UC-NRLF Examination Manuals No. I. Irving Stringham || WENTWOKTH & HILL'S EXAMINATION MANUALS, No. I. ARITHMETIC. BOSTON: GINN, HEATH, & COMPANY. 1884. Entered, according to Act of Congress, in the year 1883, BY GEORGE A. WENTWORTH AND GEORGE A. HILL, In the Office of the Librarian of Congress at Washington. J. 8. CUSHING & Co., PRINTERS, BOSTON. PREFACE. THIS Manual consists of two parts : The first part contains one hundred and fifty examination papers, the questions for which have been selected mainly from the English, French, and German collections of problems. These papers may be divided into three groups. The first fifty papers are confined to the Simple Rules, Fractions, and Weights and Measures ; the next fifty papers cover all the subjects treated in ordinary text-books except the Metric System ; the last fifty also include the Metric System. In each group the earlier papers will be found somewhat easier than the later ones. The papers are intended to be hour papers, but if any of them are thought to be too long for one hour, the time may be increased, or the length of the paper reduced by omitting one or more questions. The second part - of the Manual is a collection of recent examination papers actually set in various American and English institutions of learning. The Manual may be used in two ways. First: To test the learner's knowledge in the usual way by means of an examination. For this purpose the class will come to the recitation-room provided with the Manual and blank books, and the teacher will simply designate by number the paper to be worked. Secondly : To review^ the subject-matter of Arithmetic. This may be done by assigning problems to be worked in the class-room, 800568 IV PREFACE. or by assigning to each pupil a paper with directions to hand in the solutions, neatly worked out, at a subsequent recitation. The Manual will be found especially useful in preparing for written examinations. Answers to the problems in the first one hundred and fifty papers, bound separately in paper covers, can be had by teachers only, on application to the publishers. G. A. WENTWOETH. G. A. HILL. SPECIMEN PAPER WORKED OUT, 1. In 674,381 inches how many miles, furlongs, rods, etc. ? 12)674381 in. 3) 56 198 ft. 5 in. 18732yds. 2ft. 2 11)37464 half-yds. 40) 3405 rds. 4^ yds. 8)85 fur. 5 rds. 10 mi. 5 fur. 10 mi. 5 fur. 5 rds. 4| yds. 2 ft. 5 in. -4ns. 10 mi. 5 fur. 5 rds. 5yds. Oft. 11 in. 2, Find the G.C.M. of 269,178 and 352,002. 6)269178 352002 44863 ) 58667(1 44863 4)13804 3451)44863(13 3451 10353 10353 Ans. 6x3451 = 20,706. The common factor 6 is first taken out from both numbers. Fit>m the remainder 13,804, the factor 4, which is prime to 44,863, is ejected. The resulting number 3451 is contained 13 times in 44,863, and there- fore the greatest common measure is 6 x 3451 = 20,706. EXAMINATION MANUAL. 3 Simplify m P ilty -- 3 11 W 396 12 1 _2_ 7 _ _7_ = 264 + 144 + 231 - 14 3 11 24 396 792 iofA = _2_ ; 1-ofl^JL. Irfl.i. 3 11 33 11 132 24 3 72 12 l_J__l__jL = 792 - 48 - 42 - 77 = 625 . 33 132 72 792 792' 625 . 625 - A l 792 "792"" 1 ' 4, Divide 0.025 by 500, and 0.03625 by 0.29. 0.125 500)0.02500 29)3.625 0.00005 29_ 72 58_ 145 0.00005 \ A 145 0.125 j ' 5, Make out the following bill : 3J pounds of tea at 64 cents per pound ; 1 pounds of coffee at 40 cents per pound ; 62- pounds of loaf sugar at 10 cents per pound ; H pounds of butter at 34 cents per pound. How much change out of $5 should Mr. Smith receive? Mr. JOHN SMITH, Dr. to JAMES HORN. 1883. Aug. 17. Silbs. of tea @ 64 cts. . . . $2.08 li- Ibs. of coffee @ 40 cts. ... .60 6| Ibs. of sugar @ 10 cts ..... 65 1| Ibs. of butter @ 34 cts. . . . _ .51 $3.84 Received payment, Ans. $5.00 -$3.84 = $1.16. JAMES HOEN. ARITHMETIC. vii 6. If 18 men can dig a trench 200 yards long, 3 yards wide, and 2 yards deep, in 6 days of 10 hours each, in how many days of 8 hours each will 10 men dig a trench 100 yards long, 4 yards wide, and 3 yards deep ? Men, 10: 18: : 6 days. Length, 200 : 100 Width, 3: 4 Depth, 2: 3 Hours, 8: 10 9 2 3 JLfi X W iX^X^Xj X ft _ 27 _ 13J. ra v- 5 ina y 2 y '> \ s C 2 2 .Ans. 13J days. 7, What alteration will be made in an income by selling $10,000 of 4 per cent stock at 89J, and buying 5 per cent stock at 105 ? Income from 4 per cent stock = 0.04 of $ 10,000 = $400. Proceeds of 4 per cent stock = 0.89J of $ 10,000 = $ 8925. $1 of 5 per cent stock costs $1.05 ; therefore, Amount of 5 per cent stock = $ 8925 H- 1 .05 = $ 8500. Income from 5 per cent stock = 0.05 of $8500 = $425. Increase in income =$425 $400 =$25. 8, A room measures 16 feet by 21 feet, and is 11 feet high. There is one door 7 feet by 3 feet, and two windows 8 feet by 4 feet. Find the cost of papering it with paper 2 feet wide at 5 cents a yard. Distance round the room =16 + 16 + 21 + 21 =74 ft. Area of walls of room = 11 x 74 = 814 sq. ft. Area of door and windows = 21 sq.ft. +64 sq.ft. = 85 sq.ft. Area to be papered = 814 sq. ft. - 85 sq. ft. = 729 sq. ft. Area of one yard of paper =3x2 = 6 sq. ft. Number of yards required = 729 -=-6 = 121 \. Cost of the paper = 121-J x $0.05 = $6.07. Am. $6.07 L V. Vlll EXAMINATION MANUAL. 9, A jar full of water weighs 1.325 kg ; filled with mercury it weighs 12.540 kg . What is the capacity of the jar, and its weight ? The specific gravity of the mercury is 13.59. 12.540 1.325 11.215 k 8 13.59 1 12.59*8 0.89078 1 . 12.59)11.215 10072 11430 11331 9900 8815 10870 Mercury in jar weighs 11.215 k more than water in jar. A liter of mercury weighs 12.59 k s more than a liter of water. Capacity of jar 11.215 of a liter - 0.89078 1 . 12.59 Weight of water in jar = 0.89078 k . Weight of jar = 1.325 k s - 0.89078 k s = 0.43422 k s = 434.22s. Ans. 0.89078 1 ; 434.22*. 10, Extract the cube root of 5 to five places of decimals. 5.000(1.70997 3 x 10 2 = 3(10x7) = / == 300 210 559 259 3 x 1700 2 = 8670000 3(1700x9)= 45900 9 2 = 81 8715981 45981 3 X 1709 2 - 8762043 4000 3913 87 000 000 78 443 829 8 556 171 7 885 838 7 670 332 30 613 343 01 1. 709.97 ~Ans. For explanation of the method, see Wentworth and Hill's Prac- tical Arithmetic, page 282. EXAMINATION MANUAL. ARITHMETIC. 1. 1, Write in words 15,006,021, and state how many times a number is increased by annexing three ciphers to it. 2, Multiply 2,035,674 by 3096. 3, Divide 275,487 by 736, and prove that the result is cor- rect. 4, How many times is 195 yards 1 foot 8 inches contained in a mile? 5, Find the number of cubic inches in 1 cubic yard 24 cubic feet 760 cubic inches. 6, How many grains of gold in a cup weighing 8 ounces 4 pennyweights ? 2. 1, How much must be added to sixty million four hun- dred six thousand two hundred ninety to make three hundred twenty million? 2, Multiply 456,978 by 789. 3, Divide three hundred thirty-seven million one hundred three thousand twenty-five by eight hundred sixty- one. 4, In 674,381 inches how many miles, rods, feet, and inches? 5, Find the difference between 30 years 8 months 3 weeks 6 days and 44 years 3 months 1 week 5 days. EXAMINATION MANUAL. 3. 1, Write in words the sum of 4,300,702 ; 6,070,506 ; and 341,318. 2, Find the number which, subtracted from 80,000, leaves 57,735. 3, From the sum of eight million seventy-nine thousand six hundred ninety, and three hundred eighty-five thousand seven hundred nine, subtract their differ- ence. 4, Divide 19,094,867 by 4009. 5, The circuit of a race-course is 137^ yards. How many times must a bicyclist go round to complete 5 miles ? 6, Take 156 miles 160 rods 216 yards from 191 miles 80 rods 2 yards. 4. 1, Write in figures two million twenty thousand eighty- seven. 2, Express in words and in figures the excess of the value of one 5 over the other in the number 658,457. 3, Multiply seventeen thousand nine hundred forty-three by five thousand seventy-nine. 4, Divide five hundred one million five hundred by three thousand eight hundred fifty. 5, Reduce 125 square rods 23 square yards 6 square feet 108 square inches to square yards. 6, How many grains in a pound Avoirdupois ? in a pound Troy? ARITHMETIC. 5. 1, Write .in figures ten million eighty-three thousand six hundred eighty. 2, Divide the product of 37,800 and 7950 by 630. 3, What number multiplied by 6702 will give 218,773,386? 4, How often is 1 17s. 6cZ. contained in 28 2s. 6cZ.? 5, An engine draws a train of 23 cars, each containing 5 long tons, 2123 pounds of coal. What is the weight of coal in the train ? 6, A square drill-yard required 869 square slabs, each measuring 3 square feet 86 square inches. What is the area of the yard in square feet, etc. ? 7, Eequired the weight of a guinea, if 45 can be coined from a pound of gold. 6. 1, A person walked 136 miles in 40 hours 48 minutes. How many minutes was he in walking a mile ? 2, How many times must we take the number 7 to make 819? 3, By how much does the thirty-seventh part of three thousand six hundred sixty- three fall short of a hundred ? 4, Reduce 7,896,432 grains Troy to pounds. 5, If 56 acres of land cost $700, what will be the value of 13 acres 80 square rods? 6, A man agreed to buy a haystack, paying $ 30 for each load. He found his wagon held 1 ton 392 pounds, and that the whole stack weighed 10 tons 1288 pounds. How much has he to pay ? EXAMINATION MANUAL. 7. 1, Find the circumference of a carriage wheel which re- volves 1848 times in a journey of 3 miles. 2, In 120,505 square feet how many acres, etc. ? 3, If the moon moves forward in her orbit 57 13' 18" in 13 days, find the distance she averages a day. 4, A man can buy a white hat, which lasts 4 months, for 0.75 ; he can buy a black hat, which lasts 9 months, for $1.75. Which is the cheaper? What is saved in 3 years by wearing the cheaper hat ? 5, Find the number of pounds Troy equal to 78 pounds 4 ounces Avoirdupois. 6, Reduce 1 acre 91 square rods 2 square yards to square inches. 8. 1, Reduce 100,196,196 square inches to acres, etc. 2, Reduce 40 pounds 8 ounces 5 drams 1 scruple 7 grains to grains, Apothecaries' weight. 3, Find the cost of half an acre of ground at 63 cents per square yard. 4, The distance between two towns is 18 miles 40 rods 44 yards. How many telegraph poles will be required between them, the poles being 8 rods apart ? 5, If $328 equal 74 2s. I0d., by how many pence does a dollar exceed 4 shillings ? 6, How many cubic yards, feet, and inches in 175,983 cubic inches ? ARITHMETIC. 9. 1, In 36,845,371 ounces Avoirdupois, how many long tons, cwts., etc. ? 2, In 1,749,134 seconds how many weeks, days, etc. ? 3, The latitude of St. Paul's in London is 51 30' 49", and that of St. Peter's in Home, 41 53' 54". What is one-fifth of the difference of their latitudes? 4, Reduce 875,679 chains 25 links to miles, rods, etc. 5, Reduce 7658 square chains 625 square links to acres, square rods, etc. 6, Change 35 pounds 8 ounces 7 pennyweights 17 grains Troy to Avoirdupois weight. 10. 1, Express in figures nine thousand seventeen million fifty-nine thousand ninety-six. 2, How many days will 9867 pounds of hay last 13 horses, if each horse eats 33 pounds a day ? 3, A boy has a bag containing 2360 chestnuts ; he takes out 7 dozen for himself, and then divides the rest among 19 school-fellows, keeping those remaining over. How many chestnuts did he then have, and how many did each of the other boys have ? 4, A city containing 758,043 inhabitants has 5 districts. The population of the first is 78,967 ; of the second, 139,753; of the third, 145,069; the other two dis- tricts have each an equal number of inhabitants. Find the population of each of these two districts. 5, Reduce 367 acres 155 square rods 25 square yards 8 square feet 74 square inches to square inches. 6, Reduce 1,186,126 inches to miles, etc. EXAMINATION MANUAL. 11. 1, Reduce 2 miles 3 furlongs 20 rods 1 yard to inches. 2, What do 12 dozen chains weigh, if each contains 2 ounces 9 pennyweights 3 grains of metal ? 3, Find the greatest common measure of 203 and 2291. 4, Find the least common multiple of 12, 21, 28, 30, 35. 5, Multiply T 3 T of If by 5J of J. 6, Add together 0.0023, 2.38, 250, 0.527. 7, Reduce 3 quarts 1 pint to the decimal of a gallon. 12. 1, Reduce 1 furlong 15 rods 1 foot 6 inches to yards. 2, If a person spends $2226.50 a year, how much does he spend each day in an ordinary year ? 3, Find the greatest common measure of 2163 and 504. 4, Find the least common multiple of 18, 16, 63, 24, 56. 5, Find the value of 21 X If of l&X 3J of 1^. 6, Subtract 2.03 from 20.2. 7, Find the value of 0.625 of a gallon. ARITHMETIC. 13. 1, Eeduce 357,000 inches to miles, furlongs, rods, etc. 2, At a festival 23,760 persons entered the enclosure be- tween 10 AM. and 4 P.M. What was the average per minute ? 3, Find the greatest common measure of 5292 and 1520. 4, Find the least common multiple of 4, 9, 16, 28, 42. 5, Divide 5J by -|. 6, If I sell -f of |- of an estate, what part of the estate have I left ? 