is
equivalent to investing at 3% compound interest half-
yearly, interest being $1218. As the sum to be advanced
on a note of $1000 due 70 (73) days is only $998, the second
way is equivalent to investing at such a rate that $998
produces $1000 every 73 days .*. amount of $1 in 1 year
=(-AW* or 1.06223. Difference between the two ways
D
m
ii
50
RESULTS AND HINTS FOR
1244.46—1218=26.46. (10.) In question there should
be only a comma at " balance," and a period at " lot."
B expects to pay at end of 1 year $75-j-l ytJar's interest
on $160; at end of 2 years $75+1 year's interest on $75.
But he has to pay at end of one year $75 -J- 3 years' in-
terest on $75; at the end of 2 years $75 -|- 4 years' interest
on $75. Excess at end of 1 year=13.50— 9.00=4.50;
at end of 2 years=l 8.00—4.50=13.50. Present loss=
-\W+(V'tfl?2 =$15.74. (ll.)Income=400+^3^-|=800.
At quoted rates $16 invested gives $1 annual income;
.'.sum must be equivalent to $10800. Allowing rate of
exchange to be that stated, viz. £1 =$4. 80. '.sum required
30
8"
XLIL— Page 21 1.
=j.0 8oja
(1.) 10% gain on half=5% gain on whole. Each of
the other transactions gives a loss and a gain of 6^% and
11^% respectively, .'.total gain 10%. Hence $594 is
10% above cost; .*. cost price per bushel is $1.50. (2.)
A has 220 ; B 352 ; and C 320. (3.) Assume a fourth
man, D. to be placed midway between B and and travel-
ling 4^ miles per hour. D is 12| miles ahead of A, who
gains on him at the rate of 1^ miles per hour. /.J-Hs
8^ hours before A overtakes D, and consequently mid-
way between B and C. (4.) Find equivalents at proof
for 1000 gals, at 35% and also at 38% above proof, and
reduce the difference to 35 % above proof ; find its value
at $5.40 per gallon, that is 23A| gals, at $5.40=$128.00.
(5.) Sugar 6 cents per lb. ; tea 45 cents per lb. (6.)
Stock=$15600. A's = $819, B'3 = $234, C's=$351.
(7.) $600. (8.) B's rate -=: 26 miles per day. (9.)
Price of flour per bbl.=$7.00. Agent's 1st commission
h\ % l^^ves Mj% %. Then for every $104 the agent re-
EXAMTN'ATION PATERS.
51
)uld
lot."
trest
75.
in-
rest
.50;
ss=
800.
me;
fce of
lired
ceives$4, .*. for 94^ he receives 3^^; .•. total commission
is 6T^+3^^=8f. Hence merchant loses $912.50. (10.)
'* The square of two sides of a triangle is equal to twice
the square of half the base, together with twice the squarf
of the line joining the vertex and the middle of the base."
Line joining vertex and middle of base= 17.27 nearly,
XLIII.— Page 213.
(1.) 6 months, 9 months. (2.) $8. (3.) Cost=
$4.50X70=315; selling i)rice=$315X|M •'• 315XU|i
_^/70x3X^HX|X3X^g\ ^3^9^^ (4.) Solve by
similar triangles : 30 Ans. (5.) $336 ; $2016. (6.) 25
-«-f X2X|=time second set would take if they worked
same number of hours a day ; but they work half as long ;
.-.their time is 30X|X2=135. (7.) i^gz-V-X3 =
2ii%. (8.) fiXii=|^i. -.$27,561-^1^1 =$25. (9.)
Length and breadth are easily found to be 18 ft., 24 ft.
Ans. 9 ft. high. (10.) (5^ - 33)X.5236Xi§§=13.23871bs.
XLIV.— Page 214.
(1.) Agets$li; B$3|f; C $6|f. (2.) (mXIB?,)
=181 pi'oceeds flour=: amount invested in tea ^y^ ; pro-
ceeds flour=:whole commission=$220, whence $8120=:
proceeds flour, and |§|X8120=:$7900=amount invested
in tea. (3.) 2.|Q.=73j ft.=:sum of rates per second;
^^^'irzzHf ft.=difierence of rates per second ; whence 44
ft. and 29^ ft.=rates per second; or 30 miles and 20
miles per hour. (4.) (J-}-2Xi+3XT'3) whole X rate %
gained on the i=j| whole X rate % gained on the J=26 %
-whole .'.f I rate% gained on the J=26% ; whence 12%=
rate of gain on the J.-. 12%, 24%, 36%, Ans. (5.)
142f yards. (6.) 1568ff. (7.) 37J% and $1.65.
I
<i
■ i I
52
RESULTS AND HINTS FOR
(8.) $3357.031 §^. (9.) The ginss on field and 12 weeks'
growth will feed 360 oxen for 1 wo?k ; or, the grass on
field and 8 weeks' growth will feed 320 for 1 week ; .*. 4
weeks' growth will feed 40 for 1 week ; .'. 1 week's growth
will feed 10 for 1 week. Or 10 oxen can eat the growth
of grass;.'. 30 oxen can eat the first grass in 8 weeks, or
240 oxen can eat the first grass in 1 week ; ^^^=48 oxen
can eat grass in 6 weeks; 48-|-10=58 oxen can eat
grass and growth in 5 weeks. (10.) $7600.
XLV.-Page 2i6.
(1.) $180. (2.) 9h. 21 min. A.M. (3.) $2500.
(4.) 1107|^. (5.) 9^ miles. (6.) 36 boys, 27 girls.
(7.) 5 : 9. (8.) 5 per cent. (9.) Lost $/g, or ^^ per
cent. (10.) 1120.
XLVI.-Page 2i8.
(1.) One side of a square acre is 66 -j/lO ft. The cost
of the four walls, not taking into account the corners,
,4XC6|/10X10X5X2X9
is $
2X45X4
The price of the four corners is $
$660|/10=$2087.10+
5X5X10X4X2X9
2X2X45X4
$25. $2087.10+25=:$2112.10+. (2.) 11^%=^, and
9|%=^/j. A gain of \ of proceeds is equal to a gain of
\ of cost; hence J-f-/2=/2 of cost=$35 ; co8t=$^-^^?--^-
=160; proceeds-=$180. (3.) 43J%=f|. His marked
price on the second supposition is 10 cents higher than
his first selling price, but he throws off 10% of first
marked price, and 10% off 5 cents, or J cent, and he
gains ^\j of his outlay less. Hence -f^j^ of cost — 9 J cents
=^j^ of cost ; Jg^g of cost=9J=J2* cents. Cost=80
cents; selling price, $1.16. (4.) Only $4040 of first
payment will be applied to the stock ; the interest on
$4040 for 6 months, and $2000 for 2 months, is $188.26§;
EXAMINATION PAPEllS.
63
I
iienco the last payment is $1771. 73J, and the rate is
■'Vo%'AW^=6|.|r/,. (5.) $71)^. (6.; $120. (7.) He
would have saved $18 by discounting the note at true
discount. (8.) XS^^. (9.) 189 gallons of wine is equal
in value to 540 gallons of boer. This is sold so as to
gain the price of 94J gallons of beer. The 72 gallons of
beer is sold so as to lose the value of Si gallons of beer.
Hence there is a gain of 90.9 gallons of beer, but the
gain is $27.27. Beer is 30 cents per gallon ; wine is 85^
, , 88X300 124
cents per gal. (10.) innyQAQ of selling price=T7r^ of
124X100X308
cost. Hence selling P"ce=-j-Q^ gg—^Q^-- = 1.44|
of cost. 44|% Ans.
XLVIL— Page 219.
(1.) Breadth of farm will be found to be 41|- rods ;
length 201 §, of which the G. C. M. is f §, giving 44 lots
in length, 9 in width, or 396 each fiXf§=21f]4 sq.
rods. (2.) See Canadian Edition of Hamblin Smith's
Arithmetic. (3.) A makes a revolution in 3.^ days ; B
3|; C 10^ ; D 3|— L.C.M.=462, &c. D travels 210 miles
more than B. (4.) Int.=3'g of sum ; disct.=5^;y (see H.
Smith's Arithmetic, Can. Ed.) .-. 3^— /7=3t||^=$98 .-.
sura=$5700. (5.) 5 yds. cloth, 10 yds. Uning, (6.)
Shares of daughter, wife and sonare evidently in proportion,
1, 2, 4 ; .-. son to 4, wife f , daughter 4. §— f =vfj.=$2400,
&c. If only a son left, dowry=$2 100. (7.) 5 hrs. 32
min. 18,63 sec. (8.) B helped 2/g days, C 3^4^. (9.) $2.50.
(10.) Inc. from Deb. =4^^ of sum invested ; inc. from B
stock=Trf of sum invested : if same sum had been invested
in each, income from stock would have been increased 3^^
of 500=$47^f
€1
j?y=100+47A3, &c. $4700 in
Deb., $4200 of stock (costing $4000). Stock held $4,200
x-l- Of =.1^2000.
if
64
RESULTS AND HINTS FOR
XLVIIL— Page 221.
a) lOs. mid. (3.) tJu of i=;iVocap.=profitof
first, f^jf cap.=profit of second, ^^^ cap.=profit of third ;
.'.profit of first : profit of second ; profit of third II 14:
6:2; whence $1000=profit of first ; $.3574=profit of
second ; $142f =profit of third. (4.) 25 %. (5.) Man $3 ;
woman $2; child $1.20. (6.) | ,r ^ (21120000+26253)3
—211200003 \. cubicfeet=|nr -j (21120000X21146253
+262532) y^ 26253 |- =number of cubic feet of air. }4^X
mfXi"^ -i (21120000X21146253+262532)X26253 [
= 4770080222737777554 lbs.=weight of air (7.) A
$12800 ; B $19200 ; C $24000 ; D $28000. (8.) $257.80.
(9.) XI 19s. (10.) Let p be the perpendicular ; then 3X
4=2 area, andjoX5=2 area; .-. ^ X 5=3X4 ;^=2|,
XLIX. -Paiere 223.
(1.) $700. (2.) A's gain in 6 months is $240, or $1
gains $2'^ per month, B's stock is in trade 12 months ;
.-.each dollar gains ^1 ; then $2400-5-1 J=$l 600. C's stock
gains 640 X. 2'$ per month, $400-^26f=15 months. (3.)
43.65. (4.) $1287.87. (5.) 8% of any sum invested in
stock at 80 gives the same amount as 10% invested at
par. $13750--1.10X.08=:$1000. (6.) 6Hf|. (7.)
Amount of $1 paid yearly=Lj — LL. =4.3746. Amountof
$3000=3000 (1.06)4=3787.4307, 3787.4307^-4.3746=
$865.77. (8.) Ibjll minutes past one. (9.) Produce
the side of A B to E, making a right-angled triangle A
E D. Let x=-=rB C, then (220)»+£c==(880— «)=' or x=
412^ yards. Similarly C D=B E—990 yards ; then hori-
zontal distance from A to D=|/(1210)"+(^412J)», and
EXAMINATION PAPERS.
55
thence distance between tojpa of A and D =
|/J:T210)«+(412J)» H- (18^)' = 1278.61 yards. (10.)
|/1260-5-(5 X 7)=6 ; 30 rows, 42 trees in a row ; 16 acres,
2 rods, 25 poles, 23J yards.
56
RESULTS AND HINTS FOR
CHAPTER VI.