7, Multiply 3.26 by 1.02. 14. 1, A dozen persons hire an omnibus for $9.25. How much more must each pay than if the party were fifteen in number? 2, Find the greatest common measure of 3575 and 4719. 3, Find the least common multiple of 6, 15, 18, 35, 72. 4, Divide 20 T \ by 17 T V 5, Find the value of -| of an acre. 6, Divide 998.824392 by 0.018. 7, Reduce 5 ounces 12 pennyweights 16 grains to the deci- mal of a pound. EXAMINATION MANUAL. 15. 1, Find the greatest common measure of 5292 and 8316. 2, Find the least common multiple of 8, 12, 18, 24, 27. 3, Add together , -J-, -J. 4, Find the value of -ff^ of a bushel. 5, Divide 2 weeks 3 days by 3|. 6, Divide 160.68 by 3.9. 7, Reduce 3 quarters 3 pounds 2 ounces 2.816 drams to the decimal of a long ton. 16. 1, Find the greatest common measure of 731, 2329, and 3502. 2, Find the least common multiple of 3, 8, 17, 40, 153. 3, Add if A, A- 4, Which is the greater of 4 or J of 5, and by how much? 5, Find the value of 21 of 5 bushels -j- 1J of 2J pecks. 6, Divide 0.3964 by 0.75. ARITHMETIC. 17. 1, Keduce f of a pound Troy to the fraction of a pound Avoirdupois. 2, Divide 52 by 3.2. 3, Express 0.305 as a common fraction in its lowest terms. 4, Add together 2f , 41, 3 T \. 5, Find the greatest common measure and least common multiple of 125, 175, 225. 6, Divide f of by f of f . 18. 1, Which is the greater f of 1| or -f of 5J, and by how much? 2, Simplify 21 -f f of 5|- + 4 T 7 T + 5. 3, Add together -| and 2f , and subtract their sum from 4. 4, Multiply 0.026 by 3,3 ; by 0.33; by 33 ; and by 0.033. 5, Divide 1.8 by 500. 6, Express 0.0075 as a common fraction in its lowest terms. 10 EXAMINATION MANUAL. 19. 1, Add together 3J of 1| and 2f of If 2, Subtract I of H from J of 2f. g3 3, Reduce to a simple fraction ~. ** 4, Divide 611 by 0.13. 5, Reduce 7.2 feet to the decimal of a rod. 6, Find the value of 0.065 of an acre. 7, Reduce -J-|ff to its lowest terms. 20. 1, Subtract from f ; -f- from ; and $ from 1^ ; and add together the results. 2, Multiply 2 yards 1 foot 7^ inches by ^-. 3, Reduce -f^ of a pint to the fraction of a gallon. 4, Divide 2175.68 by 100. 5, Reduce ^ff to its equivalent decimal fraction. 6, Reduce 15 square rods to the decimal of one-half an acre. 7, Find the value of 0.009943 of a mile. ARITHMETIC. 11 21. 1, Find the value in English money of 1572.4185 francs, when the exchange is at 26.675 francs per pound. 2, Divide 101 by 1.01, and 0.101 by 10.1. 3, Reduce 14 hours 15 minutes to the fraction of 3 J days. 4, Reduce to a simple fraction ^ J o + T 5, Find the greatest common measure and least common multiple of 144, 176, 272. 6, How many plots of 2 1 acres each can be made out of an estate one mile square ? 22. L A man steps 2 feet 8 inches at each step. How many steps will he take in 2 miles? 2, Reduce to its lowest terms |j J. 3, Subtract 121| from 202. 4, How can you determine that a number is divisible by 3 without actually dividing by 3 ? 5, Two pipes together fill a cistern in 1 hour, and one of them alone fills it in H hours. How long will it take the other alone to fill it ? 6, Divide 3.52 by 2.2 ; by 0.22 ; and by 22. 12 EXAMINATION MANUAL. 23. 1, In 640,825 seconds how many weeks, days, etc. ? 2, Reduce -J-f-fyJ- to its lowest terms. 3, Add 16ft, 1, i A- 4, Subtract 3 1 from 30^. 5, Find the product of 1-fo X 3^-f X -^ X 6, If T 7 ^- of an estate be worth 3003, what is the value of the estate? 7, Reduce 213 rods 1 yard 2 feet 6 inches to the common fraction of a mile. 24. 1, Divide 0.05625 by 0.0275. 2, Reduce 3 15s. 6.5 d. to the decimal of 4. 3, Westminster Hall is 237 feet long by G8 feet wide ; Brussels Town Hall, 264 feet by 50 feet. How many more persons could Westminster Hall accom- modate than Brussels Town Hall, allowing f of a square yard to each person? 4, Simplify 2^ + | X |- 21 5, Multiply 9-3^ by 16} of 1 T V 6, Divide 5& -|| by If of 8j. ARITHMETIC. 13 25. 1, Find the value of jJt-^J*L multiplied by & of 6. ^ 6~ + 2" + -g" 2, Reduce to its lowest terms J|-f|f. 3, A can do a piece of work in 10 days, B can do the work in 15 days. In what time can they both do it work- ing together ? 4, Arrange in order of magnitude 2.5 X 0.075; 2.625-^-7; 5 X 0.05. 5, Reduce 0.972 to its equivalent common fraction. 6, Reduce to a decimal T f f -3-. 7, Reduce 0.9 of a pound Avoirdupois to the decimal of 5 pounds Troy. 26. 1, How many cubic inches in a brick that is 9 inches long, 4 inches wide, 3 inches thick? 2, Reduce to a simple fraction 3| X 3 T % X 2f\- X 2-^- X -5. 3, What fraction of J- of a mile is 1 J feet ? 4, Reduce 6|- of 365^ days to the fraction of 3 years. 5, Express in figures seventy-three ten-thousandths. 6, Reduce 0.536 to a common fraction. 7, Divide 0.005868 by 0.036, and arrange the divisor, divi- dend, and quotient in order of magnitude. 8, Divide 0.5 by 25 ; 87.5 by 2.5 ; and 0.055757592 by 0.009207. 14 EXAMINATION MANUAL. 27. 1, Divide 10.8528 by 1.02 and express the quotient as a common fraction. 2, Reduce 2.5 gills to the decimal fraction of 3 gallons. 3, Find the value of 14.1275 acres. 4, What is the value of 40 acres 132 square rods at $37.50 per acre ? 5, A railway train goes 200 miles in 8 hours. In what time will it make a journey of 40 miles ? 6, How long will a journey of 15 miles 24 jods 3 yards take at the rate of 3 miles 204 rods 3 yards in 56 minutes ? 28. 1, A race-horse goes 5 miles in 32 minutes. How long will he be in going 1650 yards? 2, Reduce -J of ^ of a mile to the fraction of f of -jf of 8 miles. 3, Reduce 5.018 to its equivalent common fraction. 4, Simplify 5, Express 2 feet 3 inches as the fraction of 4 yards. 6, Resolve 18, 16, 36, 44, 45, 48, 63, 121 into their sim- plest factors, and find their least common multiple. ARITHMETIC. 15 29. 1, Sound travels at the rate of 1120 feet in a second. How far off is a thunder cloud, when the clap follows the flash of lightning in 10 J seconds? 2, The four sides of a field are 23 chains 19 links, 17 chains 34 links, 6 chains 85 links, 24 chains 62 links. How many yards around the field ? 3, Reduce 10,000 square yards to acres, etc. 4, Find the sum of 8 cubic yards 13 cubic feet 1234 cubic inches, 5 cubic yards 14 cubic feet 976 cubic inches, 2 cubic yards 5 cubic feet 854 cubic inches, and 7 cubic yards 10 cubic feet 1012 cubic inches. 5, Express 1 peck 6 quarts 1 pint as the fraction of 6 bush- els 1 peck 3 quarts. 6, Express 13 hours 15 minutes 17 seconds as the fraction of 6 days 1 hour 48 minutes 7 seconds. 7, Find the value of -fa of 3 long tons 5 cwt. 101 pounds. 30. 1, There are 7 miles of road in a certain district. If the average width of the road is half a chain, how many acres of land consist of roads ? 2, Reduce 1012 quarts to bushels. 3, Reduce 673,856 seconds to days. .4. A dishonest milkman mixes a pint of water with every two quarts of milk. How many gallons will he make in this way out of 20 gallons of pure milk ? 5, A well is 18 yards 2 inches deep, and the wheel is 4 feet 2 inches round. How many turns of the wheel will raise the bucket ? 6, Express 1 day 1 hour 50 minutes 42 seconds as a decimal of a day. 7, Express in days, hours, etc., the true length of a year, 365.242218 days. 16 EXAMINATION MANUAL. 31. 1, Find the least common multiple of 8, 10, 12, 25, 30, 36. 2, Add f of a score to -f- of a dozen, and subtract from the result | of a hundred. What is the remainder ? 3, A cistern can be filled in 20 minutes by one pipe and in 30 minutes by another. In how many minutes will it be filled by both together ? 4, Express If of 7 yards 2 feet 9 inches as a fraction of 13 yards 7 inches. 5, A man walked 111 miles in 3 \ hours. How long would he be in going 20 miles at the same rate ? 6, Divide 723.6 by 22.5 ; and 7.236 by 0.0225. 7, Find the value of 3.5 X 0.8. 32. 1, Find the value of 0.3 X 0.27. 2, If -| of a ton of coal costs $4, what will \\ cwt. cost? 3, Find the value of 0.2625 of a mile. 4, The highest mountain in the world is Dhawalaghiri, in the Himalayas, and is 28,000 feet above the level of the sea. Express this as a decimal of the earth's radius, 4000 miles. 5, From 1 pound Troy of standard gold are coined 46.725 sovereigns. Find the weight in grains of each sov- ereign. 6, The depth of a canal is 6 feet 4 inches, the width 19 feet 8 inches, and the length 20 miles. How many cu- bic feet of water will it hold ? ARITHMETIC. 17 33. 1, Add together -^, -^-, $, and -|. 2, Divide -^ by 6|. 3, Reduce 789,654,328 inches to miles. 4, Reduce 25 16s. Sd. to the fraction of 15 10s. 5, The upper floor of a house is 18 feet 4 inches above the ground and is reached by two equal staircases, separated by the landing of the first floor. How many stairs are there in each staircase, if each stair is 11 inches high ? 6, How many hurdles will it take each 5 feet long to make a square sheep-fold, each side of which is 40 rods? 7, If a quantity of wheat fills 1155 sacks, each holding 8 bushels 4 quarts, how many sacks will it take to contain the wheat when each sack holds 6 bushels 3 quarts ? 34. 1, If 64 gallons of wine and 16 gallons of water are mixed, how much wine is there in 2 quarts 1 pint of the mixture ? 2, Find the total weight of 5792 iron bars, each weighing 23 pounds 10 ounces. 3, Reduce 0.056 of a square rod to the decimal of an acre. 4, Find the value of 0.58 of a common year. 5, The price of gold being 3 17s. 10 d. an ounce, find the weight of a nugget worth 341.0925. 6, Find the greatest common measure and least common multiple of 161, 253, 299. 7, Simplify 1^- + f of ^ - H of 6. 18 EXAMINATION MANUAL. 35. 1. Add 0.60457; 46.70056; 5.80007; and 4.7896. 2, Divide 5.0666 by 21.56. i 3, Reduce 2.025 miles to yards. 4. Find the difference between 0.44 of 1 week and 0.125 of 8 days. 5, If the weight of 1 cubic foot of water is 62^-f pounds, find the error in calculating the weight of 1000 cu- bic feet, on the assumption that 1 cubic foot weighs 1000 ounces. 6. Supposing the quick-step in marching to be 2 paces per second, and the length of each pace to be 28 inches, find the time in which a regiment will march 35 miles. 7, Simplify H-(H of J). 36. 1, Reduce 186 yards 2 feet 8.04 inches to the decimal of a chain (22 yards). 2, Add together -fa of a square mile, y 7 ^ of an acre, and -f of a rood, giving the result in acres, roods, and square rods. 3, Simplify 1 + 61 xM-^xJ, 4, Reduce 3 cwt. 14 pounds to the decimal of a long ton. 5, Find the rent of 215 acres 45 square rods at $5.62 an acre. 6, If 4-J ounces Avoirdupois cost $8|^-, what will Sj-f pounds cost? ARITHMETIC. 19 37; 1. If a bankrupt has assets to the amount of $1020, and debts to the amount of $3225, how many cents on a dollar will his creditors receive ? 2. Two farmers bought a crop of hay. One took -| of it, and paid $ 12. What had the other to pay ? 3. In a town of 450 people, 0.44 were men and boys, 0.38 were women and girls, and the rest were chil- dren. How many were there of each ? 4. If the carriage of 12i cwt. for 50 miles cost $3^, what will it cost to carry 17? cwt. the same distance? 5. Simplify (2 J + i)-f-(2f-i). 6. If | of a yard cost f of $1, what will || yards cost? 7. Divide 7.584057 by 11.7. 38. 1. In 4,076,412 dwts. Troy, how many pounds, ounces, etc. ? 2. Divide lOOf by 35. 3. Divide 18,454.9239 by 0.1225. 4. In 17,630,754 square inches, how many acres, etc.? 5. Subtract 8^ from 12^. 6. Subtract 6.04083 from 12.7. 7. A person sold of his estate, bequeaths f of the re- mainder to his son, and leaves the rest to be dis- tributed equally among 3 charities. If each of these charities receives $136.25, what is the value of the estate? 20 EXAMINATION MANUAL. 39. 1. Find the value of -ff of a mile. 2. Keduce 2 weeks 2 days 19 hours to the fraction of a month (4 weeks). 3.. Reduce y 5 9 Q- to a decimal. 4. A bankrupt's liabilities are 3768 17s. 6 d. "What are his assets, if he can pay 13 s. 7? d. in the pound ? 5. Subtract -f-% dwt. from 2.6 ounces, and give the an- swer as the decimal of a pound Troy. 6. Divide 218.4 by 0.168. 7. Divide 12 by 40. 1. Express 13 minutes 7 seconds as the decimal of 1 hour. 2. Add 6, l\, ^, and ft. 3. Find the cost of 11 miles 120 rods 165 feet of railway at 32,500 per mile. 4. Add 2.6 days and 0.85 of an hour, and give the an- swer in minutes. 5. In 156,704 square inches, how many square yards, etc.? 6. Divide 8.4605 by 0.248 to three places of decimals. 7. Subtract 6f from Sf ARITHMETIC. 21 41. 1. In 57,625,318 square inches, how many acres, square rods, etc. ? 2. A bankrupt's estate amounts to 910 3s. Hd, and his debts to 875. How much can he pay in the pound ? 3. -What is the circumference of a wheel which makes 514 revolutions in passing over 1 mile 467 yards 1 foot? 4. Find the value of 5f 4f + -f-^ If 5. From 21-J-31 take -i-Xf X-f-Xf. 6. Divide 18.13 by 0.00037. 42. 1. A piece of cloth, when measured with a yard measure that is -f of an inch short, appears to be 10 yards long. What is its true length ? 2. Divide 120,987.2 by 400. 3. Add |f 3-J-, 1/ T , and -fr. 4. Simplify y A -4y A U^ 5. The weight of a cubic inch of water is 253.17 grains ; that of a cubic inch of air 0.31 grains. Find to three places of decimals how many cubic inches of water are equal in weight to 1 cubic foot of air. 6. Find the price of 5 acres 72 square rods of land at $47.50 per acre. 22 EXAMINATION MANUAL. 43. 1. Reduce 42 rods 1 yard 8 inches to the fraction of a mile. 2. Find the value of 1.46875 acres. 3. Divide the product of 6.225 and 8.25 by 0.0025. 4. What fraction multiplied by f will give f ? what frac- tion divided by f will give -| ? what fraction sub- tracted from -^- will give 5. Arrange in order of magnitude 6. A and B start at a distance of 64 miles from each other. A walks 3J miles an hour ; B, 2. If they start at the same time, how many miles will they each walk before they meet ? 7. A ship left England at noon, January 1, 1851. She reached a port in Australia at midnight (Greenwich time), April 23. If the length of the voyage was 18,225 miles, what was her average rate per hour ? 44. 1. Subtract 17.2398 from 27.06. 2. Multiply 46.2375 by 0.0074. 3. Divide 92.3784 by 0.623 to three places of decimals. 4. Find the product of T \, ^, 9f , and 2f 5. Subtract 4.42 of an hour from 3.64 of a day. 6. Reduce 136,240 square feet to acres, etc. 7. Reduce 234,567 grains to pounds, ounces, etc., Apothe- caries' weight. ARITHMETIC. 23 45.. 1. The imperial gallon contains 277.274 cubic inches. What is the size of a pint pot in cubic inches ? What Aveight of water will it hold, if a cubic foot of water weighs 1000 ounces? 2. What number added to the sum of -f , f , f, and f will make 4? 3. A field of 3 J acres is divided into 28 equal parts. What fraction of an acre is there in each part ? 4. Find the sum of 17.01, 0.1303, 500.42101, 0.001, and 6.6. 5. Divide 6.2301533682 by 8.8964. 6. If 7 tons 336 pounds of coal cost $32.50, what will 1232 pounds cost? 46. 1. Find the wages of a man for 3 weeks 4 days 8 hours at $8 per week, reckoning 6 days to a week and 10 hours to a day. 2. Eeduce 30 rods 2 yards 1 foot to the fraction of 150 rods 4 yards 2 feet 1 inch. 3. If f of an estate is worth $870, what is the value o of it? 4. Express in the simplest form 3-| + -J of T8 5. What number multiplied by ^ will produce 90J ? 6. What number added to l I 7 - 5 - + 3^- + 2^- + -j s will make the sum total 10 ? 7. Give in feet the value of 7.0125 miles. 24 EXAMINATION MANUAL. 47. 1. Given the fractions -g%, T 3 / T , and -^ 7 ; express the differ- ence of the first two as a fraction of the difference of the last two. 2. Reduce ]||| to its lowest terms. 3. Divide 16.9 by 0.0013, and also by 1.3. 4. Reduce 0.53 and 0.00987 to equivalent common frac- tions. 5. Find the value of 0.3925 of 2 years, each year contain- ing 365i days. 6. Reduce 6 yards 2 feet 7.5 inches to the decimal of a mile. 48. 1. What decimal of 1 day is 23 hours 15 minutes 6 seconds? 2. Find the average of 21f , 73 , 0, 3^, 82, 17^, H 3. Add ^ of 5, $ of 9 13 s. 2| d., and -^ of 2s. 6d. 4. A and B can do a piece of work in 7 days, B and C can do the work in 8 days, and all three together can do it in 5 days. What part of the whole work can each do in 1 day ? 5. What will be the cost, at 18 cents a square yard, of paint- ing the walls of a room 17 feet 3 inches long, 15 feet 5 inches wide, and 13 feet 6 inches high, allow- ing 54 square feet for windows, etc. ? 6. Find what fraction the sum of -^ $, -jV> anc ^ IT * s f 2^ of 1| of f ARITHMETIC. 25 49. 1. A person possessing -^ of an estate sold y of y^- of his share for $120.62*. What would -J- of T 8 T of the whole estate sell for at the same rate ? 2. Express as a fraction of $5 the difference between $7|- andf of $7. 3. Subtract 2.63 dwts. from 12.13 ounces Troy, and express the answer in pennyweights. " 4. In 76,128,976 inches how many miles, etc.? 5. Divide 78 by 361.059 to three places of decimals. 6. Find the value of 2.5 + - 6.002. 50. 1. Find the average of 12Jf , 21, 7f , 0.034, 3.125, 0, 24.5, and 12^. Express the fractional part decimally. 435.1x0.0046 2. Reduce to the simplest form 0.125 3. Divide the sum of 14.4 and 1.44 by their difference, and express the result as a common fraction. 4. A can build a wall in 3i days, and B in 5 J days. In what time will A and B together do it? 5. A brick 9 inches long, 4J inches broad, and 3 inches thick weighs 9 pounds nearly. What would a brick weigh if it were 12 inches long, 6 inches broad, and 4 J inches thick ? 6. Subtract 73.4698 from 108.30125. 26 EXAMINATION MANUAL. 51. 1. Add , 2-f , and 13 T % ; divide this sum by 13^ ; and subtract the result from 5 T 3 Q-. 2. A cistern can be filled in 50 minutes by one pipe, and in 1 hour 5 minutes by another. In how many minutes will it be filled, if both are open together? 3. If a 4 per cent stock is at 82|, what will be the cost of $1000 stock, and what sum will be gained by sell- ing out at 86i ? 4. An army is besieging a town in which are 1000 men, with provisions for three months. How T many must . leave at once, in order that the rest may be able to subsist a year ? 5. Divide 7.619 by 0.0019. 6. Arrange in order of magnitude ^ -fj, -J-J, ^. 52. 1. A room is 20 feet 6 inches long, 15 feet 6 inches wide, and 16 feet high. It has two doors, each 8 feet by 3 feet 9 inches ; it has one window 5 feet by 7 feet, and two windows, each 5 feet by 4 feet. What will it cost to paper the room with paper 1 yard wide, at 20 cents per yard ? 2. Divide 0.101 by 0.5; by 0.05; by 50; and by 5000. 3. Eeduce to a common fraction 0.01034. 4. Divide A of # by T % of -ftf 5. Find the square root of 488,601. 6. Find the simple interest of $1025 for 13 years at 43 per cent. ARITHMETIC. 27 53. 1. If -f of a yard of cloth cost -| -of a dollar, what will -j^- of a yard cost? 2. Find the greatest common measure of 2526 and 2947. 3. Subtract 0.002 from 11, and multiply 0.01 by 1.01. 4. Divide 2f of If by 3 of f of . 5. If 0.5 of 1 buys 0.4 of a gallon, how much may be bought for 6s. 3d? 6. A steam engine and a horse start together. The engine does the first mile in 5 minutes, the horse in 4 min- utes. After this mile the rate of the engine is 30 miles per hour, that of the horse 20 miles per hour. Which wins in a three-mile race, and by how much? 54. 1. Divide 1.44 by 1.2 ; by 12 ; by 0.012 ; and by 120. 2. Find the square root of 449.44. 3. What is the cost of carpeting a room 21 feet by 30 feet with carpet half a yard wide, running across the room, at 75 cents a yard ? 4. Divide 1300 into three parts, in the ratio of 6, 4, 3. 5. If 12 men do a piece of work in 15 days of 12 hours each, how many days of 9 hours will 10 men take to do it? 6. Find the income produced by investing $4500 in 3 per cent bonds at 90 ; and that produced by investing $2850 in 3J per cent bonds at 95. 28 EXAMINATION MANUAL. 55. 1. Reduce 12 s. 6 d. to the decimal of a pound sterling. 2. Divide -J of of 4f of 2J- by of 4-J- of 3| of If 3. Find the compound interest on $100 for two years at 10 per cent. 4. If 24 men do a piece of work in 14 days of 9 hours, how many men will do it in 12 days of 7 hours. 5. Find the least common multiple of 10, 14, 15, 21, 30, 42. 6. What sum invested in 3 per cent bonds at 92 will pro- duce an income of $ 100 per annum ? 7. The gross receipts of a railway company are $231,100. After deducting 35 per cent for working expenses, and paying 6 per cent interest on $2,500,000 bonds, what sum is left for dividing among the share- holders ? 56. 1. Express as a decimal fraction the sum of -|, J, -|, J, T 9 -^, 2. Simplify _ _ ; and O I 6 - 3. Divide 36.33 by 210 ; 35 by 0.05 ; 0.002 by 200. 4. Find the square root of 22.1841. 5. If 3 pounds of tea at $1.56 per pound, 5 pounds at $1.20, and 7 pounds at $.60 are mixed, at what price per pound must the mixture be sold to gain 2 per cent? 6. Find the interest of $ 535 for 9 months at 41 per cent. ARITHMETIC. 29 57. 1, Find the greatest common measure of 124,321 and 197,451. 2, Reduce 0.075 of a pound sterling to the common frac- tion of 4 s. 6 d. ; and 2 square rods 9 square yards 4 square feet 72 square inches to the common fraction of 1 acre 60 square yards. 3, A man buys eggs at 11 cents per dozen, and sells them at 2 cents apiece. What does he gain per cent ? 4, What sum, if put out at 3& per cent for 6 years, will produce $28.87i-, simple interest? 5, Divide 1.69 by 0.13 ; 12.1 by 0.011 ; 0.001 by 0.01. 6, Find the square root of 4.1209. 58. 1, Find the simple interest on $387.50 for 5 years 3 months at 3 per cent. 2, Find the least common multiple of 3, 5, 7, 9, 15, 63. 3, Divide l-a + i + ^) by 1-Jof 1 of ^. 4, Multiply 0.000725 by 31.25 ; and divide the product successively by 6.25, 625, and 0.0625. 5, At what price per hundredweight must goods be sold, which were bought at $5 per ton, in order to gain 6 per cent ? 6, A manufacturer makes a profit of 20 per cent, whole- sale dealer 25 per cent, shopkeeper 40 per cent. What is the first cost of an article bought at a shop for $4.20? 30 EXAMINATION MANUAL. 59. 1, Divide $ 154 among 4 persons in the proportion of , i i i 2, In how many days of 12 hours will 72 men do a piece of work which 60 men can do in 30 days of 9 hours ? 3, Find the interest on $354.27 for 3 years 2 months 12 days at 2i per cent. 4, $4500 is divided among A, B, C, and D. A receives i of the money, B and C each f of the remainder. How much is left for D ? 5, Express as common fractions 0.001375 ; 0.03 ; 7.19318. 6, A can walk 10 miles in 2i hours, and B can walk 11 miles in 2 \ hours. They start to walk a match of 55 miles. Which will win, and by how much time ? 60. 1, The profit made by selling beer at 1 d. per pint above cost is 50 per cent. What is the gain per cent by selling it at 6 d. per gallon above cost ? 2, Find the compound interest on $66.67 for 2 years at 9 per cent. 3, How much money must be invested in 3 per cent bonds at 92 to secure an annual income of $150? 4, Find the L.C.M. of 12, 84, 120, 132, 156. 5, Keduce -|-|-|-f to lowest terms. 6, A piece, of work can be done in 50 days by 35 men. After 12 days 16 men strike. How soon will the rest finish the work ? ARITHMETIC. 31 61. 1, Find the greatest common measure of 5522 and 6006. 2, Divide T V- T V by 3 T V-2ff 3, Express as common fractions 0.06125 and 0.1237. 4, If a room is 27 feet 5 inches long, 14 feet 7 inches wide, 12 feet 10 inches high, how much paper -J- of a yard wide is required to cover the walls ? 5, "What is the amount at simple interest of $1275 in 5 years 8 months at 3|- per cent ? 6, If I buy sugar at $7 per cwt., at what rate per pound must I retail it to gain 7-f per cent ? 62. 1. If 8 men can reap 40 acres of wheat in 7 days, how many acres will 24 men reap in 28 days ? 2. Find the square root of 2,900,209. 3. How many cubic feet of air in a room 10 feet long, 8 feet 6 inches broad, and 6 feet 6 inches high ? 4. A 4f per cent stock can be purchased at 91. What per cent interest will this investment yield? 5. When the Centigrade thermometer marks 25 degrees, what will Fahrenheit's thermometer mark ? 6. Find the greatest common measure of 210 ; 258 ; 903. 32 EXAMINATION MANUAL. 63. 1. amplify -I, and g^. * 2. Express as decimals -^ yf TT anc ^ ' ^ db 1 3. How many miles will a ploughman walk, in ploughing an acre of ground, if each furrow is a foot in breadth ? 4. A room is 12 feet by 10 feet, and 7 feet high. How many yards of paper 2 feet 6 inches wide will it take to paper the room, if the waste is ten per cent ? 5. A plank is 3 inches thick, 18 inches wide, and 30 feet long. How many board feet does it contain ? 6. Eggs are sold at the rate of 5 for 4 cents. At what price were they bought if the profit was 20 per cent? 64. 1. Find the square root of 0.00027 to four places of decimals. 2. If I sell $2500 3 per cent stock at 95, and invest the proceeds in 4? per cent stock at par, what difference does it make in my income ? 3. What is the cost of papering a room 16 feet long, 12 feet wide, 10J feet high, with paper 21 inches wide at 7 cents per yard, if the waste is 12J per cent? 4. Express -%fa as a decimal; and 0.1236 as a common fraction. 5. Divide 22.4615 by 0.167 ; and 0.004095 by 0.273. 6. Find the least common multiple of 3, 8, 15, 21, 18. AEITHMETIC. 33 65. 1. A owns of a vessel, B J, and C ^, and the rest belongs to the master. What is the master's share ? 2. If two acres will maintain 3 horses for 4 days, how long will 6 acres maintain 6 hordes ? 3. Divide 9.3828 by 1117; by 11.17; by 0.01117. 4. What is the difference between the simple and com- pound interest on $550 for 3 years at 5 per cent? 5. A merchant sold goods for $750 more than he paid for them, and cleared 15 per cent. What did he pay for them ? 