FIRST-CLASS CERTIFICATES AND UNI-
VERSITY HONORS.
I.— Page 225.
(1.) L. C. M. of i|{S i|i»-, ifl^, is -Vt^. (2.) $6545—
$5928.24=$616.76. (3.) $120, and $36 duty. (4.)
llg^iyly, invoice being $877. (5.) August 1st. (6.) Log.
i=:colog. 2=T.6989700;.-.J log. |=L8494850; log. f=
1.8239087 ; .-. J log. J=r. 94 13029— J log. f =0.0312346.
Sum of these=T.8220225. And — fX 1-8220225= I
(3— 2.4660675)=.1067865. (7.) He gained $7686.567
— $7633.588=$52.98. (8.) B has ^'3 of gain in 1 month,
C 4^5 ^^ 1 month, and $42000 for 1 month takes | of
gain, &c. B's $3062.50; C's $5468.75. (9.) 40 —
20|/2 (areas are as squares of like sides). (10.) JX3^
X26X22I sq. chains=457.41696. (11.) 102x7X3^
"^6=256. (12.) Taking slant height 7, radius of sphere
= -^^ ; height (perpendicular)= j/40=2|/10. Contents
of glass=3^X(i)^Xl/40^J. Solidity of sphere=34
IL— Page 227.
(1.) 5\=Gr. C. M. of nums.-5-by L. C. M. of denoms.
(2.) See Canadian Edition Hamblin Smith's Arithmetic.
(3.) 75|%. (1st 91J%, 2nd 86|, 3rd 80, 4th 66§, 5th
70, 6th 60.) (4.) Labor, $750; Materials, $1875.
EXAMINATION PAPERS.
67
Take labor for unU, then l/5-{-2f=|2872.50, &c.
(5.) 1192/g. See "Ex. Papers," page 17, q. 7. (6.)
Gained $1753}^ ; 80X195+4200 (cost of new issue)—
120Xl79y8g. (7.) $3955--.98|=:3994.94. (8.) $647xV
36%=3»Tj duty on -jSfg of co8t=198, &c. (9.) £9 arc
found=$43.40 .-. 3.40-J-40 X 100=8 J% premium. (10.)
1 lb. at each price. See rule, Canadian Edition Hamblin
Smith's Arithmetic. (11.) 31/j, 16||. (12.) Area_of
second is 10 times that of first. '.cost of fencing=750j/10.
III.— Page 228.
(1.) 720 days. (2.) Month=30 days. Discount on
$100 for 2Jg months at 2% a month=$4i .*. 954 gives
2 in 1 month, and 100 gives 2/;y2g=% per month. (3.)
See Canadian Edition Hamblin Smith's Arithmetic. (4.)
Mathematically $6 due in 1 year, $6 due in 2 years, &c.,
and $100 due in 6 years; the sum of these p. ws. (comp. int.)
will give the true result=$82.57+. But if the city be
allowed only 6% on its annual payments, an easier for-
mula is had, viz. : 100 X (106)6 _^ (1.1)6=$80.07+
(5.) 3.544068. (log. 10— log. 2)+(log. 7— log. 10000).
(6.) $1442.9+. See " Ex. Papers," page 31, q. 20. (7.)
Capitals >vill be in proportion of 62, 45, 36 : A, 14926/^ ;
B, $4263/5 ; C, $3410i§. (8.) 7 % cost + 15 % net
gain=:=22 % .'. 1 cost realizes 1.22 ; 1.22~.94=amount
on which interest must be reckoned. ,'. ^^^-Xl'()^=
1.33|:f, &c. 33|| %. (9 .) Eatepercent.=/2X100, &c.
$503.70. (10.) |/99225==315 persons. (11.) 80X4X
2i =$720, Perimeter of rectangle=112 |/10, which
costs ;3796.89+ .'. difference=$76.89.+
IV.— Page 230.
r Dividends at first 140000; afterwards 840000,
&c. 26,000,000. (2.) 1 bushel weight requires {0| mea-
• S
58
RESULTS AND HINTS FOR
sure ; .*. |J J X *t?cV =$4624.49. (3.) Whole oost=$183J;
J of which=jy^XTiAj ^^ selling price, which .*, =
^^Ui^ ^^X336=No. gallons sold; ap/gi^^^-j-J-figW^
65-|-cents (4.) Selling price=14 cost, which .'. :=
87 J cents; .*. on 1 lb at $1.20, he loses .32 J ; on 1 K> @
$.80 he gains 7J, &c., 3 : 13. (6.) 15 months. (6.) 85
days. (7.) (1.045)«— 1 : 24.8+%. (8.) Euclid iii. 35,
6 (2 depth of water+6)=402 .-. depth=130J inches.
(9.) Sum of squares of two sidcs=twice square of half
base -j- 2 square line joining vertex and middle point.
5 i/"IO. (10.) |jr (234-33)=-L4ii;r=volume of required
sphere ; J-|A;t-i-|7r=r» .-. r==3.271066.
v.— Page 231.
(2.) 2\of (f)8 =576, &c. $4166§. (3.) .0306; the
proposed pointing in effect makes the quantity 10 times
less, the multiplier .*. is -1/10=3.162 — which multiplied
into the erroneous result, .009676, gives approximately the
true result. (4.) £3 17s. 10^d.=£3i|§(£l =$4^), and con-
tained j^X 480=440 grs. fine gold .*. $1 contained 440 X
J 6 X /^=25.42+grs. ; by the new rate $1 contained rS^ X
258Xfo=23.22grs., and the former is about 9J% greater
than the latter. (5). Oats 1, barleyli, wheat 2f ; then 1.1+
2.97+1.128=$2599 .*. $500 in oats, $600 barley, $1375
wheat. (6.) Boy 90 cts., man $1.60. (7.) "Deduct his
commission at 2 J% ;" flour sold for ii>^fQ.x%^^Xiji\^
=$6.86+. See "Ex.Papers," page 17, q. 7. (8.) f^ —
13000=4, (fee. ; $12235^. (9.) TV-GV+/g)=?3'ao=
$3_5g8^, &c. $5000. See "Ex. Papers," page 33, q. 23.
(10.) The 4% being at 88|, money is worth 4 J% ; Interest
on £6000 for 4 months at 4J%=£90; gain=£330=5^%.
(11.) Area of figure formed by radii and tangents=r *v^3;
area of sector of circle=^ n y^ . • . area of figure =r*
(1/3 -i«).
EXAMINATION PAPERS.
69
Vl.—Page 233.
(1.) f— ^^=360 marks.-. 2400=aggregate, and 1800
minimum for pass. (2.) In first case 460 roubles«=£40; in
second, £28 . •. broker gains £1 IJ. (3.) First is J (4-f ^7),
second is l-J-y'T, &c. (4.) Taking capital for unit'.^^ — ^^
=||=remainder end of first year; || of || — ^^ end of sec-
ond year, &c.; .*. (||)°-
2 J /2 6\n_
-n_
26
:^5"
n(log. 26
(7.)
5 6-2 ft
log. 25)=log. 2 : n=17.67. (5.) 4|. (6.)
cargo=|900, &c. Owner loses J-i5^6flA_j_|
(112500)Xt1j\f=|26560. (8.) It will be found that 35%
of yearly receipts=$5 40000, &c. Weekly receipts=
$29670|fi (9.) $1 of A's stock gains $3%, of B's ^§, of
C's $^|; B's stock was in trade 2 months longer than A's
.'. ^§ — j^^=z^^ gain in 2 months .•. - in 1 month: A's
8mos.; B's 10 mos.; C's 12 mos. (10.) LaiLfi^7^ga><ii
=2722221 sq. inches. (1 1.) Produce C A to L, making
A L=A C ; join B L .*. B L=K D. But in any triangle
sum of squares on two sides=twice square on half the
base and twice square on line joining vertex and middle
of base; .-. L B2+B 0^=2 A 02+2 A B^ ; B L=K D .-.
K D2=3625. Similarly E F2=2800; HG2=1825.
Area=8250. (12.) 3:1.
VII.— Page 236.
(1.) Asking price=$1.40; reduces this 15%. .M.40
X. 85=1. 19, selling price=gain of 19%, &c. $5263/9.
(2.) $4.8665— $4.84 = $.0265 = gain on $484 = fff%.
(3.) Bank discounts 5300 x J x rate per nnit ; true dis-
count=5300 — 5300-f-(l + ^%)= 1.5900r. ~ (400-|-3r)
53r2_24r=3200 : .-. r=8. (4.) 25% on i=18f% on
whole ; 10% loss on J=2J% on whole .-. 18i— 2J=
AlLO^Oj)x}X
16 J% = real gain=1000 .-. AiLO^<UIXcost ;
60
RESULTS AND HINTS FOR
1
TO
'■i3~ — loss, "^T3 '^TOO — 13" — g**" • • *"SS —
xfioo_76ii. (5.) 5^X100X17^X10000^^23213,3
By direct exch. :£20*5f j- /. gain=£276|gf . (6.) 10160
lbs. of Ist, 16240 of 2nd, 25400 of 3rd ; cost $7620 +
one year's interest $533.40+rent $200=$8353.40-}-5%
of this:=:$8771.07 to be realized by end of year. First
sale=$4572=interest 9 months, $240.03=$4812.03 ;
second sale~$8894-interest6 months,$31. 1 1 J=$920. 1 1 J
.*. Amt. to be realized on remaining quantity=$3038.92J,
which divided by 12700 gives 23^2- cents. (7.) Total
stock $14600. A gets $62^ gain in 1 month ; B $40 ;
C $80; prop.=25, 16, 32: A $5000; B $3200; C 6400.
(8.) At the time of purchase there is due $18, in 6 months
$218, in 12 months $12, in 18 months $212, in 2 years
$6, in 2i years $206. P. W. of these at 8% comp. int.
are $18, $219.62, $11.11, $188.75, $5.14, $169.83. (9.)
By similar triangles and Euclid iii. 36 1 P. Q. X P.B. =
(~^), r,r' being the radii. (10.) [a] 12.5664; [6]
7.79-f'; [c] 78.54; [d^ 3.4641016.
Vlll.-Page 238.
(1.) Multiply bo,h terms of second fraction (in the
brackets) by 2 », of third fraction by 2* , &c. 3. 1 41 59 +.
(2.) (f)4 of capital— $2684=18052. Capital=$10000.
(3.) $5100; $4850. See "Ex. Papers," page 17, q. 7.
(4.) P. W. by Bank discount=P— Prt. ; this in t
years will amount to P — P r^ t^ instead of P ; error=
P r* t* ; .*. error varies as square of time, P and r
being constant. (5.) 6:4. See "Ex. Papers," page 30,
q. 18. (6.) ^%\ (^^ of liabilities + $2000)=fVu <>**
liabilities, &c. Liabilities=$20000 ; assets=$15000.
EXAMINATION PAPERS.
61
(7.) $236/^. See " Ex. Papers," page 31, q. 20. (8.)
J>.ooiixl.04+^^^«|-X.99=10075g\V /. 75^^^ gain.
(9.) Correct solution, as may easily be shown from
analysis of q. 7, page 17, "Ex. Papers." (10.) Depth of
waterX9=36X36 (Euclid iii. 35). .•.depth=:144 inches.
(11.) (a) 84.63+ long; 52.39+ wide, (b) 34.6 long;
25.5 wide; 13.84 thick.
IX.— Page 240.
(1.) I at loss of 12%=5% on whole; j\ do=4J% on
whole ; j% at gain 40% = 12% gain on whole, &c. |% =
$25. .'. cost = $3000. (2.) See Canadian Edition Ham-
blin Smith's Arithmetic. (3.) Cost = $1400000 ; con-
sumption in second case = $980000, rud revenue =
$198000, which is 25% of $784000. .*. there is a falling
off of $196000 = 20%. (4.) Tea, T5 cents ; coffee, 32
cents. (5.) 146 guns. 5 rounds in 8 minutes = | round
in minute, and 8 rounds in 10 = ^^ in 1 minute, &c.
(6.) P.W. of $1 (simple interest) - $|, which amounts to
2|- in 4 years. .*. loss = ^^ = $160 ; and debt = $1000.
For two years loss would be $40 ; for 8 years $640. See
Paper VIII. q. 4. (7.) 5400 miles. (8.) Amount in-
sured =$11520 ; .*. value of goods + premiiim of insur-
ance +$40 =$11520. Value of goods = $11048. (9.)
$1298.67. See "Ex. Papers," page 31. q. 20. (10.)
(a) Similar solids are as cubes of like dimensions .*. 105."
2268::73:x3:42 length. (b) l:J::183;x3, Slant
height = 9 (2 -^4).
X.--Page 242.
(1.) (1.20) (1.37J)=$1.65 end of 2nd year ; $1.65X.60
=.99 end of 3rd year; $1.00— .99=$.01 loss on every
dollar: $20,000. (2.) $4.70=cash price $4.70-J-.94=
63
RESULTS AND HINTS FOR
$5, 6 months* price; $5-r-1.3 =$3.84^ = cost price;
$6X.96=:$4.80=3 months* price $4.80—3.84^^=95/5
cents. (3.) 16 miles. See " Ex. Papers," page 26, q. 12.
(4.) £96=1920s. ^\ of 1920=288, do of 56=8|;
66— 38=18. -.(18—81) XNo. quarters=288 ; No. quar-
t('rs=30. (6.) It will be found that 17 of first gang=
6 of second gang. . • (-i^^-^-^j^) of second gang an do
work in 1 day, &c. J\^ men.*. 8 is least number. (6.)
Interest (payable annually) =$1200. Then a sum (a)
must be raised annually, to amount to $20,000 in 10
years, i.e. 20,000=rt (1.069+1.068+ ...+1), and a
=$1517+together with $1200 interest. (7.) 6.78064 ;
1.8377+. (8.) 90 oxen. See "Ex. Papers," page 24,
q. 6. (9.) A*s profits=|Xi+J=fl ^^ H yea»»- In
last 2J years his profits=|Xi|§X|=jf||. .*. his
total profits=if|^+f§=f|^|=$17180, and • annual
profits=17180Xll52-f-3719. (10.) (a) A right angled
triangle. •.area=638X 720-4-2 (links)=2.2968 acres.
(6)169.17X3.1416. (c) 12.76275.
XL— Page 244.
(1.) Cost=$23.34, duty=$2.91f .•.totalcost=$26.25j.
Also 189 sold for 192, at 25 cents=$48, giving gain
$21.74i=82%. (2.) $20000 cost in N. Y. $21600
currency. Again, exchange being at 9f , we give 109| for
109 J . • . In London cost is 70 J Xfo||x^f §F X \M =
$19961.09 currency. . • . Gain $1538.91 currency by
buying in London. (3.) $73 due at once (April 6), $146
in 33 days, and $600 in 100 days : p. w. at 5%=73+
144.34+591.90=809.24, which amounts to$818 (=sum
of debts) in ^%\% of a year=78+days, (4) T. P.— b.D.
Prt Prt
=Prt.— Yj:^=0:^Xrt.=rt% on theT. D. (5.)
24% of outlay=$586=24% of j^ of cost, &c. $1875.
EXAMINATION PAPERS.
63
(6.) 300XH=^^i received $2.38 .*. loss $1.G2.
For every orange eaten ljc.-|-4§c.=6c. . • . 162-j-62=7
oranges eaten : 273 sold. (7.) $310. (8.) A 1 row in
2*5 hour,B 1 in j\ hour, CI in | hour; Ij.CM.=^^ hours.
. • . sums in prop, of 10, 9, 6. A, $20.20; B, $18.18 ;
C, $12.12. (9.) $8500 — expenses and commission=
$8046.70. $100| of this gives consignor $100, &c.
$8016.63. (10.) B's as unit (=1), A's 4. . •. (1-|-|)
(1.1)4=$14641, &c. A's $4838.70, B's $6451.61. (11.)
(a) 12 ; (6) vol. of cavity as unit, then 2 is that of shell;
r, ?' radii ; then r^ : r'^ : : 1 : 2 . ' , r'=r f^2 ; thickness
=r^2— r=r(^2— 1).
il !
i:
XIL—Page 246.
(1.) It is found that discount = y^f of face of note:
8% per 360 days=j'3% per day, or discount =55*^0 of face
perday .-. J7-j-55'5o=265 days. (2.) tVij— tVo =^ 7^5=
80; .-. 2000 votes. (3.) A begins work at 6 o'clock a.m.;
in the afternoon B's energy diminished in ratio of 4 ; 3.
A's work in 6 hrs. — B's work in 5^ hrs.=2'^, &c. A will
be found to do -^^j of the work in 1 hour, and li j^f^j.
.-. A will have done ^|f, and B ^Jf; 132:109. (4.)
151
■5^ X 4| X 1.09J X 1.35=value in N. Y. without duty. /.
^^ K 44 X 1.09J X 1.35 X 1.50 X 1.25=$9.701. (5.) R=
amount of $1 for one year at given rate. Then 200 (R^
+ R + 1) = 800, &c.; rate% = 30.27 + . (6.) (1.04)=
value of each $1 stock end of year. 100 (1.04^ — 1)-
.16 = interest due end of year on each $100 stock ; .*.
nearly. (7.) Sterling cost = go^^g x
8.16 x?| = 7.2%
Ifi. = 126*. .'. M ^ ^¥ ^ (1.09J + J) + 75c. = 3.67J total cost.
.-. gain ■= 76^c. on $3.67J ; cost = 20i|j^%. (8.) A's gain
64
RESULTS AND HINTS FOR
$258; B's $105. (9.) 44 yds. in 3 sec. = 30 miles per
hour; 44 yds. in 2j\ sec. = 43^ do. .*. A and B approach
each other at rate of 13.2 miles per hour. When tho
train met B it was 15 miles ahead of A, and A and B
15
are 15 miles apart. .*. ^ x 6 = 6 j^'j = distance A makes
after train met B, but he had also travelled 3 miles while
train was going to B. .*. 6j®y + 3 = 9/y miles. (10.) Of
plane quad. figs, square has greatest area, &c. $521,432.
XIII.— Page 248.
(1.) Expression:
•025'5(3« + 25) __
g\, or .078125.
.0254(3*— 3^ + 20
(2.) 2f% = $198.25 .-. net income = $7209 ,'j.;
.-. amount before repairs, &c., are paid for = $7209y'y x
1 AQ4
-j^ j also of $100, $95 remains after paying agent's fee.
$7209 jV ^
1084
ir _ 95
of gross rents, which.*. =
$82387 4
"TT
100
(3.) True p. w. =i:j^rt, commercial p. w. = A
—Art. Then (1) diflference = -y;^, &c. (2) 71||§==
^and63^-J = ^^.-.n = 8,«kc. .'•.p = 574i3^ rate % =
{i\. (4.) Amount of $1 @ 3% half-yearly = |/ 1-03
fjuarterly. Amount of $1 for 23 payments=(]/r03)2 3
Amount of $1 for 22 payments-=ri/1.03)23 &c., &c.
. •. Total amount = Vl^_*lzzJ = h^l\^JzJ. Also amt.
V1.03 - 1 \/1.03 — 1
of $1000 for 6 years at 10% = 1000 (1.1)«. .-.1000
(l.l)«-^above result = &c. (5.) $1701 = cost. $340.20 =
legitimate gain. .-. moi+MiiLM of 1 yd=2 ft. 11441^
*=* ° $171 l+$379.a0 '' 3467
inches. (6.) $120000000. (7.) mand M mass of E. and
J. respectively, r and R radii, a and A attn. Then m R^ ',
M r^;;al A. But mass is proportioned to vol. x density
EXAMINATION PAPERS.
65
and radii to cube roots of vols. .*. 1 x 1 x R* : 1387.431
X .22 X r2 : la; A, (fee. 39.40+. (8.) See " Ex. Papers."
p. 27, q. 14. (9.) See " Ex. Papers," p. 29, q. 17. ( 10.)
[a] Find radius of circum. icirc. := 20 x 30 x 26-^^4
-/^ ft V j> 5 V 1 5 V as ^^ j Observe that quant, under
y 2 2 It n ^j \=5«x 3^x7-1-24,
radix sign. ) j-^^ jg^^
XlV.—Page 250.
(!•) inh^ii-^m of 100 = 136if : Ana. 36i«%.
(2.) Six months* credit price of silk = $2,101; .•. he should
receive for the silk (2.16f x 60)^-2 = 65 yards. (3.) A's
gain on $1 in 1 month is $7^^ ; B's gain for unknown
time = $j5. .•. -,*5-r-Y^5=10 months, B's time. C's stock
will be found to be $1000. (4.) 2400-7-20=120, annual
payment. 177.60 — 120=57.60 interest on sum not yet
paid; but interest is ^^^ of that sum .*. sum=$960 : Ans.
12. (5.) Both hands together must have passed through
all the spaces of the dial plate. Minute hand 60 spaces,
while hour hand 5 (both=65) .*. |§ of 5=4^^5 min. opaces,
what the minute band was in advance; at 2 o'clock .'. the
minute hand had 10 + 4j®3 spaces to gain ; gains 55 in 60;
.-. 15i|f Ans. (6.) 3 months. (7.) 16f f% gain. 13J x
21 X 1000 =29333?, francs ; this wmwy commission (146§)
gives gain 41864|, &c. (8.) $424.61-f'?3. iVec income=
$2040; sells for $3000 x 24 = $72000. New income=
/^j X 72000 = $2215.38 A, &c. (9.) 49f feet = 7146
inches; IJ x 1^ x 2 = 4.5, and 7146 -4.5 = 7141.5 ^con-
tents of 6 square boards the box is made from .•. 7 141.5 -f-
6=1190.25, sq. root of which = 34.5 ; 34.5 + 1.5=36.
(10.) 2040-94 + . Let H + F=:width of house, E position
of eye, A B that of fence ; draw B D perpendicular to
Jl
vd
HESULTS AND IIINTft FOR
E A produced ; then since tiinngle A B D is right
angled and isos. we have 2 A D«=A B''=90'; B D=63.64
rods, and the similar triangles E F H and E D B give
HF: ef::bd: ed=i760.i ft., &c.
XV.— Page 252.
(1.) (1) 19.104, or 19.105. (2) It will be found that
y/G=y^2 + 1/.3 + |/2 — 1/3 which divides the numerator;
giving (^2^73)2—^/4=3"+ (|/2=73)2 = 3. (2.) 6 J
months. (3.) The No. will be of form a + 10b + lO^c +
103d+... Subtract a + b + c + ... .*. Remainder -(10
— 1) b + (102— l)c + (108— l)d + ... when each of the
expressions 10 — 1, 10* — 1, &c., consists of a series of
nines and is .•. divisible by 9. Also if N be a number
and 8 the sum of its digits, N = 9?? s, where 9n contains
3 and 9 whatever n may be. .*. !N will be a multiple of
3 or 9 if « is. (4.) | x j\ x j^^ = tj\ (of cost) = increase in
materials ; j[)<^><i^i = 9u ^increase in cost of labour.