6. Two boats row a race of 1 mile 720 yards. One rows 31 strokes a minute, and clears 30 feet each stroke ; the other rows 33 strokes, and clears 28 feet. How many yards ahead will the winning boat be when it passes the winning post ? 66. 1. What is the price of a Turkey carpet 20 feet 6 inches long by 12 feet 9 inches wide, at $5.04 a square yard? 2. If I invest $3570 in 7 per cent stock at 2 premium, what income do I derive from it ? 3. A grocer bought 40 pounds of tea at 60 cents, and 90 pounds of coffee at 42 cents a pound. He sold the tea at 96 cents and the coffee at 36 cents a pound. What did he gain or lose ? 4. Find the least common multiple of 34, 51, 85, 120, 170. 5. Simplify 12.4 + 0.064-0.066, 0.002 6. Add i of | of 5s. 4rf., | of f of 6s., f of f of 2s. 34 EXAMINATION MANUAL. 67. 1. Find the cost of papering a room 21 feet long, 16 feet wide, 10J feet high, at 15 cents per square yard. 2. A can run 10 yards to B's 9. How many yards start must A give B in a mile to make an even race ? 3. Simplify i H-H-I). . i 4. If I sell out $10,000 of 3| per cent stock at 94, and buy with the proceeds 6 per cent stock at 105, what will be the alteration in my income ? 5. Find the true discount on $1025.62^ for 6 months at 5i per cent per annum. 6. Reduce to its lowest terms IH4M. 68. 1. Find the L.C.M. of 2, 3, 4, 5, 8, 12, 72, 84. + f a ofA 3. Find the cost of paving a passage 15 yards 2 feet 6 inches long, and 3 yards 6 inches wide, with tiles costing $3.60 per square yard. 4. Add together 53, 36.875, 4|, I of 7J, and divide the result by 0.01. 5. If 6 men can dig 5 acres in 8 days of 10 hours, in how many days of 12 hours can 4 men dig 6 acres ? 6. At what rate of interest will $2560 amount to $3328 in 5 years ? ARITHMETIC. 35 69. 1. If I sell out $1000 from 3 per cent stock at 88, and buy 5 per cent stock at 110, what alteration do I make in my income ? 2. If a man buys 560 tons of coal at 14s. 8>d. per ton, and sells it at lie?, per cwt., what is his gain per cent? 3. Divide 42.5 by 0.017 ; and find the value of 0.625 of 3 pounds Avoirdupois. 4. Simplify 3 -ft + !)- 5. Find the square root of 1.00060009. 6. The gross yearly rental of an estate is $2100 ; taxes and repairs amount to 25 per cent of the rental. The owner sells the estate for 21 times the gross yearly rental, and invests the proceeds in 3 per cent stock at 98. What does he gain or lose in his net income ? 70. 1. If $1350 at simple interest amount to $1570.50 in 1 year 8 months, find the rate per cent. 2. If by selling wine at $3 a gallon I lose 6 per cent, at what price must I sell it to gain 17 per cent? 3. Find the compound interest on $750 for 5 years at 2J per cent. 4. Eeduce 347,894,178 square inches to acres, etc. 5. If $850 amounts to $913.75 at 2 per cent, find the time. 6. A room is 10 feet high, 5 yards long, and 3 yards wide. It contains a door 8 feet by 4 feet, two windows each 5 feet by 4 feet, and a fireplace 6 feet by 4 feet 6 inches. How many square yards on its walls require to be painted ? 36 EXAMINATION MANUAL. 71. 1. The distance between the posts of a railway telegraph is 60 yards. Find the rate of a train which passes 11 posts in 50 seconds. 2. Find the income from an investment of $5308.33 in 3 per cent bonds at 91. 3. A invests $1200, B $2400, in business. The net profit at the end of the year is $ 720. How much should A and B each receive, and what is the rate of interest upon the investment? 4. Find the least common multiple of 5, 7, 16, 28, 48, 21. 5. If i of a ship be worth $292.25, what part of her will be worth $1002? 6. If 10 men can reap 20 acres in 4 days, how many men can reap 70 acres in 10 days? 72. 1. What sum of money will amount to $276.25 in 1 year and 3 months at 5 per cent simple interest ? 2. When 3 per cent bonds are at 75, what sum must be invested to produce an annual income of $ 120 ? 3. Find the present worth of $1836, due 4 years hence, at 5 per cent simple interest. 4. What is the rent of a field containing 112 acres 109.5 square rods at $2.64 an acre? 5. Divide 1368.2394 by 2400.21, and by 0.00240021. ARITHMETIC. 37 73. 1. Find the value of 2-f-i- of 140 10s. 6rf. + f of 1 Is. 2. Find the greatest common measure of 1288, 1736, 104. 3. If 120 men build a house 60 feet high in 15 days, how many will build a house 55 feet high in 10 days? 4. Find the difference between the simple and compound interest on $955 at 6 per cent for 4 years. 5. A garrison of 1000 men have provisions for 30 days. At the end of 10 days a reinforcement arrives, and then the provisions last only 5 days. What is the number of the reinforcement? 74. 1. Express 0.466 as a common fraction. 2. A sum of money was borrowed at 5 per cent simple in- terest. In 7 years it amounted to $810. What was the sum borrowed? 3. If 100 men in 6 days of 10 hours can dig a trench 200 yards long, .3 yards wide, and 2 yards deep, in how many days of 8 hours can 180 men dig a trench 360 yards long, 4 yards wide, and 3 yards deep? 4. Find the cube root of 42,508,549. 5. How many rods of fencing are required to enclose a square park containing 832 acres 105 square rods? 6. Which is the better investment, 4 per cent stock at 120, or 2$ per cent stock at 75? 38 EXAMINATION MANUAL. 75. 1. What is the length of the edge of a cubical cistern which contains as much as a rectangular one whose edges are 154 feet 11 inches, 70 feet 7 inches, and 53 feet 1 inch ? 2. For what must I sell a horse that cost me $75.50 so as to gain 5J per cent? 3. By selling 12 pounds of- tea for $7.56, 1 gain 5 per cent. What do I gain or lose per cent by selling 50 pounds of the same tea for $31? 4. Find the amount of $4250 for 2 years 6 months at 5 per cent compound interest. 5. Reduce f ff and -|~f|-f to their lowest terms. 6. How can you tell without dividing whether a number is exactly divisible by 11 ? 76. 1. Find the amount of $7234.25 at 4J per cent simple interest, in 22 years 2 months 20 days. 2. If 20 men build a wall 800 feet long, 10 feet high, and 18 inches thick in 14 days of 8 hours, how thick a wall will 15 men build 900 feet long and 15 feet high in 21 days of 9 hours ? 3. Subtract 0.992748 from 1. 4. Find the cost of 3 acres 145 square rods of land, at $ 120 an acre. 5. What is the price of a silver bowl weighing 5 pounds 9 ounces 8 dwts., at $1.40 per ounce? 6. Add together &, f , -&, &&. ARITHMETIC. 39 77. 1. How many tiles, each 7 inches square, will be required to cover a floor 19 feet 3 inches by 13 feet 5 inches ? 2. Extract the cube root of 0.145531576. 3. If a tradesman, by selling an article at $1.98, loses 17 per cent, what should he have sold it for to gain 40 per cent ? 4. What is the income of a man whose income tax at 4 d. in- the pound amounts to 23 guineas? 5. If 2 horses can plough 7 acres of ground in a day, how many horses will plough 161 acres in \\\ days? 6. In 1,250,784 seconds, how many weeks, days, etc. ? 78. 1. Divide 2054.95 by 0.0563. 2. A merchant sells tea to a tradesman at a profit of 60 per cent; but the tradesman, failing, pays only 12 cents on the dollar. How much per cent does the merchant lose by the sale ? 3. When a 3J per cent stock is at 93, find what price a 4J stock must bear that an investment may be made with equal advantage in either stock. 4. Find the cube root of 134,217,728. 5. Find the product of 10, &, ff and l. 6. If 14 men can mow 168 acres in 12 days of 81 hours, how many acres can be mowed by 20 men in 11 days of 7| hours? 40 EXAMINATION MANUAL. 79. 1. Between the years 1841 and 1851, the population of England increased 14-^- per cent. In 1851, the population was 21,121,290. What was it in 1841 ? 2. A merchant has teas worth $1.08 and 84 cents per pound respectively, which he mixes in the ratio of 3 pounds of the first kind to 2 of the second kind, and sells the mixture at $1.04 per pound. What does he gain or lose per cent ? 3. A person invests $5460 in 3 per cent stock at 91 ; he sells out $2000 stock when it has risen to 93?, and the remainder when it has fallen to 85 ; he invests the proceeds in 4| per cent stock at 102. What is the alteration in his income ? 4. Extract the cube root of 5.78 to three places of decimals. SO. 1. If 48 pioneers in 5 days of 12 J hours can dig a trench 139| yards long, 4J yards wide, and 2J yards deep, how many hours a day must 270 pioneers work for. 42 days, in order to dig a trench 4910 T 1 g- yards long, 4-J yards wide, and 3i yards deep ? 2. If a man rows 10 miles in 2J hours against a stream, the rate of which is 3 miles an hour, how long will he be rowing 5 miles with the stream ? 3. Find the price of 5 acres 127 square rods and 88 square yards at $161 per acre. 4. If a person selling sugar at 9J cents per pound loses 1.0 per cent, what did he give per hundredweight ? ARITHMETIC. 41 81. 1, A square contains 40,092.0529 square feet. Find the length of one of its sides. 2 Simplify ( - 75 X - 75) ~ (Q - 05 X J ~ 0.75 0.05 3, A person invested $4706 in 3 per cent stock at 90 \ . A year afterwards, when the 3 per cent stock had fallen to 89, he sold out one-half of his stock and re- invested it in 5 per cent foreign bonds at .52. What change did the reinvestment make in his income ? 4, If 50 men dig a trench 120 yards long, 5 feet broad, 10 feet deep in 3 days of 10 hours, in how many hours will they dig a trench 175 Yards long, 4 feet broad, and 8 feet deep ? 5 Simplify Si+iiiH Si 1117 X 82. 1, Find the least common multiple of 14, 36, 84, 108, 144. 2 Einmlifr 9 *- 8 + 6 *- 5 * y 8^-7|f + 6i-5f 3, If with a capital of $ 500 a tradesman gains $ 50 in 7 months, in what time will he gain $ 60.50 with a capital of $385? 4, A certain 4i per cent stock is at a discount of 23. What income should I get from $ 385 invested in it ? 5, Find the cost of papering the walls of a room 10 feet 8 inches wide, 19 feet 4 inches long, and 9 feet high, with paper 2 feet wide at 5 cents a yard, allowing 10 yards of the paper for waste. 42 EXAMINATION MANUAL. 83. 1. If 1 inch of rain on 4840 square yards gives 18,200 gallons of water, how many gallons will 0.875 of an inch on a square mile give ? 2. If the amount of property liable to income tax be 525 million pounds sterling, how many pence in the pound must the tax be to produce 17 million pounds ? 3. The circumferences of two of the wheels of an engine are 25 feet and 16 feet respectively. How many more times will one turn round than the other in 4J miles? 4. If the shadow of an upright pole 9 feet high be 7 J feet, what will be the height of a church spire which casts a shadow 247? feet long? , Q . ,., 5. amplify 84. 1. Find the value of 3.75 of half-a-crown (2|s.) + 4.4 of a guinea (21s.) + 1.024 of 22. 2. Find the length in yards of the side of a square enclosure which contains 4 acres 144 square yards. 3. A plot of ground 50 yards long and 40 yards wide is to be covered with sods 1 feet long and 6 inches broad. If the sods cost 75 cents per hundred, what will be the -expense for turf alone ? 4. Find the present worth of $122.80 due 7 months hence, at 4 per cent. 5. In a town where the annual death rate is 2 per cent, the average number of deaths a week (52 weeks to the year) is 228. What is the population of the town? ARITHMETIC. 43 85. 1. A person transfers $3000 from a 4 per cent stock at 90 to a 3 per cent stock at 72. How much 3 per cent stock can he purchase, and what will be the differ- ence in his income ? 2. A cistern 5 feet deep, 16 feet long, 4 feet 6 inches wide, is filled by one pipe in 45 minutes. In what time will a cistern 6 feet deep, 20 feet long, 5 feet wide, be filled by 3 similar pipes ? 3. Multiply 0.416 by 0.025, divide the product by 3.25, and reduce the result to a common fraction. 4. A -clothier gains 25 per cent by selling cloth at $ 5 per yard ; but a bale of 80 yards being damaged, he has to reduce the price 10 per cent. What is now his profit on the bale, and his gain per cent ? 5. Add 12^, 13 fV> 17 i and T&- 86. i. 2. Find the difference between ^- of 200 rods and -f$ of of a mile. 3. What fraction of 560 pounds is equal to 0.1590 of a long ton ? 4. $13,000 of 31 per cent stock is sold at 98. How much money must be added to the sum realized in order to secure an equal income in 3 per cent stock at 87 ? 5. An army of 120,000 men lost 15 per cent by desertion to the enemy. What increase per cent did the enemy gain, their number previously being 64,000? 44 EXAMINATION MANUAL. 87. 1. In 1870 three towns had populations of 17,650, 19,600, and 18,760 respectively. In 1880, the population of the first had decreased 18 per cent, that of the second had increased 21 per cent, while the popula- tion of the three towns had increased by 4691. Find the change per cent in the population of the third town. 2. What fraction of V5| is V0.000225? 5^ - 0.042 - 2.4 + ?| ' 16ft-*- 601 4. Find the square root of 1,079,521 and 0.1079521. 5. "What is the gain by investing $1950 at 971 and selling out at 104, the brokerage on each transaction being i per cent ? 88. o 1. Find the value of - - correct to four places of - -, -, Vl9 - 4 of decimals. 2. Find the simple interest on $281.60 at 3 per cent for 4 years and 2 months. 3. By selling a carriage for $73.15, I should lose 5 per cent. At what price must I sell it to gain 15 per cent? 4. Which is the better investment, 3 per cent stock at 64i, or 5 per cent stock at 1021 ? 5. A person has a certain capital, half of which is invested in 3 per cent stock at 90, and the other half in 5 per cent at 110. His total income is $6883.50. What is his capital? ARITHMETIC. 45 89. 1. At what rate per cent will a given sum of money double itself at simple interest in 30 years ? 2. A grocer has tea, which he must sell at 84 cents per pound to gain 40 per cent. If he mixes it with tea which cost him 54 cents per pound, in the ratio of 7 of the best kind to 3 of the poorest, and sells the mixture in 10-pound packages at $7.76, how much does he gain per cent? 3. How many times is 224 pounds 2 ounces contained in 6 long tons 8 cwt. 8 pounds ? 4. Find -|- of 8 miles 145 rods 3 yards 1 foot 6 inches. 5. The sides of two squares contain 77 yards 1 foot 9 inches, and 7 yards 2 feet 4 inches, respectively. Find the side of a square whose area is equal to the sum of the areas of the two squares. 90. 1. If a railway journey of 177 miles 120 rods takes 3 hours 56? minutes, what is the rate per hour? 2. Multiply 209 acres 145 square rods 3 square yards by 13. 3. Two wines worth $8 and $6 per gallon respectively are mixed together. If the mixture is worth $6.87? a gallon, in what ratio are they mixed? 4. A tradesman pretends to charge 10 per cent above the wholesale price, but he has adulterated his goods with 50 per cent of a poorer kind, which costs only - of the price. What is his real rate of profit ? 5. Express as decimals -%, -^g-, and -/%. 46 EXAMINATION MANUAL. 91. 1. If the 2-penny loaf weighs 15 ounces when wheat is at 8 shillings, how is wheat selling when the Ss-penny loaf weighs 2 pounds? 2. Find exactly the cube root of 1,277,289^-. 3. Reduce -^-ffflr to its lowest terms. 4. What fraction is 1 week 7 hours 12 minutes of the time from Jan. 1, 1800, to Feb. 20, 1864, both days in- clusive ? 5. Find the circulating decimal equivalent to 1 ^ 1 . 6. At what rate per cent will a person receive interest who invests his capital in 3 per cent stock at 91 ? 92. 1. At what price must a person buy 8 per cent stock to receive interest at the rate of 3 per cent? 2. If a vessel sails 500 miles in 2 days 18 hours, how far will she sail between May 20 at noon, and 8 o'clock on the morning of July 10 ? 3. A person buys coffee at $24 per cwt., and chicory at $10 per cwt., and mixes them in the ratio of 2 of chicory to 5 of coffee. He retails the mixture at 30 cents per pound. What is his gain per cent ? 4. A and B enter into partnership. A puts in $2100, B $1500. Four months after, C enters the partner- ship with $2700. At the end of the year the profit is 10 per cent on the whole capital. What share of the profit belongs to each ? 5. If oranges are bought at the rate of 20 for 25 cents, how many should be sold for $12 to gain 40 per cent on the cost ? ARITHMETIC. 47 93. 1. Find the ratio of the rates for freight on two railroads, one of which charges $5.62J for carrying 4200 pounds 44 miles, and the other, $7.86 for carry- ing 5376 pounds 52| miles. 2. If the discount on $127.925 for 20 days be $0.175, find the rate per cent. 3. A gold wreath, weighing 3 pounds 7 ounces 12 dwt., cost $1275. If it is made of gold worth $19.37| per ounce, what is charged for the manufacture ? 4. Divide 24.109932 by 301.28. 5. Find the value of 0.90625 of a cubic yard. 6. Simplify 3 \ + 3 T % + 2^ + 2 94, 1. Reduce 18 days 5 hours 40 minutes 20 seconds to the fraction of 31 days 21 hours 30 minutes 10 seconds. 2. Show that the greatest common measure of two num- bers is the least common multiple of all their com- mon measures. 3. A bought 63 sheep, and sold $ of them at a profit of 15 per cent, \ at a profit of 50 per cent, and the rest at a loss of 25 per cent. What did he pay for the sheep, if his gain was $19.25 on the whole? 4. Find the simple interest on $500 for 8 years 3 months at 1J per cent. .5. Find the cost of 369 miles 120 rods 22 yards of tele- graph wire at $73.33^ per mile. 48 EXAMINATION MANUAL. 95. 1. What sum will amount to $5431.80 in 6 years at 4J per cent simple interest? 2. Reduce 11 rods 4 yards 4.5 inches to the decimal of a mile. 3. Find the greatest common measure of 14,938, 23,474, 32,010. 4. Find the number of seconds from the beginning of the year 1883 to Dec. 17, 9 A.M., and express the result in words. 5. Extract the cube root of 5 to four places of decimals. 96. 1. Supposing the area of a circle to be 3^- times the square of the radius, find the weight of a circular disc of cast iron 7 feet in diameter, and 1-J inches thick, knowing that a plate 1 foot square and 1 inch thick weighs 37-^ pounds. 2. If of a sheep is worth $-f, and f of a sheep is worth y 1 ^ of an ox, what is the value of 100 oxen ? 3. Find the entire surface of a cube, the volume of which is 14 cubic feet 705.088 cubic inches. 4. Find the cost of a draft for $400, payable 60 days after sight, exchange being J per cent discount, and interest 7 per cent. 5. A man bought a horse for $125 and sold him for $100. What per cent of the cost of the horse did he lose ? 6. Multiply 4 acres 67 square rods 19 square yards 4 square feet 72 square inches by. 27. ARITHMETIC. 49 97. 1. In what time will the simple interest on $375, at 4 per cent, amount to $91.25? 2. Divide the number 702 into 3 parts, proportional to , i, and \. 3. Divide 75 miles, 79 rods, 3 yards by 75. 4. How many bricks, each 9 inches by 4J inches by 3 inches are there in a pile 36 feet long, 9 feet wide, and 12 feet high ? 5. Find the face of a draft, payable 60 days after sight, that can be bought for $1250, when exchange is at i per cent premium, and interest 7 per cent. 6. Find the square root of 0.9 to four places of decimals. 98. 1. After paying ^ of my money to one person, -J to an- other, and -fa to a third, I had 7 cents remaining. How much had I at first ? 2. A person walks at the rate of 3^- miles an hour. Three hours after he has set out on a journey, he is fol- lowed by another person, walking at the rate of 5 miles an hour. In what time will he be overtaken ? 3. A grocer mixes 72 pounds of tea at 69 cents a pound with 90 pounds of tea at 60 cents a pound. At what price per pound must he sell the mixture so as to gain 10 cents a pound ? 4. Extract the cube root of J- to four places of decimals. 5. At what rate per cent will $3000 produce $250 in- terest in 1 year 2 months and 24 days ? 50 EXAMINATION MANUAL. 99. 1. Find the interest of $1721.84 from April 1 to Nov. 12 at 4|- per cent. 2. At what rate per cent will $1025.20 produce $25.72 interest in 4 months 9 days ? 3. Find the principal that will produce $1339.28 in 2 years 7 months 24 days at 6 per cent compound interest. 4. Find the time in which $793.875 will amount to $805.84 at 5 per cent. 5. Find the proceeds of the following note : DETROIT, Feb. 2, 1881. Four months after date I promise to pay to the order of John Horn four thousand five hun- dred fifty and f-fa dollars, value received. JAMES THORN. Discounted at a bank at 5| per cent, Feb. 16. 100. 1. A bankrupt has goods worth $975, and, had they real- ized their full value, his creditors would have re- ceived 81-J- per cent of their claims ; but of the goods were sold at 17-J- per cent, and the remainder at 23J per cent below their value. How many cents on the dollar did the bankrupt pay ? 2. Find the value of 157 miles 144 rods of telegraph wire at $57.50 per mile. 3. Reduce fffi , -J^ff to tne i r lowest terms, and express their difference as a decimal. 4. Extract the cube root of 1250.6894. 5. Extract to six places of decimals the square root of 19. ARITHMETIC. 51 101. 1. If a person steps 80 cm at each step, how many steps will he take in walking round a square field containing 18 ha 625 qm ? 2. How many cords of wood can be piled in a woodshed 128 feet long, 42 feet wide, 12 feet high, allowing for a driveway 10 feet wide, running from one end of the building to the other ? 3. The true discount on a bill of $470.89, due 4 years hence, is $85.62 ; find the rate per cent. 4. If the retail price of a book is $6, and 25 are sold for $ 102, what rate per cent of discount is allowed ? 5. A merchant insures a cargo whose value is $4500 at 5 per cent. For what sum should he insure so as to cover both the loss of the cargo and the premium ? 6. A man sent $500 to his agent in Chicago, with which to buy flour. The agent bought flour at $5 a bar- rel, charging 2J- per cent commission for buying. How many barrels of flour can he buy, reserving for himself his commission, and how much money will be left over ? 102. 1. Find the sum of 1871 ccra , 541 1 , 4.51 hl , and give the answer in liters. 2. What is the commission on goods worth $767.73 at 7|- per cent ? 3. Kequired the equated time for the payment of $700 due in 6 months, $800 due in 9 months, and $600 due in 10 months. 4. When 3 per cent stock is at 91 f, find how much can be bought for $540, allowing i per cent commission upon the stock bought. 5. Find the cube root of 0.75 to four places of decimals. 6. If 2 men can reap 2-J acres in 2f days, how long will it take 11 men to reap 15 acres? 52 EXAMINATION MANUAL. 103. 1. If it takes 25 minutes for a man who reads 2 pages in 3 minutes to read a certain document, how long will it take a man who reads a page a minute to read a document 3 times as long? 2. A man sells $7500 of 6 per cent railway stock at 120, and invests half the proceeds in 3 per cent stock at 93, and the other half in 5-|- per cent stock at 90. Find the alteration in his income. 3. A piece of land 2449 m square is sold for $35 a hektar. How much does the land bring ? 4. If cloth is sold for $3.75 a yard at a loss of 10 per cent, what should be the selling price a yard to gain 18 per cent ? 5. Find the cube root of 0.3 to four places of decimals. 104. 1. A company whose capital is $2,500,000 pays an annual dividend of 6|- per cent, besides paying a tax of 1-J per cent on its whole capital. Find the total annual receipts, the expenses being 60 per cent of the gross receipts. 2. Bought 4 lots of wool at $652.50 each, and sold the whole at 20 per cent profit. What was the selling price per lot ? 3. If the increase in the number of male and female crim- inals is 1|- per cent, while the decrease in the num- ber of males alone is 4f per cent, and the increase in the number "of females is 9 per cent, find the ratio of male criminals to female criminals. 4. Find the cost of a carpet 75 cm wide, at $4.25 a meter, for a room 5.25 m long, and 4.75 m wide, strips run- ning across the room, if there is a total waste of 3 m in matching the pattern. 5. Extract the square root of 0.2 to five decimal places. ARITHMETIC. 53 105. 1. An army lost 18 per cent of its strength by sickness and desertion, and then lost 14 per cent of the re- mainder in battle. The number left was 84,624. Of how many did the army originally consist ? 2. If 6 iron bars 4 feet long, 3 inches broad, and 2 inches thick weigh 288 pounds, how much will 15 weigh, each 6 feet long, 4 inches broad, and 3 inches thick ? 3. Find the cost of plastering a room 13 m long, 12 m wide, and 7 m high, at 30 cents a square meter, if 115 qm are allowed for base-board, doors, etc. 4. Find the cube root of 25 to three places of decimals. 5. In 1841, the population of Great Britain was 21,476,000, and that of Ireland 7,310,000. In 1851, the popu- lation of Great Britain had increased 8.45 per cent, and that of Ireland had decreased 12.5 per cent. Find the increase per cent in the population of the whole kingdom. 106. 1. A ship, valued at $14,500, is insured at 3? per cent, and her cargo, valued at $32,000, is insured at 5 per cent. Find the whole cost of insurance. 2. Into how many pills of 325 mg each can a mass of 23.4 g be made? 3. The solid contents of a cube is 37 cubic feet, 4 cubic inches. Find the cost of painting its outside at 33i cents per square foot. 4. What must be the side of a cubical cistern, which will contain exactly 1000 imperial gallons of water, if an imperial gallon contains 277.274 cubic inches? 5. If a compound consist of 1185 parts copper, 715 parts tin, and 100 parts zinc, find the percentage of each metal in the compound. 54 EXAMINATION MANUAL. 107. 1, A rectangular cistern 9 feet long, 5 feet 4 inches wide, 2 feet 3 inches deep is filled with a liquid that weighs 2520 pounds. How deep must a cistern be that will hold 3850 pounds of the same liquid, if its length is 8 feet, and its width 5 feet 6 inches ? 