.*. ultimate cost = 1 + Vf + 50 = ^tIoo* •*• ^®* S^^^ = ^20
— ^Tiiu~Tl8u = 2A%* (^0 '^^^ circuitous course is
more advantageous by 124.8325 milrees. (6.) Bate of
St. is represented by J(5 — 3) = 1 ; rate of boatman in still
water is represented by J (5 + 3) = 4. . '.rate of st. = J his
rate in still water. Also in second supposition ^(2 + 1)
= 1^ represents rate in still water, and 2 — 1 J - J rate of
current = Jrate in still water. .•. ^ — i = T2 ®^ ^^^ ^^
still water = J mile per hour. .*. rate = 6 miles. (7.)
$3138.92 + . (8.) 6^^:2||. (9.) 9/j minutes past 8.
(10.) Sides containing the right angle ^ — '
XVI.— Page 254.
(2.) 12 hours. (3.) (1)12X18X5X25=27000. (2)
L. 0. M. of 49J and 52J=940J ; they will pass tho
EXAMINATION PAfFnS.
67
))oint every 940^ minutes, i.e. 19th train on first track
and 18th on second. Again, 52 J— 49^=2}, and 27i-=-2f
=10 i. e, 10th (on first track) passes at the given time,
and 9 are still to pass .*. 9X49J=445}. minutes. (4.) 8J
percent. (5.) a-flOb+10''c-f-10M-|-...beoneNo. andc-f-
lO a-j-lO'^^+lO'^-f ...socond Ko. with same digits. .•.
difference=:(10 — 1) a -f (10"— 10) b — d (10'— 10»)— c
(102—1) 4-. . .=(10—1) a-f 10b (10«— 1)— lOM (10—1)
— c (lO'* — 1)4" ••when each expression is divisible by
10 — 1=9. (6.) If O be the point which A passes an
hour ahead of B, the required point will be 2}^ miles
from O; the time will be 3f hours. (7.) See Canadian
Edition of Hambiin Smith's Arithmetic. (8.) A pays
$74 j I too much, B pays $39.75 too little, C pays 35y'g
too little. (9.) In 7^' 12 taps empty the quantity -f-
which runs in in 7J'. In T 1 2 taps empty f^ of quantity
-fwhat runs in in 1' So in second case : in !'• 7
taps empty j*g of quantity -|- what runs in in 1'.*. 5 taps
empty /j — 15=35^ ^^ ^' > ^^^ ^^ ^^^^ ^^ found thpt what
runs in in 7J'=|^ of the quantity in the tank at first, &c.
4 taps, Ans. See " Exam. Papers," page 24, q. 6. (10.)
2^/19 — 4. The chord is side of equilateral triangle and
bisects radius; if a;=side of square, then (IS-f-a;) (5 — x)
='^^, &c.
XVII.-Page 256.
(1.) $99^3 each cask. Capital as unit then ff +jj of
12=111=6x104.50, &c. (2.) [a] $l9.23T'g ; interest
=10 .*. 20 for twice time= J^ of principal.*. discount=y^j^
[6] 250--(l+r)"=:240.-.(l+r)"=||§ and 240--||oJ
$230.40; 250— 230.40=$19.60. (3.) 320| yardslcost
price=$!ff ; gain at cash price=$§— $|f=3'^g2^, <kc
(4.) Let a be the sum payable every two years. Preseu ;
68
RESULTS AKD HINTS FOB
value=a-?-^ (1.05)2—1 |. .-. 1000=^^^-4-^ ^^iSj-^and
o=$102.50. (5.) 59 jl seconds. See " Solutions," Sec.
v., Prob. 9. (6.), Board contains 3242 sq. inches; 2.5
X2.5=6.25 inches, 3242— 6.25=3235.76, which divided
by 7 gives 462.25, sq. root of which=21.6. And 21.5
4-2.5=24 inches the width of box, height 12, length
48; inside dimensions 19, 7, 43, .'. contents=5719 cubic
inches. (7.) A should have received f of 90=50^?., B
& C I of 90=40*.: but B suffers 3.75if. loss by employing
C. Hence the following : — B's sum; A's sum (=505.); ;
B's loss (=3.756'): A's loss.-. B's sum X A's loss=50x
3.75=187.5s.*. also, it is easily found that B's sum-f-A's
loss=36.255.: half of this is 18.125 and (18.126)2—187.5
=:square of half difference of B's sum and A's loss, and
the sum and dif«irence of these being known, we have
30j?.=B's sum, and 6.25, A's loss. B received 30if., C 40
—30=105. 1^X5=15 days, B's time; and T7gX2=18,
C's time. (8,) A $3, B $3.60, C $4. A 5 inches, B 7^
inches, C 18^ inches. (Small fractions neglected in the
solution.) (9.) 2.445 +inches.
XVIII. - Page 258.
(1.) § of 1st bar is silver, y®y of 2nd bar is silver.
There are to be 24 lbs. of metal in new bar ; if whole of
it were taken from 1st bar it would contain 16 lbs. of
silver ; but it is to contain 19 lbs. of silver, a loss of 3
lbs., but loss from every lb. not taken from 2nd bar is
^^, and then No. of lbs. that should be taken from 2nd
bar is 3 lbs.-^■/3=19|, and 24— 19|=No. of lbs. to be
taken from 1st bar=4^ lbs. (2.) 46080. (3.) The last
clause should read ; " A will then have $200 more than
B." After Ist transaction A's will be $200 less than it
EXAMINATION PAPERS.
69
was, and B's ^ of A's first capital less $240 ; after 2nd
transaction A will have § of his first capital — $240, and
B will have | of A's first capital— $200, but this is $200
less than A's .-. f of A's==g-f-240, j^=.:$240 .-. A's capital
was $1 200 and B's $900. (4.) There is a common factor,
and 8 times this factor is No. of l)ii3hols in 1st kind ; 9
times this factor is No. of bushels in 2nd kind ; 8 times
this factor -f- 12 bushels=No. of l)usho]s of 1st kind after
the 12 bushels have been added, &c. 96 of 1st kind and
108 of 2nd kind. (5.) 2 years @ 10% per year is same
as 20% for 1 year.-. 600—^ of notc=| 1000— note.-. ^
of note=$400 .*. note $500. (6.) The commission mer-
chant gets on an average j'g'g of all he invests, but he
gets 2*j of the cash he invests, ^j of the value of pork,
and g^5 of wheat. Now, by allegation it is easy to find
what proportionate parts must bo taken of cash, pork
and wheat to give an average of |] ; then divide $13300
in the ratio of these proportionate parts — one answer —
cash $1540, pork $1900, wheat $9800. (7.) $4000 in 4
years amounts to $4802,025 .-. interest for remaining
time=5000— $4862.025::- $137,975 ; but interest on
$4862.025 for 1 year:.^$243.10125 .-. the time will be 4
years-j-aWiVA °^ ^ year--- 4 yeat«, 109 days. — Ans.
(8.) $4.70. See Paper 10, r^. 2.
(10.) 50.99.
XIX.--Page 259,
(1.) 32 days. A $2,70 ; B $1.80.
estimated cost, a the actual cost, R^ the rate of increase
of debt through accruing of interest from date of issue of
debentures to date of first payment ; R the annual rate
of increase thereafter, n the original number of payments,
m the number of payments still due at time of adjust-
ment, there having been n — m payments made. Hence
(9.) 4 weeks.
(2.) I>;t Abethe
!■
I j
TO
RESULTS AND HINTS FOB
I
at date of last made payment the amount yet due is by
estimate ? A, but up to date the accrued value of excess
of estimate over actual cost is (A — a) R^ R"~"^^ ; hence
the amount actually due is- A — (A — a)R^ E"""*"^, and
the annual payment will be ^ — "^ B} R"-™-*, plus the
accrued interest on the unpaid part of "*~^ — (A — a)
Ri Ri-™-i. Suppose p=:the number of payments yet to
make, and not being greater than m, the first of
these will be ^ n — ^ R^R """"^ J- -j J9 R — (p—l) }■ ',
since this is the first payment after n — p have been
made it may be called n — 2^~{'^ payment. A=$79.
a=$76, R*=||fB§, R=1.06; n=5, m=2, p=2 and
1 ; hence the fourth and fifth payments should be
respectively $^ 15.80—1.50 x 37|08 ^ loG^ j. x 1.12=
$15.74, and $] 15.80 — 1.50 x 37 8g8 ^ i.06 [ x 1.06=
$14.90. In the second case the fourth and fifth payment,
may similarly be found to be $18.98 and $17.96 respect-
ively. (4.) 1 eagle=232 grs., 15432 grs.=l kilo, pure
gold, 9 kilos, pure gold:=10 do. st. gold, 1 kilo. st. gold
=3100—6.30 francs.-. 1 eagle=51.6765 francs. (5.)
3:2. (6.)25r=3— 3-j-(l+/2)»2o. (7.) This depends on
the principle that if a No. N consists of n digits a, b, c . . s
then N — a-j-b — c-j- ... is divisible by 11. From this it
follows that N will be of the form 1 b*-j-(a — b-|-c — d-f- . . . ),
or l\n-\-(&-\-c. . . .) — (b-j-d . . . ), and will .-.be a mul-
tiple of 11 if (a-f-c-f . . .)— (b+d+ . . .) is so. (8.) 200
@ 50, 500 @ 70, 250 @ 90. (9.) {2.Q0X-i%%~2.60
X{§g)-^2.60x}§e=17%. (10.) A B=:25, B D=25i/3,
D C=50i/3, B C==75.
XX.— Page 261.
(1.) The difference between siiuple anc "ompound
interest for each year is the interest on the interest. The
EXAMINATION PAPERS.
71
amount of $45 for 4 year.s=.'$54.697781-5, or the amount
of $l=-§^i-^/3'!^&i^=1.21550625=(1.05)4 ;. 1.05 is the
amount of $1 for one year, hence the rate is 5% ;
sum=.^|=|900. (2.) fr^+^T^«+f«Tf =11092.51, Ans.
(3.) l+(1.04)H-(1.0iVi^-(i.04)3=4.246464=amountof
an annuity_of $1 for 4 vears ; iJL(L><_4;2_4 fi_l«4^$580.7832.
(4.) If |/3 be the depth, the radius of the base is 1, .'.
area of base=^jy*-, aica of baseX^ l/^=if )/'^=voI.
when the depth is |/3. Similar cones are to each other
o2\/3~
as the cubes of their like dimensions ^^-~- ; 400 gals. X
274.274:: (-1/3)3=31/3 : 66.14 inches or 5 feet 6
inches. Ans. (5.) Present worth of $620 is $600=
cash cost of goods; 600-j— 'To^^=$660=cash selling price ;
1.01JX660=$668J=credit selling price; 668^+10-=
$678J= credit selling price in second case. Present
v.orth of $678i for 6 months at 5%=$661ff ; there-
fore $600 gained -^Glf f, or $100 gained $10y^T«3. (6.)
2o><fio-i200j._ 6100c., cos of 90 fi)S. or 6^7|c. per
lb.=cost of mixture of the tii^ii and second kind. By
selling the whole mixture at $1 and allowing 10% dis-
count to the purchaser and gaining 10% would make
the cost of the mixture 81y'*j cents per pound ;
Sl-JLif^^^'l^^^i^^^f^^JJl The rektion between the 90
" H 100/ = 14g4j = 1390 )
pounds and what was mixed with it at $1 per pound
1800 : 1390 : : 90 : 64 J pouudb = required quantity.
(7.) "-^^l^^|F=24l74 yards nearly; 24174X.12=.
$2900.88= credit sale price of cloth. The present woitli
of $2900.88 for 1 year at 8%=$2686 ; $130 for three
months at 8%=$127|j; $200O+$127|f=$2127|f =.
money lulvaiaee^ wkieii gained i$2G88 — .*!i52127f|, or
Ib^Si
If $2117^; g»ius {|5r)8r:« .iJ^lOO will gain $20'
72
BESULTS AND HINTS FOR
$4.8.
nearly. (8.) 6:5. (9.) 3 feet. (10.) 120-f-iy+ji||,«
=$333||=present value of fencing ; ^g^^^-f 333y==
1933||— the money invested; 20 years' purchase is
equal to 5% .'. the income from the farm is ^f^^ —
:|94. If 1933|| gains $94, $100 will gain
XXL— Page 263.
(1.) A 15 days; B 30 days. (2.) |/L06=1. 029563;
multiply by 1000 and subtract the principal. $29,563
Ans. (3.) If whole distance is only 3 miles, and each
sec. 1 mile, it will require (sV+^V+iV) °^ *^ ^0^^'
to run 3 miles. .*. 8-j-this time=34||. (4.) Present
value of notes=$894-$41.ys=$l 30.98, which put out
for-J||-f-of year amounts to S135 ; divide $130.98 by
$135 gives present value of $1 ; find the time. In the
work there will be the og. 9.98687 or T.98687, which is
really — 0.01313, and requires to be put in this form.
(5.) Nine weights, 1, 3, 9, 27, 81, 243, 729, 2187, 6561.
7961 can be weighed by puttiii;^ 27, 2187, and 6561 in one
scale, and 1, 3, 81, 729 in the other. A pcculiasr question.
Every number can be evidently expressed in the ternary
scale, and no number need be greater than 1 if we intro-
duce a( — 1 ) when meceasary, (6).
1000(1.03*0-1)
1.0.^-1 -=1368.19.
(7.) $6000 ; 1^ per cent. (8.) 2| per cent. (9.)
^110.40. (10.) $150. (11.) 6 years. i20(i-t-/2)=
24 x(l+3j''5), solve.
XXII.— Page 265.
(1.) ^1 : .640625. (2.) 381.46; 27.6. (3.) 2s. 4/5d.
(4.) It loses 2 min. 24 sec. a week. (5.) .8 nearly.
(6.) 128|l^ grains. (=f^X 123X^1 XSX-',/^.) (7.) 5%.
Fair gain+ J^+-J^ of fair gain^^^^.-. fair gain=2*g=
6%. (8.) $14000; l|%=g^^ .-. 1800— 225— g'^ cost =
Jft cost, .-. &c. (9.) 35 : 32. (10.) 18J minutes.
EXAMINATION PAPERS.
73
XXIII.-Page 266.
(3.) A $720; B $600. (4.) 60 miles. (6.) 20 gal-
lons water, 120 gallons wine; cask 160 gallons. (6.)
Cost to retail merchant+lOyYT o^* cost=|1.34, .*. cost=
$1.21= selling price of wholesale merchant; but cost to
wholesale merchant -}- 1^% cost =$1.21 .*. cost to whole-
sale merchant=$1.10=buying price-f 10% of duty, .*.
buying price=$l. But duty off, aiid original price fall-
ing 10%, the buying price is 90 cents, wholesale price
99 cents, retail merchant's price 99 XjJi cents=$1.09Y\,
.*. he should sell it at a decrease of 2^j\ cents. (7.) $3000.
(8.) 200 shares® $60, and 100 @ $110=$21000, .-.
he invests $3000 in stocks, of which $60 pays $6 dividend
(paying $76 for $60 stock) .-. $3000X;7''5=$240. Also
income from 200 shares and 100 shares @ 4% and 8%
respectively=$1600.*.$2000=new income. But from
$3000 he gets $240 .'.from $18000 invested in Merchants'
Bank at 90 he gets $1760 (from 200 shares), .*. 1 share
gives 8J and half-yearly dividend=4|%. (9.) $2982^,.
(10.) The mixture in cask A will be 26 gallons wine A,
19 wine B, 19 wine C ; the mixture in cask B will be
26 gallons wine B, 19 wine C, 19 wine A; the mixture
in cask C will be 26 gallons wine C, 19 wine A, 19 wine
B. And these mixtures being sold at $182.60, $188.20,
and $192.40, the selling price of wine A is $2.20, of
wine B $3.00, and of wine C $3.60 ; .*. cost prices aro
$2.00, $2.50, and $4.00 respectively.
XXIV.— Page 268.
(2.) A gives B a start of ^^j mile=480 feet ; at end
of 2 minutes A is 180 feet behind ; he has .'.gained 150
feet per minute. A 1650 feet; B 1500. (3.) 10%.
(4.) Neglecting expenses, gross gaii\=847 — 122=$725;
V4
RESULTS AND HINTS FOR
gain on 1 bushel=$(| — 1)==/5 ' ^^^^ ^^ ^^^ bushels
lost=$637, .-. number bushels sold=(7254-637)-5-jt=
6107J ; number bought=455+5107i=5562J. (5.) Had
he bought \ less at original price amount would=$45
less, .'. number books=$45-^-50 cent8=90 ; 1st number
=1 of 90=120; cost of each=$l80-i-120=$1.50 :
selling price=/Q^jj of $160=$1.42J; marked price=
1.42^+.22^=$1.65. (6.) | of 90=1 12J yards; retail
selling price=$25 less than cost of 262J yard8=cost 252
yards— $9.26 ; .*. cost of 10iyards=$15.75:|1.50 a yard.
(7.) Let buying prices of teas be 6 and 7 monetary
units respectively, .*. selling price of first mixture==
l><l+3><fiXf=-2^5^=also selling price of second mixture,
.*. buying price of second mixture=:j^X -3^5® =■'55^ which
is greater than cost of the green by ||, and leos than
that of the black by g^g. .-. ratio is 6:59. (8.) $6000.
(9.) $68+$67=$135=9% on the total, which .-. =
$1500, interest on which at4%=$60; .-. 68—60=8
interest on first sum at 1%. $800 ; $700. (10.) Area
ofcircle=(14400X6X3.1416)-i-(4X3.1416)=6x3600
=area of rectangle=6 squares each of area 3600=
rectangle. 3 of these squares long and two wide =180
yards long and 120 wide ; .•. perimeter=600 yards. Cost
of fencing, $360.
XXV.- Page 270.
(1.) 38fV miles. (2.) B's profit $1500 ; whole amount
invested $8333J. (3.) $9702ff|. (4.) 4__^^xHJ-
T^uXi=--16000,&c. $12738i§9=valueofship;$6369|fl|
=value of cargo. (5.) $6|| per barrel. (6.) $31250.
(7.) His dividends amount to 8(1.04)^-)- 8(1.04)4-f
8(1.04)3 -I- 8(1.04)2 ^ 8(1.04) -f- 8= -^^'^^^"^^
n<
$
1
J.04-1
:53J
EXAMINATION PAPERS.
76
. 4 .
T5-
nearly ; 180+53J=233i : a|fil=119J very nearly. (8.)
^90 will bring 3, or 100 stock will bring $4.86§X3=
$14.60; sell, out at 90— J=89i; No. of dollars will be
1.4.^ X89i.-. income will be J3W X ^^Xisgi* &c.
Stock held will be £5525 17s. 5d., nearly. (9.) Amount
given for the mortgage will be such that when put out on
compound interest at 8% for the time to expire it will
amount to 800 -[-interest on different instalments at 8%.
If there are four instalments still due, then statement will
be: A(1.08)4 = 60(1.08)4+248 (1.08)3+236(1.08)2+
224(1.08)+212. (10.) He pays 1400(1.084+1.083+
1.08' + 1.08 + l)=5000(l+r)« ; /3(^^^^)=(l+0^
XXVI.-Page 272.
(2.) L. C. M. X C^- C. M. = product of the two
numbers; then 100793 X 17 = 1713481 = product
of two numbers; -^2*- ~ = 612 = difference between
arithmetical mean and each of numbers; then
1713481+612*=2088025=square of arithmetical mean
1/2O88O25 = 1445=arithmetical mean. 1445+612=
2057 number; 1445—612=833 number. (2.) $288=
income from 4 J% ; ^-*'/j^^=:price of 4J% stock ; -and pro-
ceeds of 4%=|f>fe'|j8^«i;==$94=price of $100 stock after
broker's charge is deducted ; 94+^=:94|=price of stock.
(3.) Buying price— ^^!^?PjJ'JJi&Jerl^=&'-'3j'^sj'-'i^X (100— buy-
ing price)=selling price. This is greatest when buying
• price X(ir^ -buying price) is greatest; that is, when buy-
ing price=i§A =X50, when selling piice == £25. (4.) A's
rate of work ; B's '. ', B's time before noon : 8f A's time
after noon. A's rate of work ; B's '. [ 6 B's time after noon
l A's time before noon; hence B's time before nooniSf: I
6 ; A's time before noon, hence 8| X 6 =^product of A's
and B's time; ^: 2^,^= difference between mean time
:
76
RESULTS A^i^ Hi;.TS FOP.
and time of each man ; then as in (1) v 8iX6-f(J)-=■
^5*=mean time, and A's time==^*4-i = 7J hours, and
he began at $4.30 a.m. (5.) 5% ordinary stock4-7^% of
je400000 or .£29000=6% ordinary stock+6% of £400000,
or £24000.-. £5000=1% ordinary stock; £500,000=
ordinary stock. (6.) 1 tap in 1' discharges 3/5X17 of
what cistern holds -j- 3^5 rf what goes in in T; also 1 tap
in 1' discharges 3^3 of what cistern holds-f-jV ^^ what
goes in in 1'; then (y}^ — ^l^) of what cistern holds=
(tj^j — 2^g) of what goes in in 1'; then ^f of what cistern
holds= amount going in every minute; whence cistoin
and what flows into it in 26 j'/ will be emptied by 19
taps. (7.) The sum of the gains is y^^ (sum of squares
of two parts of 90), and this latter sum is least when each
part==^3f-=45, hence sum of selling prices cannot be less
than $90+-VoV-' ^^ $130.50. (8.) Faster requires to
gain 2" so as to make its stroke at same time as slower,
whether it is 2" before or behind the slower ; faster gains
this 2" in two strokes, since it gains 1'' every stroke ;
then when faster makes its 3rd stroke the other strikes
also, and this afterwards happens at the seventh and
eleventh strokes of faster, and no other. But whole
number of strokes heard being 19, the faster must have
struck 11. (9.) 4|/i^gJ^=1.10, increase=10%. (10.)
144.21 feet. (11.) 6lX200+31Xrequired payment =
61X660 — 61Xi'eq"ii*ed payment, whence 92 X required
payment = 28060 ; required payment = '^^^.^^-^^ = $305.