2, Reduce to prime factors, and then find the greatest com- mon measure of 35,035, 41,580, 24,255. 3, How many; square slabs of marble 150 qcm on the surface will be required to pave a court whose area is 50.70 qm ? 4, A person sells out his 3 per cent stock at 86 1, and gets $34,000 ; he invests one half of this sum in 4 per cent stock at 97, and the remainder in 3 per cent stock at 94. Find the alteration in his income. 5, If 56 cubic feet 1044 cubic inches of timber are required to floor a room 29^ feet by 25i feet, what is the thick- ness of the boards ? 108. 1, A merchant has teas worth $1.12? and 87-J cents per pound respectively, which he mixes in the ratio of 3 pounds of the better kind to 2 of the poorer kind, and sells the mixture at $1.08i per pound. What does he gain or lose per cent ? 2, How many revolutions will the wheels of a carriage make in travelling 41 km , if the wheels are 125 cm in diameter? (The circumference is 3.1416 times the diameter.) 3, In what proportion must wines worth $3, $4, $5.20, $6, per gallon be mixed, so as to give a profit of 14|- per cent when sold for $4.80 a gallon? 4, Extract to four figures the cube root of 20. 5, If a railway train goes 27f miles in 2f hours, how far will it go in an hour? ARITHMETIC. 55 1O9. 1, In what time will 2275 amount to $2673.12 at 5 per cent, simple interest? 2, If a horse trots 23f miles in 2? hours, what is his rate per hour ? 3, If twelve men can build a wall 6 feet high, 3 feet thick, in 9 days, how many men would build a wall of the same length, 5 feet' high, 4 feet thick, in 24 days? 4, A man pays $12,000 for 5 a of land, and sells it for $25.20 a square meter. How much does he make? 5, A river 30 feet deep and 200 yards wide flows 4 miles an hour. Find the number of cubic feet of water that passes a given point in a minute. 6, Extract to four figures the cube root of 0.002. 110. 1, A cistern has two pipes, one of which can fill it in 2 hours, the other in 3 hours. A third pipe can empty it in 5 hours. If all these are opened when the cistern is empty, in what time will it be filled? 2, A pile of wood is 8.50 m long, 2.66 m wide, 2.60 m high. How many sters of wood are there? 3, A clock is set at 12 o'clock on Monday ; at noon on Tuesday it is 3 minutes too fast, What will be the true time when the clock strikes 4 on Thursday afternoon ? 4, If 20 men can do a piece of work in 12 days, how many men will do another piece of work six times as great in -^ of the time ? 5, If 5 per cent be lost by selling an article at $2.50, find the gain or loss per cent by selling it at $ 3.12|, 6, Find the square root of 53107.2025. 56 EXAMINATION MANUAL. Ill 1. Reduce 167,948,604 square inches to acres, etc. 2. A man contracts to perform a piece of work in 30 days, upon which he employs 15 men. In 24 days it is only half finished. How many additional men must he employ to finish the work in time ? 3. A cistern can be filled by a spout in 2 hours, but on account of a leak in the cistern the spout takes 2-j- hours to fill it. How long will it take the leak to empty the cistern ? 4. A country, the population of which is |LO millions, has births yearly of 1 in 20, and deaths 1 in 30. What will its population be 5 years hence ? 5. A beam is 14.14 m long. Its other dimensions are 51.6 cm , 174 mm . Find its volume. 6. If a trader sells 13|- pounds for 14 pounds, how much per cent does he gain fraudulently ? 112. 1. A wine which contains 7J per cent of spirit is frozen, and the ice, which contains no spirit, is removed. The proportion of spirit in the wine thus is increased to 8J per cent. How much water in the shape of ice is removed from 504 gallons of the original wine ? 2. Find to four places of decimals the square root of 0.001 and of 0.5 ; and also find what numbers have 0.1 and 0.03 for their square roots. 3. The diameter of a carriage wheel is 4 ft. Two persons calculate the number of its turns in a given distance, one calling the circumference 3 times the diameter, the other 3-f times ; their results differ by 100 turns. Find the distance. 4. A package of candles which weighs 465 g is sold for 28 cents. What is the price of 10 kg of the candles ? 5. Reduce to its lowest terms the roduct of 1 ARITHMETIC. 57 113. 1. Resolve into prime factors 5940, 19,008, and 269,568, and write the greatest number that will divide them all without remainder, and the smallest number that they will all divide without remainder. 2. Divide 181.3 by 0.00037, and by 37,000. 3. Find the cost of carpeting a room 18 feet 6 inches long, 12 feet 6 inches wide, with carpet f of a yard wide, at 75 cents per yard, strips running lengthwise, and 3 yards being allowed for matching the patterns. 4. If 3 men mow 20 acres in 11 days of 11 hours, how many men will it take to mow a rectangular field 384 yards long and 300 wide, in 4 days of 12 hours ? 5. The difference between the simple and compound inter- est on a sum for 3 years at 5 per cent is $23.12J. Find the sum. 6. How many hektars in a square kilometer? 114. 1. A box is 3.75 m long, 3.50 m wide, and 50 cm high. Find how many liters of olive oil it will hold, and the weight of the oil in kilograms, the specific gravity of the oil being 0.914. 2. If A can do f of a piece of work in 4 hours, and B can do f of the remainder in 1 hour, and finish it in 20 minutes, in what time will they do it, all work- ing together ? 3. When a common fraction is reduced to a decimal, in what cases will the result be a terminating decimal, and in what cases a circulating decimal ? 4. If by selling goods for $272 I lose 15 per cent, how much per cent would I have lost or gained if I had sold them for $336? 5. If oranges are bought at the rate of 20 for a dollar, how many should be sold for $28 to gain 40 per cent? 6. Find the cube root of 84.9 to three places of decimals. 58 EXAMINATION MANUAL. 115. 1. If a man walk 11 yards in 5 seconds, how long will lie be in walking a mile ? 2. A cubic foot of water weighs 62-1 pounds, and a room 18 feet 9 inches by 13 feet 4 inches is flooded to a depth of 2 inches. What is the weight of water in the room ? 3. Assuming that 3 hektars contain 35,881 square yards, and that one hektar contains 10,000 square meters, find the length of a meter in yards. 4. Add together 536.421, 53,642.1, 5.36421, and subtract the result from 100,000. 5. If the price of candles 8J inches long be 18 cents for a half-dozen, and that of candles of the same thick- ness and quality 10* inches long be 22 cents a half- dozen, which kind would you advise a person to buy, and what would be the saving per cent if your advice is followed ? 116. 1. Find the weight in kilograms of the air in a hall 23 m long, 16 m wide, and 10 m high, the specific gravity of air being 0.00129206. 2. A cubical block contains 9 cubic feet, 1029 cubic inches. Find the number of square yards, etc., in its surface. 3. A bar of metal weighing 100 ounces 16 dwts. is made into coins, each weighing 1 ounce 8 dwts. How many coins are there ? 4. A person investing in a 3 per cent stock received 3i per cent interest on his money. What is the price of the stock? 5. A bar of gold, weighing 196 pounds 10 ounces 10 dwts., is cased in lead, weighing 24 pounds 14 ounces. Find the weight of the whole in Avoirdupois weight. ARITHMETIC. 59 117. 1. A merchant buys 4000 bushels of wheat, one-fifth of which he sells at a gain of 5 per cent, one-fourth at a gain of 10 per cent, one-half at a gain of 12 per cent, and the remainder at a gain of 16 per cent. If he had sold the whole at a gain of 11 per cent, he would have made $35 more. "What was the cost of the wheat per bushel ? 2. If 1000 square yards of land produce a load of hay, how many loads will 25 acres produce ? 3. Assuming 8000 meters to be equal to 5 miles, find the number of square meters there are in an acre. 4. A person having a certain sum of money to invest finds that an investment in 5 per cent stock at 11 7? will yield him $29 more interest annually than an in- vestment in 3 per cent stock at 92J. How much money has he to invest ? 5. Find the simple interest on $281.63 at 3s per cent for 4 years and 2 months. 118. 1. A freight train is 8 miles ahead of an express that travels at the rate of a mile in H minutes. 20 minutes later the express runs into the freight train. At what rate is the freight train running ? 2. A man bought 240 cows at Rotterdam, paying $71.50 for each. He paid -^ of their cost for their trans- portation, and exchanged them for 299 horses which he sold for $ 75 apiece. What did he gain per cent on his expenditure ? 3. If a square field contain 10.24 ha , find the length of its side in meters. 4. Find the amount for $512 for 3 years at 6| per cent, compound interest. 5. If a field containing 5i acres produces 112 bushels of wheat, what is the area of a field which will pro- duce 400 bushels of wheat at the same rate ? 60 EXAMINATION MANUAL. 119. 1, Multiply 4 acres 67 square rods 19 square yards 4 square feet 72 square inches by 27. 2, What is the weight of a cubic centimeter of water ? of a liter of water? of a cubic meter of water? If a cubic meter of gravel weighs 2.11 metric tons, what is its specific gravity ? 3, If 7 men, working 16 days, can mow a field 1320 yards long, and 880 yards wide, what will be the length of the side of a field 1320 yards wide, which 4 men can mow in 42 days ? 4, Divide 1.765 by 2470 to five places of decimals. 5, If 8 acres produce 220 bushels of corn, how much will 22 square yards produce ? 120. 1, If 3 acres of land cost $465.90, how much can be bought for $6716.725? 2, From 0.315 of a gallon take 2.25 pints. 3, $19.68f is 2^ per cent of what sum? 4, A, B, and C rent a farm for $270. A puts 200 sheep on it ; B, 150 ; and C, 100. After 6 months A sells f of his flock to C, and 3 months later B sells f of his to A. How much of the rent should each pay at the end of the year ? 5, How many times a minute does the 'wheel of a carriage turn, when the carriage is driven at the rate of 14 km an hour, and the diameter of the wheel is 120 cm ? ARITHMETIC. 61 121. 1, If a man walks ll m in 5 seconds, how many kilometers can he walk in an hour at the same rate ? 2, Find the cost of repairing a road 87 yards 1 foot 10 inches long, at the rate of $4 a rod. 3, A cask that weighs 236 pounds 4 ounces just sinks in a square cistern of water, whose edge is 2 feet 6 inches. If the cask is removed, how far will the water sink in the cistern, reckoning the weight of a cubic foot of water to be 1000 ounces ? 4, A man paid $45.10, including a duty of 10 per cent, for a watch. How much was the duty ? 5, If 19 men can build 38 yards of wall in 12 days, how many will build 96 yards 2 feet 3 inches in 214- ' i? 122. 1, Find the amount of $875 at the end of 1 year and 3 months, at 4 per cent per annum, compound inter- est, the 'interest accruing quarterly. 2, If 12 men build a wall 60 feet long, 4 feet thick, and 20 feet high in 24 days, working 12 hours a day, how many men will it take to build a wall 100 feet long, 3 feet thick, and 12 feet high, in 18 days, working 8 hours a day ? 3, If the specific gravity of sea-water is 1.026, and that of olive oil is 0.915, what is the weight of a hektoliter of each in kilograms ? 4, What must be the length of an inner edge of a cubical box which will hold 10 cubic feet ? 5, An agent, charging 2i per cent commission, receives for his services $313. Find the amount of his sales. 62 EXAMINATION MANUAL. 123. 1. An agent received $5922 with which to purchase goods, and is allowed 5 per cent commission on his pur- chase. If the $5922 covers the cost of the goods and his commission, how much was his commission? 2. How much per cent above cost must a man mark his goods in order that he may take off 30 per cent from the market price, and still make 30 per cent on the cost? 3. If a pint contains 2&J cubic inches, how many pints are there in a cubic foot of water ? 4. If 14 liters of water be poured into a vessel containing ' 6 liters of sulphuric acid, specific gravity 1.84, and the mixture shrink to 19.944 liters, what is the spe- cific gravity of the mixture ? 5. Find 0.015 of 17 acres 130 square rods. 124. 1. If 5 needlewomen can finish a certain quantity of work in 10J- days of 9f hours each, how long would it take 3 needlewomen to do twice the same work, reckon- ing 10 hours to the day ? 2. Find the square root of 0.196 to four places of decimals. 3. Find the greatest common measure of 837, 1134, and 1347. 4. A ship carries 5 chronometers, and estimates Greenwich time by the mean time of the five. Two of them lose respectively 39 seconds in 35 days, and 4.3 seconds in 6 days ; the others gain respectively 5 seconds a week, 1.3 seconds a day, and 23 seconds in 14 days. By how much will the estimated time be in error after a cruise of 176 days? 5. How many square meters of surface will 240 sheets cover, if the sheets are 303 mm long and 195 mm wide ? ARITHMETIC. G3 125. 