(12.) 80 and 20.
XXVII.-Page 274.
(1.) 64J=| of 86%. .*. he will receive J as much at
36 as at 64%. 7% on f =5}% on whole, so that he gains
(54— 5):r-:J% amiually ; gain on $1 bonas=.00J==6%
2;
cc
EXAMINATION PAPERS.
77
wrs, and
f-U% of
^00000,
0,000=
X17 of
so 1 ttt])
>f what
hoItls=
cistorn
cistern
by 19
squares
en each
be Jess
ires to
slower,
•' gains
troke ;
strikes
^ and
whole
have
(10.)
mt=s
uired
^305.
h at
:ains
of y^^ cents, which =.*. cash gain on $1 of bonds;'//
cents gain represents $1 bonds, .'.1^208.33^ represents
$G200 stock. (2.) 4 bales+S times their increase in
volue for 1 month keep 12 Indians 9 weeks.*. 4 bales
-f-24 increase in value of 1 bale 1 month keep 108
Indians 1 week, and 1 bale -f- 6 increase in value of 1
bale 1 month keep 27 Indians 1 week ; so from second
supposition, 1 bale -f- 10 increase in value of 1 bale 1
month keep 21 Indians 1 week .'.4 times increase in
value of 1 bale 1 month keep 6 Indians 1 week, &c. I
1 bale=12 times increase in value of 1 bale 1 month, &c.
172 Ans. See " Ex. Papers," page 24, q. 6. (3.) $84=
2% of $4200=1 J of total cost of furs, storage, duty, and
commission, which must .'.be $4000=^^ § of total outlay
in furfc, storage, and commission, which outlay .*. =
loi)yOx.l.io ; but storage and commi8sion=250+84=334
.-. original cost=3971.63yVT— 334=$3637.63yVT- (*•)
Amount giving eldest son $1 on coming of age=$l-f-
(l.OS^'* ; so for second son $l-j-(1.05)^ ; and for young-
est $l-f-(1.05)8; .♦. eldest son's share = $160000 X
($1 -- 1.054) ^ (1 ^ 1.058 + 2-^-1.05«-|-l^l•05^) =
160000xl.05'*-^(l-}-2Xl.0524-1.05'«), which when he
comes of age will amount to 160000Xl.058-j-(14-1.053)2,
which divided by amount paid for his ^ihare must equal
amount of $1 for the given time and requ^'red rate, i.e.=--
(1 -{-interest for 1 year)"*. The fourth root of the above
quotient=1.052x20-?-1.45Xl3=|^4=1.16fff. .'.rate
% = IG^fif. In the question $16000 should be $160000.
(5.) $4282.80. (6.) 22.9176; 13.7505. (7.) 35 + B +
C = 37. (8.) See Appeadix Canadian Edition of Ham-
blin Smith's Arithmetic. $7065.04. (9.) Let x=length;
then since area is 40 rods, *x**=breadth. x + V*=min.s=
p., from which r is found to be 2^/10, and breadth 2|/10.
;ji
>' I
iii
78
RESULTS AND HINTS FOB
XXVIII. Page 276.
(2.) Tho error in each case diminishes the value of the
fraction ; hence the debt less 4s. 7d. is to the debt less
28. 6d. as 99 is to 100. Tho debt is therefore XIO 10s. lOd.,
and the decimal is .25. (3.) ^i%'f|«.-tii + J = ^-^-f ^li^jj'^^'"
= 84J = price. $6800 stock bought and sold. (4.) 24 lbs.
of gold-t-24 lbs. of silver are worth $1293.75 ; 24 lbs. of
gold are worth $1236.00 ; 24 lbs. of silver are worth
$57.75 ; 1 lb. of silver is worth $2.40 If the mixture
were all gold it would be worth $1236.00. The silver in
it reduces its value $386.25 ; 1 lb. of silver would reduce
its value $49.09| ; hence there must be $386.25-^
$49.09f = 7||j^f lbs. of silver. 24 lbs. gold +24 lbs.
silver = $1293.75 ; 24 gold = $1236 .-. 24 silver = $57.75 ;
and 1 silver = $2. 40|, price per lb. (5.) The present
value of the mortgage is the present worth of $1232>
$1184, $1136, $1088, &c. ; or $1140.74 + $1015.089 +
$901.793 + $799.712 + $707,806, &c. = $6649.377. (6.)
The ratio of the time required by one train to travel any
distance to that required by the other to travel the same
distance is constant, hence AM.inmin. .- iso mm. ^^ere ans.
, 871 mln. Ana. Ininln.^
denotes the number of min. they were travelling before 9
o'clock ; hence ans. = |/37^ x 150 = 75. The trains started
45 minutes past seven. (7.) The borrower has the use
of $573 for 3 months and $535 for 9 months, and he
j>ays $95 for the use of these sums at the end of the year.
.$573 for 3 months = $1719 for one month; $535 for 9
months = $4815 for one month; $1719 + $4811 for one
month = ~y|^ for one year; hence rate per cent, per annum
is 17y*Q%, Ans. (8.) True discount on $? = 5||c. ; bank
discount on $1 - 6c. .'. banker's gain is -l| on $1 *.• 28.44
-j-i^ : $8374 face of note ; $8374 x ^^gg = $602.44 bank
EXAMINATION PA, FRS.
Tl
of the
)bt less
|s. lOd.,
discount ; $8374— !|502.44 - $7871.56; then ^VaWVai*
.-$4.98^ price per yard. (9.) A'b $975.61 nearly ; B's
$1050. Kate per cent, is 2J. (10.) jf ( j| pay-f-pay) a
$2040; pay = 025|f.
XXIX. -Page 278.
(1.) $54. (2.) 892. (3-) 66J (4.) 106 days. (5.)
S4973.314+. (6.) $10. (7.) 224.701 days. (8.) 29
(lays, 12 hours, 44 minutes, 2 seconds. (9.) 25.35 days.
Note. — The number of apparent rotations of the sun in
a year will be -f^ 11^ ^^ 13.4, but as the earth makes
one rovolution around the sun in a year, therefore the snn
must make 14.4 real rotations in a year, and consequently
the time of one real rotation is ^'^Yi%^-- or 25.35 days.
(10.) 27.2 lbs. Note.— First find what a pound of ter-
restrial matter would weigh at the distance of 426292
miles from the earth's centre. This is found as follows :
4262922 ; 39602 • 1 ; iMh)"" '^ *^cn dMhyy
314700=27.2 Tuw v. xk is most expeditiously per-
formed with the aid of logarithms.
XXX. -Page 280.
(1.) Rent=$960, rate=$72,acres=120. (2.) A, 15
miles; B, 10 miles; distance=150 miles. (3.) 11
o'clock. (4.) By indirect ^route=$4000 — agent's com-
mission at Cuba=$4000— 20=3980 ; premium at 4%
=153.08, .-. amount of bill on N.Y.=$3826.92. Again,
after agent's commission in N.Y. we have $3807.79, .•.
3807.79 X 5.30=20181.287 francs. Direct route=$4000
— 20— 3980=(@ 5 francs) 19900 francs. Premium at
1% = 19900— 197.03 = 19702.97 = amount of bill on
Paris, .-. 20181.287— 19702.97 = 478.317 gain by eir.
route. (6.) E'a i8tock=$ 15000, C's time=7 months.
i
80
RESULTS AND HINTH FOR
10
(6.) (Quostion should read ^ A, B, D, ^ A, B, »137
respectively.) It is evident that A's -; ^ of A,B,0,D — J
A's=137, .-. f A's=137— i of all, .'. A'h^^-^ of 137—^
of all, also B's=^ of 137— J of all, also C'ti=^'i of 137— i
of all, also D's=g of 137—^ of all, .-.(^ + ^+1+1)01
U7—Q + i + i + i) of all =sum of all, .'. (1 + i + i +
J + l) of all=Q + |+| + f) of 137, .-. sum of all = $317.
This value substituted gives A =47, B=77, C = 92,D=101.
(7.) The series formed by body falling=100, 60, 25. . . .
&o. Sum=200. The series formed by body rising=:50,
26, 12^, 6 J, &o. Sum=100. Total distance=300 feet.
The time required for first series = (tqT ) (tqt)
p &c., &c., to infinity. This is a G. series first term,
/^3)^ratio= J,|/2,&c..-.sum=J-^^^ Second series-
^^?^P? These series added give 12£+V^^ =
14.6 + seconds. (8.) Consider first two partners; the
capital Ci for time t^ and Ca for time t^ ; compare their
shares A^ and Aj with the shares of a fictitious partner
Aj having capital=Ci for time=t2, we have A^ ; A3 ; *
tj ; ta, and A3 I Ag II C^ ; Cj, . *. multiplying we have
Ai A3 I Aj Aj I Ci t| I C2 tjj, or divide first and second by
A3=Ai I A2 I Ci ti I Catjj, which was to be proved. (9.)
Last payment=$28, deduct interest = $26| .•. debt=
26f X 5=$133J ; first instalment in 73 days=$26.6G§ +
interest on $133^ for 73 days=$28 ; second instalment
in 146 days=$26.66§ + interest on 106§ for 146 days=
$28.80; similarly third instalment=$29.06§ ; fourth=
$28.80 ; 5th=$28. (10.) Let A, B, C, D be centres of
the inscribed circs, and circum. do. respectively; G, F, N,
points of contact by circum. ciic O F, H, G=168
fe
fiXAUlNATIOM PAPERS.
81
feot each. Let 6x, 7x, 8x=radii ; then A 0=1 5x, 6 G
c=13x, A B=14x ; then in triangle A B (where D
is perpendicular to A B). AB : A C + B : : A C— B :
A D— BD, &c., &o., &c. ; hence A D=9x, B D=5x,0 D
«:12x, &c., &c., .-. (168— 7x)2=(12— 48|/12— x)^ +
(x + 24)a, .'. x=ll. Radii=66, 77, 88 feet.
XXXI.-Page 282.
(1.) The remaining figures may be found by subtract*
ing in order each of those already found from 9. (2.) Tho
radix is 6, hence -^^ must give a pure repetend. Reduce
Jj to a decimal ; it cannot give more than m - 1 places ;
divide this by m and it will bo evident that m - 1 places
may occur m - 1 times, but no more. (4.) The increase
in the number of teachers is 23^^7*3% more, and that of
the pupils 32^3% less than the average increase ; clearing
this ratio of fractions we find each teacher had 90 pupils
in 1876 ; then (^T- 10) 81= ji of 90T or T=90. 33J%
of 90=30 new teachers engaged. (5.) (1.4641)*=1.1.
He gives j? of 16 oz. for a lb.; his legitimate gain is
(1.1)2 = 1.21 = 21%. (6.) The total income with its int. is 100
(1.06)¥ + 110(1.06)¥ + 120 (1.06)-V^ X ... + 480(1.06)i +
490-
100(1.06)^0-490 . ■,ni a06)^°-(l-06)M _.ii.i.Qr;Qo«
(lOG)t-l + 1^ { -{(LOGH-IP 1 ^14858.35
Total expense with interest: 75(1.06)^+75 (1.05)
(1.06)¥ + 75 (1.05)2(1.06)¥ + .... 75 (1.05)3 » (i.06)» =
75 (1.06)i I ^^\^o5^Y/o^ir° I = ^11307.90. His expenses
increase in G. P., while his income increases in A. P.