1, A bankrupt owes $5050. His assets are $378.75. How many cents does he pay on a dollar ? 2, If 36 men dig a trench 72 yards long, 4 yards wide, and 3 yards deep, how many men will be required to dig one 80 yards long, 4 yards wide, and 6 yards deep in the same time ? 3, Eeduce to its simplest form the expression 3 of it of ?- 1-1- 0t * i 4, A person invests $6534 in 3 per cent stock at 90, and on the stock rising to 91 transfers his stock to 3-J- per cent stock at 93-J-. How is his annual income affected? 5, Olive oil costs 60 cents a kilogram. What is the price of a hektoliter, if the specific gravity of the oil is 0.914? 126. 1, The distance between two places measured on a military map is 156 mm . What is the actual distance between the places if the map is made on the scale of 1 to 80,000 ? 2, How many horses will be required to plough 117 acres in 35 days, if 10 horses can plough 13 acres in 7 days? 3, If I buy 3090 yards of cloth at 92| cents per yard, and sell the whole for $3205.87|, what is the gain per cent? 4, Find the amount of $7123.13 at 4 per cent, for 2 years and 3 months, compound interest. 5, How many bricks 81 inches long, 4i inches wide, 2s inches thick can be stored in a building 17 2 yards long, 10 yards wide, and 8J- feet high? G4 EXAMINATION MANUAL. 127. 1. How many panes of glass 40 cm by 80 cm will be required for the windows of a house if the total surface of measurement of the glass in the windows is 203.52 qm ? 2. A 20 horse-power engine pumps 40 gallons of water from a pit 100 yards deep in 3 hours. What quan- tity of water will an engine of 35 horse-power pump from a depth of 235 feet in 141 days, work- ing night and day ? 3. A speculator buys 280 yards of carpet, expecting to sell the whole at $1.38 a yard, and thereby make 15 per cent profit ; but 40 yards being ruined, what did he gain or lose per cent by selling the remainder at the expected rate ? 4. If a piece of land is bought for 3500, and a man who owns -| of it sells % of his share for $800, how much does he gain per cent by the transaction ? 5. Extract the cube root of 1.105507304. 128. 1. A tank is 1.50 m wide, 3.20 m long, and 80 cm deep. How many kilograms of alcohol, specific gravity 0.80, will be required to fill it one-third full ? 2. How many men working for 11 cents an hour for 23 days of 9 hours can earn the same wages as 22 men working for 11-J- cents an hour for 18 days of 9^ hours. 3. If goods cost $75.87-J-, at what price must they be sold to gain 17^- per cent? 4. A can mow f of a field in 7| days, B can mow f of the same field in 9J days. In what time can A and B together mow the field ? 5. A train travels a certain distance in 4-f% hours at the rate of 16|- miles an hour. How long will a train going 19 J miles an hour take to travel the same distance ? ARITHMETIC. 65 129. 1. A rectangular sheet of tin of uniform thickness is 85 cm wide, 2.7 m long, and weighs 536 g . What is its thickness, reckoning the specific gravity of tin at 7.3? 2. I pay for 180 yards of cloth at 92-J cents per yard, but it is measured with a yard-stick -f of an inch short. How much money does the seller unfairly take ? 3. What must a person have invested in 3 per cent stock at 93^-, if a transfer of -f of his capital to 5 per cent stock at 125 would increase his income $14.80? 4. If 20 shillings weigh 3 ounces 12 dwts. 12 grains, and contain 5 dwts. lOij- grains alloy, how much pure silver is there in a half-crown (2J shillings)? 5. Express by a common fraction the difference between 2.535 and 2.535. 130. 1. A, B, and C rent a field for $25.62. A puts in 15 sheep for 6 months, B 45 sheep for 8 months, C 81 sheep for 4 months. What should each pay toward the rent? 2. The top of a building 236 feet high is reached by a flight of steps, each 12 cm . high. Find the number of steps, if a meter is taken as equal to 3 feet Si- inches. 3. How many ars of land in a strip l km long and 7 m wide? 4. An executor of an estate finds it encumbered with debts to the amount of $4322.50 over and above its real- ized value of $10,729.50. How many cents on a dollar can he pay the creditors? 5. Extract the cube root of 437.245479. 66 EXAMINATION MANUAL. 131. 1. What fraction of a pound avoirdupois is a pound Troy, and what fraction of an ounce Troy is an ounce Avoirdupois? 2 * 3, Find the weight in kilograms of a bar of gold 10 cm long, 30 mm wide, and 25 mm thick, its specific gravity being 19.36. 4, If $15 be gained on $360 in 8 months 15 days, what sum will gain $21 in 1 year 6 months? 5, For how much must a man give his note to a bank, on 4 months at 6 per cent, to obtain $500? 132. 1, What sum will amount to $1104.75 in 3 years at 3 per cent, compound interest ? 2, What annual income will be produced by $13,000 in a 3 J per cent stock at 91 ? 3, If the circumference of a coach-wheel measures 17 feet 7.2 inches, how often will it turn round in travelling 8 miles 264 feet? 4, Keduce to its lowest terms -g-f|-J. 5, If a square meter = 1550.031 square inches, find to the fifth decimal place the number of square centimeters in a square inch, and the number of acres in a hektar. ARITHMETIC. 67 133. 1, A tradesman's prices are 20 per cent above cost price. If he takes 10 per cent off from the bill of a custo- mer, what per cent profit does he make ? 2, If a man can do a piece of work in 77 hours, and a boy can do the same work in 121 hours, in. how many hours, minutes, and seconds can they do it, working together ? 3, If the cost of papering a room 8J- yards long, 6f yards wide, with paper 2 feet wide at 8 cents a yard be $14.32, find the height of the room. 4, If 3 per cent more be gained by selling a horse for $83.25 than by selling him for $81, what is the cost of the horse ? 5, If a cubic yard = 0.76453 cbm , find to the fifth decimal place the number of cubic centimeters in a cubic inch, and the number of sters in a cord. 134. 1, By selling out $4500 of 5 per cent stock at 112J, and investing the proceeds in a 7 per cent stock, a per- son increases his income by $168. 75. What is the price of the 7 per cent stock ? 2, simplify 2fj x mn- 3, If a gram = 15.43235 grains, find to the fifth decimal place the number of pounds Avoirdupois in a kilo- gram and in a metric ton. 4, An article which costs $ 95.76 per cwt. of 112 pounds is retailed at $1.08 a pound. If there is a waste of 5 per cent, what is the rate per cent of profit? 5, Find the square root of 0.1 to four places of decimals. 68 EXAMINATION MANUAL. 135. 1, Find the L.C.M.'of 7, 11, 21, 63, 91, 99, 117. 2, A plate of iron 137 cm long, 643 mm wide, 43.1 mm thick weighs 277.54 kg . What is its specific gravity? - 3, If 135 men can dig a trench 48 yards long, 1 foot 3 inches wide, 3 feet 9 inches deep, in 5 days of 6 hours, how many men will be required to dig a trench 90 yards long, 2 feet 6 inches wide, 3 feet deep, in 27 days of 10 hours ? 4, A man has 10 13 s. 4 d. a week in rents. His tenants cheat him out of y 1 -^ of his rent ; he pays 4 d. in the pound for collection, and 9& d. in the pound for taxes. How much a week has he to spend ? 5, Divide 4900 by 0.07, multiply the quotient by 0.63, and divide the result by 0.049. 136. 1, If -f% of a cargo be worth $ 750, how much is -$ of -f$ of it worth? 2, A parcel of 5 pounds 7 ounces is carried 120 miles for 40 cents. How much will it cost to carry 16 pounds 5 ounces a distance of 90 miles at the same rate-? 3, If a meter = 39.37043 inches, find to the fifth decimal place the number of centimeters in an inch, and the number of kilometers in a mile. 4, Find the cube root of 7.6 to four places of decimals. 5, A person, by selling an article which cost 60 cents a pound at 67 -J cents a pound, makes 5 per cent more profit than if he had sold the whole for $267.67. Find the amount sold. ARITHMETIC. 69 137. 1, Find the sum of % 7 T \, 8^, 19, 10|i 12f . 2, A garrison of 1000 men, provisioned for 60 days, was reinforced at the end of 18 days, and the provisions were exhausted at the end of 30 days from that time. Of how many men did the reinforcement consist? 3, Two engines 40 miles apart ars approaching each other at the rates of 25 and 35 miles an hour. Determine the time and place of their meeting. 4, Find the simple interest on'$ 2187.50 for 219 days at 4* per cent, reckoning 365 days to the year. 5, Find the area of a field 225 m long, 100 m wide. Express the answer in hektars and ars. 138. 1, From 2000 subtract 852.2534, and divide the remainder by 16.38. 2, If I invest $1200 in 3 per cent stock at 72, what is my income, and what rate per cent do I get on my investment? 3, If $36 worth of bread will be sufficient for 12 men 8 months, when corn is $ 1 per bushel, how many men will require $100 worth of bread for 12 months, when corn is $ 1.311 per bushel? 4, Find the time required to travel 3P m 150 m , at 1 minute 28 seconds a kilometer. 5, A broker receives $6150 to invest in cotton at 10i cents a pound. His commission is 21 per cent for buy- ing. How many pounds of cotton can he buy ? 70 EXAMINATION MANUAL. 139. 1. A collector's commission for collecting taxes, at H per cent, is $41.31. What is the sum collected? 2. How many yards of carpeting 2 feet 8 inches wide will be required for a floor 19 feet 7 inches long, 16 . feet 9 inches wide, if the strips run across the room, and 2| yards are allowed for waste in match- ing the pattern. 3. Find the value of a carboy (17 1 ) of sulphuric acid, specific gravity 1.841, at 5 cents a kilogram. 4. If the ratio of the circumference to the diameter be 3.1416, find the diameter of a cylinder whose cir- cumference is 16J feet. 5. How much more income will a person have by trans- ferring $3975 of 3 per cent stock into 3|- per cent stock, if the price of the 3 per cent stock is 93f , and of the 3J per cent stock 99f? 140. 1. Find the bank discount upon a note of $587, given Feb. 29, 1880, for 3 months, and discounted April 30 at 6 J per cent. 2. Determine the number of cubic meters in a box 2 yards long, 1 yard wide, and 2} feet deep, reckoning a cubic yard = 0.76453 cbm . 3. A reservoir is 24 feet 8 inches long, and 12 feet 9 inches wide. How many cubic feet of water must be drawn off to make the surface sink one foot ? 4. Divide 200 acres into four parts proportional to the numbers 50, 35, 80, and 9. 5. Extract the cube root of 946,966,168. ARITHMETIC. 71 141. 1. If coffee worth 66 cents, 77 cents, and 57 cents per pound be mixed in equal quantities, and the mix- ture sold at 702 cents per pound, what is the gain or loss per cent ? 2. If 3 men, working 11 hours a day, can reap 20 acres in 11 days, how many men, working 12 hours a day, will reap a field 360 yards long and 320 yards broad, in 4 days? 3. Find in yards the side of a square field containing 15 acres 109 square rods 3 square yards. 4. A man walks 10J miles the first day, 16, 18 J, 27|, 21J- miles on the four following days respectively. He then returns home by the same road in four days. What was his average daily walk on his way home and on his whole journey ? 5. How many tons of air, specific gravity 0.00129206, in a space 70 m by 50 m by 35 m ? 142. 1. By selling a horse for $64.75, 1 lost 7J per cent. What per cent should I have gained by selling him for $73.50? 2. The proceeds of the income tax at 5c?. in the pound was equal to 5,250,000, How much would the proceeds be, if the tax was 5 per cent ? 3. Find the number of liters in a vat 2 m by 75 cm by 50 cm . Also find the weight in kilograms of sulphuric acid, specific gravity 1.840, required to fill it. 4. One horse goes 1} miles in 2 minutes 26 seconds ; another, If miles in 3 minutes 36 seconds. How much per cent does the first one go faster than the second ? 5. Find the greatest common measure of j-f , 2J, 4, and 5}. 72 EXAMINATION MANUAL. 143. 1, Find the least common multiple of y 1 ^-, 2-J-, 5, 6J, and -fa. 2, By selling goods for $116.85 I lose 5 per cent. For what should I sell them to gain 3| per cent? 3, A spends of his money, then i of the remainder, and then J of what he has left. He finally has $25. How much had he at first ? 4, Make out a bill and receipt it, and show how much change there will be from a twenty-dollar bill : 3J cwt. of coal, at 21 cents a cwt. ; 13 pounds of cheese, at 15J cents per pound; 2f pounds of tea, at 80 cents per pound ; 17 pounds of sugar, at 11 cents per pound; 3? yards of flannel at 47 cents per yard ; 29 yards of gingham at 21 J cents a yard. 5, Find the number of sters in a pile of wood 4.50 m long, 2 m wide, and 2.50 m high. 144. 1, If 7 men earn $31 in 9^ days, how much will 17 men earn in 2Gf days ? 2, Two persons have each a capital of $12,000. The one invests in 3 per cent stock at 90f ; the other in 5 per cent stock at 1031 . What is the difference in their incomes ? 