(7.) At the end of n years he will be worth 12000(f)"-
1000 ] (i)»-i + ay-Ki) + . . . . ay-' [ = 12000 -1 2(i)^
- (!)» [ . This will be zero when 2(|)° = (|)°, or n =
2ioa.J°^.&-iog.8 = lQ''^^« He had better close when
F
83
result;:, and hints for
1
2(f)" - (J)n is. a maximum, i.e. when 2 x J (J)" = J x (|)»»,
orh = . log-a-ios-a =6.28. For n substitute 6.28, and
3 log. 4— log.fi— losr, 8 ^ , [
the amounii of his property is easily found by using a
table of logarithms. (8.) ly\j miles per hour. (9.) The
sum of the areas i» ^ ' area of the triangle. Euclid vi. 31.
(10.) Apply Eut id ii. 12.
<**
XXXII.— Page 285.
(1.) (1) By comparing the work done by A and C in 1
day with that done by A and B in 1 day, we find that C
does as much as B + y^^ of the work : and substituting
this value of C in what B and do in 1 day, we find
what B does in 1 day, and in 2jjf days he will do 2|j^
times as much as in 1 dav, and be entitled to that fraction
of the whole pay. (2) Jp'ind what fraction of the whole
pay B might have obtained ; then the former fraction
minus the latter - $2 ; from this the whole pay or 1 may
be obtained. (2.) The amount to be received equals the
entire outlay + l|g|% of it. In order to find the face of
note described, divide the amount to be received by the
P.W. cf $1 for the given time at the given rate, allowing
bank discount. The amount to be invested may be
found by dividing the sun of money sent by $1 + com-
mission on $1.
^3.) Let A's stock be 1, and time in trade 48 months,
thenB's "will be 4, " '* 32 "
and C's " " ^j, " " 30 "
The mortgage may be treated as an annuity.
P.W. (1.05)" = $9700 {HJi^^^}; the P. W. of which
would be shared by A, B, and C in a similar manner to
that in which the gains of any partnership would be
shared by thie partners composing it. (4.) Allowing
EXAMINATION PAPERS.
/if
the merchant's original capital to be 1, we have
thus :-- ! 1 + 1(|1 + j^ji) + 1 ($1 + jljfY + ($1 -f t5o)'F -
$4374.616 ; r, the rate % may easily be determined from
data given in the question, if the following princiijle be
remembered : '' The discount off' a certain sum for a
given time equals the interest on the P.W. of same sum."
The rate,% here will be found to be 6. (5.) Let 1 be
tho cost price per lb. of dearer tea ; then, if he cleared |
of the cost price by marking at $1.54, $1.54 must equal
1 + § of cost price, or $1.10=1, cost price of dearer tea.
(6.) Since he has to pay J% commission, the stock is only
worth 104 to him; .*. for every £100 stock or £104
money he gets £4 income, or $(4 x -^ x y^§) for every
$(104 X -Y" X |^§*), the agent getting J% commission for
transferring. Then, if he can afford to pay $(104 x -Y- x
i§§i) in order to get $(f x y> x j^J), can he afford to pay
more or less in order to get $6 1 And, deducting |-%
commission from this result gives the amount which he
can afford to pay for every $100 stock in order that no
change may occur in his income. (7.) Let the distance
rowed be 1 ; the difference between the distance rowed
dow7i and the distance rowed up in 1 hour = rate of
stream per hour, and from this the whole distance, or 1,
will be found to be 2 miles according to watch time.
But the watch gains 2' on every 24 hours ; having
found, then, the correct time which it takes him to row
down and up, by a similar analysis to the above, the
whole distance, or 1, may be determined, and the difference
between the two results will be the required answer.
(8.) Time =* nsrSsTe "^ *^'^^* C^*) ^^^ yards @ 10 cents
-«$10; 80 yards at 7^ cents = $6, $16. Let 1 be the
cash price of the 100 yards, then | of 1 will be the cash
price of the 80 ys\i'ds. From data given find value of 1,
^
84
RESULTS AND HINTS FOK
or the cash price of the 100 yards, and also the cash price
of the 80 yeids. The sum of these two will be found to
be $15 .'. discuimt of $16 would have been $1, or 6^ oflF
$100. (10.) This drpends on the principle, "The sum
of the squares on the sides equals the sum of the squares
on the diagonals j^' any parallelogram,"
XXXIIL— Page 287.
(1.) 1 lb. tea and 3 lbs. sugar cost $1.20 ; 1 lb. tea
and 3 lbs. sugar cost $1.40 at advanced price"; if the price
of each had been aivanced 50% they would have cost
$1.80 .•. the 40 cents of a difference arises from the extra
increase of 40% on the tea . •. 40% of tea= 40 cents. Price
tea = $1.00, price sugar=6§ cents. (2.) Oommis-
sion on $1 for selling =3 cents; commission on $1
for investing =1 If cents .*. total commission on $1 =»
530
4ff cents; -^^^ = $10ol2 value of consignment, .'.
^«^(10812— 530) =$649.38lf. (3.) Taking 1 ounce
of each defaced ornament gives J^ ounces too much gold
in the new ornament, .*. we infer that we have taken too
much of the first and too little of the second ; but ounce
for ounce the first contains -^q ounces more gold than the
2nd, .'.we must take as much less of thp first as will
make up the j\j ounces, .*. i\-r-j%=^ ounces to» much
of first, .*. I ounces first and IJ ounces second, (4.)
m + iUh + iUy + (fMu + (f bl)* = 1949.635.1. (5.)
If he had passed all he would have gained 26s., .*.
3r2s.=value of all the coins before reduced; 299s. +
reduced coin=what he had when arrested. Twfcal loss
neglecting reduced coin = 1 3s., but by question 4s. I'lt^d. was
gained,. '.reduced coin-=13s. + 4s. 10^d.=«:17s. lOJ 1. .'. 16
so7ereigns. 19s. 6d. (6.) \^^^^=residy monwy B is
willing to receive. For every $1 A puts on hii» note he
^
EXAMINATION PAPERS.
85
. ould have to pay 2 cents for the use of D's name, and
also the bank discount on $1 for 4 months 3 days at 8%,
.-. .027334-.02=.04733 =amount taken off for every $1
put on face of note.-. .^^^g^yX-V^^f =11211.17+. .-. first,
way better by 11.17+. (7.) 8J + 6| = 15 miles,
of distance between Express and Freight when Express is
met by Mixed ; but Express had 7^ miles start on
Freight, .'. Express has gained 7| miles on Freight, .*.
2 o'clock time Express meets mixed, .*. 1 o'clock.
(8.) 5|%+2f%=8^%=/3,.-. 1/oof costX/;=l496.80.
.-.$5040, Answer* (9.) Let C B be the horizontal
plane, A C spectator, B E pedestal, E D statue. Join
A B, A E, AD, and draw A F parallel to C B, meeting
B E in F. Angle D A E=:E A B .-. ^ = | (Euclid
From this we find
vi. 3.)__
30 |/20.
8x10x12 .
4 area ^ '
-=15 i/7,
AD
A B=100
and AE:
(10.) Radius of
radius of inscribed circle=
circumscribed
2 area J
8 + 10+12'
circle =
Area j
XXXIV.— Page 299.
(1.) Rent+fl^XAu i*ent=i|^ reut=$3175; 3175
X 11 f =$2500, taxable income. (2.) JgtXlOO=|175=
price of 100 stock not considering dividend; §X 7X1^11
=:;$4||=worth of that part of dividend not due to pur-
chaser ; $175+$4||=$179||=price of stock two months
r'\^ 500 ( (1,07)^0-1 ) _
before dividend is due.
(1.07)8 ( .07
120.59, Ans. (4.) Find the time in which the sum of
the present values of each payment would amount to the
sum of the debts at the given rate. 18.4 months,. Ans.
(5.) 10|^ days. (6.) Let t be the required time ; then
86
RESULTS AND HINTS FOR EXAMINATION PAPERS.
(H)-l» whence t ,^,^,^^,,,^^^,,,
1600 1 ( l+r)^ff-l [ __
1 f 1500
3iog.2-iog.3 ==24.02 years. (7.^
{
r=rate ;
I =present worth of annuity where
{l+r)i»{ ~T" [=P'"esent worth of perpetuity
where r=rate ; then annuity better than perpetuity when
the former is greater than latter, or when log. (1+r)
greater than ^^, or when r greater than 4.7296%. (8.)
A -I m+iiVv)^-^in%)' [ = $665,265. (9.) 8 bushels
@$1.75, 40 @ $1.80 and 32 @ $2. (10.) 100000 Xt%
X|§^X|8^Xi8a=$80792.47i; 100000 X i%Xi88X
2 3==e80794.
♦ H
i
(7.)
here
uity
rhen
-fr)
(8.)
ihels
60
TOO
MxiltK Si (HoJn (Ebutational Series.
HAMBLIN SMITH'S
MATHEMATICAL WORKS,
▲RB USED ALMOST EXCLUBIVBLY
In the Normal and Model Schools, Toronto ;
Upper Canada College ; Hamilton and
Brantford CoUegriate Institutes ; Bow-
manville, Berlin, Belleville, and a large
number of leading High Sohocls in the
Provincd.
HAMBLIN SMITH'S ALGEBRA.
With Appeudix, by Alfred Baker, 6.A., Mathematical Tutor, Unlver
•ity College, Toronto. Price, 90 cents.
THOMAS KIRKL4ND, M.A., Science Mauter, Normal School.
"It is the text-book on Algebra for candidates for second-class
oeitificates, and for the Intermediate Examination. Not the least
valuable part of it is the Appendix by Mr. Baker."
GEO. DICKSON, R.A., Head Master, Collegiate Institute, HamUton.
" Arrangement of subjects ^ood ; explanations and proofs exhaus-
tive, concise and clear ; examples, for the most part fmm University
and College Examination Papers, are numerous, easy and progressive.
There is no better Algebra in use in our High Schools and Collegiate
Institutes.-''
WM. R. RIDDELL, B.A., B.Sc, Mathematical Master. Normal
School, Ottawa.
" The Algebra is admirable, and well adapted as a general text-
book."
Vf. £. TILLEY, B.A., Matlicmatical Master, Bowmanville High School.
" I look on the Algebra as decidedly the best Elementary Work vm
the subject we have. The examples are excellent and well arranged.
The <^xplanations are easily understood.
;•
R. DAWSON, B.A., T.C.I/., Head Master, High Sehot rolleville.
"With Mr. Baker's admirable Appendix, there would »tem to be
aothing left to be desired. We have now a first class book, well
idapted in all respects to the wants of pupils of all grades, from ttit.-
beginner in our Public Schools* to the most advanced student in oui-
Collegiate Institutes and Hij^h Scliools. Its publicntion is a gieat bvvu
I" the over worked nmtliomatical Uiachers of the Province.
ELEMENTARY STATICS,
BT
THOMAS KIRKLAND, M.A.,
Science Masteri Normal School, Toronto*
FRIOf: ^.oo.
V7. R. RdduiL, B.A., B.So., Mathematical Master, Ottawa Normal
School.
" From a careful examination of it I think it will be of great luo to
tliOBe preparing for the examinations of the Central Board,
Ueo. Baptib, H.A., M.B., Science Matter, Ottawa Normal ScKool.
" It supplies a great want felt by those preparing for Teachen*
Certificates. This— did it possess no other merits— should malco it a
great success. It is by far the best text book oA the sui)Jcct for the
schools of Ontario I have seen."
<3eo. H. Robinson, M. A., Head Master, Whithy High School.
"It is the work of one of the most successful teachen in th«
Dominion, and every page bears evidence that it is no hasty oomt>ila-
tion, but the fruit of matured thought and experience."
C. J. Macoreoor, U.A.rPrincipal High School, Strafford.
" In the Statics, the treatment of the subject is at once elementary,
and rigid enough to lay the foundation of accuracy in the further
prosecution of the science."
t>. C. McHe.vry, B.A., Collegiate Institute, Cobourg.
" Among the valuable text books you have rectntly published, none
is more timely than your ' Elementary Statics.' A work of the kind was
greatly needed, especially by High School Teachers ; and it is likely to
meet with very general favour. "
.1. W. (JrtNNOR, M.A , High School, Berlin.
" Mr. Kirkland has placed the teachers of Ontario under great
obligations by publishing his excellent little work. The arrangement
and clearness of the ' Book work,' and the admirable selection of pro-
blems, would of themselves place the book in the fir5<f rank of elemen-
tary treatises ; but, above all, one can trace in every page the result of
the author's practical expeaience in teaching the subject."
EXAMINATION PAPERS
ur
ARITHMETIC j
By J. A. McLellan, LL.D., Inspector High Schools, and
THOSb Sjrkland, M.A., Science Master, Normal Scliool,
Toronto. Second Edition.
PRICE $1.00.
From the GUELPH MERCURY.
. . . The work is divided into six chapters. The first is on tho
Unitary Method, and (;ives solutions showing its application to a
variety of prohlems, in Simple and Compound Proportion ; Percentage,
Interest, Discount, Profit and Loss; Proportional Part«, Partnership;
Chain Rule, Exchange, Alligation ; Commission, Insurance, &c.,
Btocks ; and Miscellaneous Problems. The second is on Elementary
Rules, Measures and Multiples, Vulgar and Decimal Fractions. Ihe
third contains Examination Papers for entrance into High Schools and
Collegiate Institutes, the fourth for candidates for third-class certifi-
cates, the fifth for candidates for the Intermediate Examination and
second-class certificates, and the sixth for candidates for third-clasi,
certificates and University Honours. It will be observed that the work
begins with the fundamental rules— those principles to be acquired
when a pupil first enters upon the study of Arithmetic, and carries
him forward till prepared for the highest class of certificates and for
Honours of the University. . . . Teachers will find in it a necessary
help in supplying questions to give their classes. Those who aspire to
be teachers cannot have a better guide— indeed there is not so good a
one— on the subject with which it is occupied.
From the ADVERTISER.
... By all who are groping after some method better than
they have at present, this volume will be cordially welcomed, and
many who have never suspected the possibility of accomplishing so
much by independent methods, will be, by a perusal of the introduc-
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From tho TELESCOPE.
. . . The plan of tho work is excellent, tlie exercises being
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The problems are all oriarinal, and so constructed as to prevent the
student usin^- any purely mechanical methods of folution. . . . We
should really feel proud of our Canadian Authors and publishing
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!
jt
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A DRILL BOOK
FOR CORRECT AND EXPRESSIVE READING
ADAPTED FOR THE USE OF SCHOOLS.
fl/ Richard Lewis, Teacher of Elocution, Author of "Domin-
ion Elocutionist," dc.
PRICE 7 6 CENTS.
J. M. PLATT, M.D., P. S. Inspector, Ptctou, Out.
. . . Lewis' " How to Read," is one of the finest little book*
ever introduced into our Canadian Schools. No efficient teacher will
fail to have his senior classeit supplied with the work at once.
J. MOKIUSON. M.A., M.D., H. M. iligh Scliool, Newmarket.
Such a book wu.s wanted and I am glad that the want has been sup-
plied by an Elocutionist of some note. I have adopted it for our Junior
dasses.
JOHN SHAW, Head Master Hij^h Scliuol, Omemee.
. . . I am pleased with it and .^huU curtaiiily introduce it at Mi(>
earliest opportunity. The publication cannot but be profitable to
teacher and pupil alike. •
B. N. RODGERS, inspectur ol P. Schools, Collingwood.
, . . We hope this l)ook will be brought to every teacher, aiffl
introduced into every school, \Ve firmly believe, that no time could be
better spent, than in learning the sim|>lf princij)les it lays down and
practising the suggestions it t^ivcs tor attniiiu^ a, &tyle of reading both
picasiqg and effective.
li. -M. B10(J, M.A.
. . . I wish it could be intriHhued into every school
W so MUCH NKBDfcD IN OUK .Si;H')t>L,S AS si CH A WORK.
NoTinso
JOriTT MAt'OUN, M.A., Head Master of Albert College Orammar
Scliipol, Prui'. of IJutany, &i\
. . . I most uiiliesitatinulv retHinnnend Lkwih' Ib'W to Rkad ti>
be immediately tntroduci d into all (iiirscbi>ols and that tiaciiers couipti
pupds in the higher cIu»hum to obtuln it, and instruct them in the use
of It evei7 day.
J. MILLER, U.A., H. M. High School, Hi tliomu
... it will create gr«at«r iutertvt in u >>ubject that sliuuld re-
ceive morn att^^ntimt.
JWiller & (Kto.'e (Ebutatioitai Strtts.
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111
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S'v^insTTOisr's
LANGUAGE LESSONS
-zxi
B. DAWSON, D.A., 0*. 0. D., Head Master High School , Uelleville.
I4iave been very much pleased by the introduction of " Swinton's
Language Lesson'»," into the list of Canadian School Books. It is
*im|ile, comprehensive, and reliable ; and sliows very clearly how easily
the study -of grammar may be made to go hand m hand with the prac-
tice of Composition, the great end for which grammar ought to be
taught. We have at last an elementary text book which may be en-
trusted into the hands of the most inexperienced teacher without any
(ear of its boing abused.
JOHN JOHNSTON, P. S. I., South Hastings.
I have carefully examined " Swinton's Language Lessons," and am
convinced from what I have seen of it, and fmm what I have heardirom
some of my most experienced teachers, that it is by far tlie best
Elementary text book on the subject that has yet been placed within
reach of our Canadian children. The simultaneous exercises in com-
position are an admirable feature. I shall recommend the book for use
|D all the schools in my district.
J. M. PLATT, M.l)., P. S. Inspector, Picton.
I am greatly pleased wltli this little work. Our best and most ex-
perienced teachers teach grammar to junior classes orally, after tbf
same fashion. Young and inexperienced teachers can do as well with
" Langiiage Lessons " as the oldest and best can do without it. Fot
pupils just entering upon this important branch, this little book in
question has no superior in the market.
W.
S. GLENDENINO, Inspector East Bruce, Walkerton.
. . . With its valuable aid the teacher will find it no difficult
task to make the study of language agreeable to even junior pupils. 1
esteem it so highly that I will use my influence to get it into the hand*
of every teacher in mj district, and, if authorized, into every school
likewise.
ROBERT MATHFSON, MA., H. M. High School, Walkerton.
. . . Language Lessons will assuredly prove a boon to teacheri
of composition. 1 find that for teuching English Grammar it is superior
to the usual treatises, as it treats o{ Grammar in a practical manner.
O. MOSES, P. S. I., County Haldhnaud, Caledonia.
I have carefully examined Swinton's Language Lessons for junior
cla.sses and consider it one of the best yet published, being admirably
adapted fur use in our public schools.
BEATTY & CLARE'S
BOOK-KEEPING;
A Treatisb on Sikolh and Doublb Entry Book-Kerpino,
FOR USE IN HIGH AND PUBLIC SCHOOLS,.
By S. 0. Beattt, Principal Ontario Comnrercial College, Belle-
ville, and Samdel Clark, Book Keeping and Writing
Master, Normal School, Toronto.
PRICE 70 CENTS.
T. O. STEEL, Inspector, P. S. Co., Proscott.
... I consider "Beatty & Clare's Book-kpeplng " plain and
simple, yet sufficiently comprehensive for all practical purposes, and
especially fitted for a school text book. ^
WM. TASSEE, LL.D., H. M., Oalt Col. Institute.
. . . Simple, clear, devoid of confusing definitions and very
practical throughout
J. W. CONNOR, B.A., H. M., H. S., Berlin.
... I consider it the best elementary work ou the subject that
I have yet seen.
D. C, Mchenry, M.A., Principal Cobourg Collegiate Institute.
I consider Beatty & Clare's Book-keeping an excellent text book.
Ai YOUNG, Principal of Berlin, C. S.
The work on Book-keeping by Beatty & Clare is the best that I
ever saw.
JOHN WILSON, Math. Master, Port Hope H. S.
. . . 1 feel safe in recommending the work to my follow
teacliers throughout the Province, as one well adapted to ensure
thorouishness in the art of Book-keeping.
HUGH J. STRANG, B.A., H. M., H. S., Goderich.
. . . Its elucidation of the subject being clear and adequate, the
work w^ll prove a valuable aid to all who may wish to make themselves
thoroughly acquainted with the principles of Bouk-keeping.
J. S. CARSON, Ins^ctor, Middlesex.
... I am assured from an examination that it is superior to
anv other work for our Canadian Schools
ENGLISH GRAMMAR
BY C. P. MASON, B.A., F.C.P.,
FoIlo%v of University College, London
With Examination Papers by W. Houston, M.A.
PIWCE 75 TENTS.
I
ALKX. SIM, M.A. . H. M., H. S., Oftkville.
Upwardn of three years ngn [ asked a tp-ommar sshool Ir.spector in
the old country to send me the uest grammar published there. Ho Im-
mediately sent me Mason.
A. P. KNIGHT, M.A., H.M., Kingston Collesriate Tnstltute.
Incomparuhly the best tcx' ))ook (or the senior classes of our high
schools that has yet been olTcrkd to the Canodian public.
J. KINO, M.A., LL.D., Principal, Caledonia, H. S.
Mason's grammar will be found a most valuable class-books fs
l^ecially for the instructiDii of advanced classes m English. The chapter
on the Analysis of ditflcult sentences is of itself sutlicient to place the
work far beyond any English grammar hitherto before the Canadian
public.
RICHARD LEWIS, H. M., Dufferin School Toronto.
As a philosophical treatise its discussion of doubtful points and iU
excellent methods and definitions cannot fail to give it a high rank in
the estimation of the best Judges of such works— the school teachers of
the country. It has reached a iwenty-first edition in England and 1
have no doubt it will meet with the same high appreciation in this
Province.
JOHN SHAW, H. M., H. S., Omemee.
. . . Mason's Orammar is Just such a book as many teachers have
been hoping to see introduced into our schools, its method being to
teach the subject by explanation, definition and abundant illustrauons
without stereotyped rules thereby making the study even attractive.
D. C. MacIIENRY, B.A., H. M. Cobourg Col. Institute.
It Is an excellent and reliable work. It will be well received bf
- tercbers and advanced pupils.
JOHN JOHNSTON, P. S. I., Belleville and South Hastlnjfs.
01' all the grammars that I have seen, I consider Mason's the best.
J. M0RRTS(3N, M.A.. M.D., Head Master, High School, Newmarket.
I have ordered it to be used in this school. I consider it by far ths
best English grammar for high school purposes that has yet apj^eared.
With " Mason " and " Fleminc" nothintr more seemn tn h« "Inah-Wi