3, If I buy 14 sheep for $157.29, and sell 6 of them for $7.20 each, for how much a head must the re- mainder be sold, that I may gain 4 per cent on the whole ? 4, Find the G.C.M. of 1908, 936, 630, 21,294, 306. 5, A hektoliter of rape-seed weighs 63 kg , and 32 1 of oil can be extracted from it. How many kilograms of the seed will it take to make a hektoliter of the oil ? ARITHMETIC. 73 145. 1, The volume of a cube is 2 cubic yards 14 cubic feet 145 cubic inches. Find its edge, and also its diagonal to two places of decimals. 2, By using false weights a grocer receives 17 cents instead of 16 cents. Find the number of ounces in his false pound, and his gain per cent. 3, A railway pays 3i per cent dividend. At what price will its shares give 4? per cent to a purchaser? 4, A person sells his 3 per cent stock for 73, and buys with the proceeds 3-i per cent stock at 81 T, thereby increasing his income $4.50. How much 3 per cent stock has he ? 5, Reduce 150 hektars to acres, supposing a square meter equal to 1.196 square yards. 146. 1, A profit of $127.60 is made by selling 2552 pounds of butter at 45 cents a pound. Find the cost per pound and the gain per cent. 2, For what sum must I insure goods worth $2192 at 2 per cent, so as to cover their value and the premium paid? 3, If $11.20 worth of paper is required for a room 25 feet 3 inches long, 19 feet 9 inches wide, and 12 feet high, when the paper is f of a yard wide, find the cost of each yard 'of paper. 4, Find the price of paving .a courtyard 25.34 m long, 18.36 m wide, at $1.08 per square yard. (Square meter = 1.196 square yards.) 5, Find within an inch the diagonal of a square field con- taining 3 acres. 74 EXAMINATION MANUAL. 147. 1, .Find the difference between 30 chains, 15 links, and 126 rods. Express the answer in yards and decimal of a yard. 2, Find the number of feet, board measure, in a stick of timber 15 inches square and 32 feet long. 3, A watch is 10 minutes too fast at noon on Monday, and loses 3 minutes 10 seconds a day. Find the time indicated by the watch when the true time is a quarter past ten on the Sunday morning following. 4, Find the cost of 5 acres 127 square rods 88 square yards at $161.33^ per acre. 5, Find the weight in metric tons of a block of stone 12.37 m long, 7.14 m wide, 83 cm thick, if the specific gravity of the stone is 2.5. 148. 1, From two places which are 154 miles apart two persons set out to meet each other, one walking at the rate of 3 miles in 2 hours, the other 5 miles in 4 hours. In how many hours will they meet ? 2, A regiment was reduced to 520 men after engaging in two battles, in the first of which it lost 1 man in every 25, and in the second -fg of the remainder. How many men were there at first ? 3, Find the cube root of 11 to four places of decimals. 4, Frenchmen, on the average, consume yearly 1160 g of coffee and 9 g of tea; and Englishmen, 473 g of coffee and 1679 g of tea. If tea be 3s. and coffee Is. 8d. per pound, and a franc be worth 10^ d., find in francs the value of an Englishman's consumption above a Frenchman's. 5, Find the value of 2 pounds 5 ounces 8 dwts. 4 grains of silver at $ 125 an ounce. ARITHMETIC. 75 149. 1. Find the cost of 30 3-inch planks, 24 feet long and 11 inches wide, at 15 per M. 2. An agent sells 2200 barrels of flour at $4.50 a barrel, and charges 2=} per cent commission. He invests the proceeds in steel at I? cents a pound, charging !->- per cent commission. What is his entire com- mission ? 3. Two circular gold plates, each 1 inch thick and 6 arid 8 inches in diameter respectively, are melted into one plate of the same thickness. Find the diameter of this plate, knowing that the area of a circle varies as the square of its diameter. 4. Find the cube root of 0.25 to four decimal places. 5. How many miles will be travelled in 1 hour 28 min- utes 21 seconds at the rate of 50 km an hour ? 150. 1. An agent sells 1000 barrels of flour at $5.50 a barrel, and charges 2 2 per cent commission ; expenses for freight, etc., are $500. With the net proceeds he buys sugar at GT cents a pound, charging 2 per cent commission. How much sugar does he buy? 2. Find the number of feet board measure in 25 joists, each 6 inches by 4 inches, and 14 feet long. 3. Find the value of 3 pounds 8 ounces 16 dwts. 12 grains of gold at 3 17s. lOic?. per ounce. 4. A pond whose area is 3 acres is frozen over with ice to the uniform thickness of 6 inches. If a cubic foot of ice weighs 896 ounces, find the weight of ice on the pond in long tons. 5. A jar full of water \veighs 1.325 kg ; filled with mercury, it weighs 12.540 kg . What is the capacity of the jar and its weight? The specific gravity of the mercury is 13.59. EXAMINATION PAPERS IN ARITHMETIC. BOWDOIN COLLEGE, BRUNSWICK, ME. Examination for Admission, June, 1883. 1. Find the difference between 0.0000005 and 0.00005. 2. Change 0.03125 to a common fraction in its lowest terms. 3. If the year is considered 365.25 days instead of 365.242264, how great will the error be in 1880 years ? 4. The dividend is 7423.973, the quotient is 12.130, and the remainder is 0.413. What is the divisor? 5. What is the cost of 60.5 tons of coal when 0.9 of a ton cost 1 6.66? 6. Find the square root of 6.7081. Of 0.004 to the nearest ten thousandth. Of ^V 7. Keduce 6453 m to kilometers. 4.15 m to centimeters. 6.45 1 to milliliters. How many decigrams does a dekaliter of pure water weigh ? II. DARTMOUTH COLLEGE, HANOVER, N.H. Entrance Examination, June, 1883. 1. Find the G.C.D. of 66, 308, and 506. 2. Divide || by Ltl 78 EXAMINATION PAPERS. 3. Give the value of the kilometer in feet ; of the kiloliter in gallons ; of the kilogram in pounds. 4. If there is a gain of 12-*- per cent on tea at 90 cents per pound, what would be the gain per cent at 84 cents per pound? I 1 23 5. Find -*! f to four decimal places. il U.Uu^jO III. BROWN UNIVERSITY, PROVIDENCE, R.I. Examination for Admission, June, 1883. 1. Reduce -J- of 6 per cent of 1.05 ~- -fa of T 7 -g- to the simplest form. 2. If 17 men can reap a field in 9 days, how long would it take to reap half of it if 5 men refuse to work ? 3. A man bought 200 m of cloth in France at 16J francs a meter ; he paid 12J cents a yard for duty and freight, and sold it in Boston at $4.62|- a yard. What was the gain ? (1 franc = 19.3 cents.) IV. MASS. INSTITUTE OF TECHNOLOGY, BOSTON, MASS. Entrance Examination, June, 1882. 1. Find the L.C.M. of 105, 476, and 306. 2. A grocer makes a mixture of which 21.5 pounds contains \ pound of rye, 12 pounds of wheat, 5 pounds of oats, and 4 pounds of barley. How much of each ingre- dient will be contained in 100 pounds of the mix- ture? ARITHMETIC. 79 3. Reduce to a decimal fraction 3 . and from it subtract 0.01 of I. a *> 4. In how many days will $3245 gain $80 at 7 per cent, simple interest ? 5. Find the G.C.D. of 119 and 231. 6. Find the cube root of 0.012326391. 7. How many liters are contained in a cubical box 13 inches long, 13 inches wide, and 13 inches deep on the inside ? (Given that l m = 39.37".) 8. How many grams of distilled water will such a box contain ? V. Entrance Examination, Sept., 1882. 1. Reduce -S^5 to its simplest form. 9 T + 5 2. Reduce ? to a decimal fraction. 3. A and B together have $136, and -f of A's money is equal to -| of B's. How much has each? 4. At $6.25 per ton, how many tons of coal can I buy for $1000, and allow 2-|- per cent commission? 5. Find the square root of 0.00028562 to ten-thousandths. 6. Floor 10 m by 6.5 m , carpet 90 cm wide ; .find cost of carpet at $1.25 per meter. 7. In a parallelogram, given base 640 dkm , altitude = 180 dkm ; find area in hektars. 8. A cylindrical vessel l m high is made of sheet-iron 2 cm thick, and holds 100 1 . What is its outer diameter ? 80 EXAMINATION PAPERS. VI. HARVARD COLLEGE, CAMBRIDGE, MASS. Examination for Admission, June, 1883. 1. Find the difference between 3J X 6ff and i& 2. A field is SS-/^ rods long, and 37? rods wide. Find its area in acres and square rods. (Acre = 160 square rods.) 3. Find all the factors common to 1001 and 616. 4. The distance from Boston to Albany is 320 km . Find the distance in miles, assuming the meter to equal 3-^- feet. 5. A man, travelling 9 hours a day, goes 234 miles in 15 days. How far can he go in 30 days, travelling 8 hours a day ? VII. YALE COLLEGE, NEW HAVEN, CT. Examination for Admission, June, 1883. 1. Divide 82.1 by 41, 8.21 by 0.41, and 0.821 by 410. Carry the result in each case to four decimal places. 2. Find the value to three decimal places of o TV -A T2 1 i 133 3. Divide * X by - 4. Some sugar is adulterated as follows : -fy is worth 8 cents per pound, % is worth 10 cents per pound, y 2 -^ is worth 12 cents per pound, and the remainder, 33 pounds, is sand. What is the mixture worth per pound ? ARITHMETIC. 81 5. Bank stock which sells at 170 pays an annual dividend of 12 2 per cent. What rate of interest does a buyer receive ? 6. Find the depth in meters of a cubical cistern which has a capacity of 30,000*. Give the. result to three deci- mal places. VIII. SHEFFIELD SCIENTIFIC SCHOOL, NEW HAVEN, CT. Entrance Examination, June, 1883. 1. Find the G.C.D. of 36,864 and 20,736. 2. Multiply f of jjf by f of i. 3. (i.) Give the table of metric weights. (ii.) A cubical cistern holds 1331 kg of water ; what is the length of an inner edge ? 4. Divide 67.56785 by 0.035, and multiply the result by . Explain the position of the decimal point after 'division. 5. How much money should be received on a note of $ 1000, payable in 4 months, discounting at a bank where the interest is 6 per cent ? 6. If a man travel 117 miles in 15 days, employing only 9 hours a day, how far would he go in 20 days, travelling 12 hours a day ? 7. Extract the square root of 10 to five places. IX. Entrance Examination, Sept., 1883. 1. (i.) Select the prime numbers between 50 and 100. (ii.) What is the least number that can be exactly divided by ^ 2, 5, % and ^? 82 EXAMINATION PAPERS. 2. Reduce 0.00096 to its simplest equivalent common frac- tion. 3. 7465 is 33 per cent of what number ? 4. A broker bought 84 shares of railroad stock at 19 per cent discount. He sold 35 shares at 27J per cent discount, and the balance at 8 per cent discount. Did he gain or lose, and how much? 5. Calculate the cube root of 3.7- to five decimal places. 6. Give the approximate value of the meter in feet ; of the kilogram in pounds Avoirdupois. 7. Find the weight in kilos of 15 gallons of water. X. AMHERST COLLEGE, AMHERST, MASS. Examination for Admission, June, 1883. 1. From 10 take six millionths. 2. Divide 3.6412 by 400. 3. Reduce 0.0625 to a common fraction in its lowest terms. 4. Find the G.C.D. of 1235 and 1495. 5. How many rods of fence will be required to enclose 640 acres of land in a square form? 6. What is the difference in time between Boston and San Francisco, the longitude of the first being W. 71 3' 30", and the second, W. 122 24' 40"? 7. Sold a pair oxen for $175, and gained 5 per cent ; what per cent would I have gained if I had sold them for $200? 8. If 6 men in 15 days earn $135, how many dollars will 9 men earn in 18 days ? 9. What is the weight of 27 hl of water? ARITHMETIC. 83 XI. WILLIAMS COLLEGE, WILLIAMSTOWN, MASS. Entrance Examination, June, 1883. 1. Reduce -f- to a decimal, and extract the square root to three places. 2. How long must the side of a square lot be to contain one acre of ground ? 3. Find the interest on $1385.50 for 23 days at 7 per cent. '4. Reduce 532 km to miles. XII. TUFTS COLLEGE, COLLEGE HILL, MASS. Examination for Admission, June, 1881. 1. Find the L.C.M. of 108, 217, 54, 31. 2. Find the prime factors of 927, 342, 861. With these prime factors get the Gr.C.D of the given numbers. 3 Reduce the fraction JLofH 2'of.I 12 f 4 11 4. If the rate of discount is 5 per cent per annum, how much can be obtained on a note for $600, payable in 4 months, discounted at a bank ? 5. If from the retail price of a book 20 per cent is deducted, and a discount of 10 per cent is made on the bal- ance, and then the book sells for $1.33, what is the retail price ? 6. What is the meter ? Name its subdivisions. In 9780 m how many kilometers ? Give the units of volume in the metric system; also, of weight. 7. What weight of mercury will a vessel contain whose capacity is 20 ccm , the mercury being 13.5 times as heavy as water? 84 EXAMINATION PAPERS. XIII. TEINITY COLLEGE, HARTFORD, CT. Examination for Admission, June, 1883. 1. From the sum of of and 4-J subtract 6^-, multiply the difference by f of J-J of 88, and find what fraction the product is of 999. 2. Find the amount of $ 342.42, from Feb. 5, 1ST. , to March 15, 1881, with interest at 7 per cent; and reduce it to pounds sterling ? 3. What is the weight of water in a tank, if it would take 98 minutes to empty it, at the rate of 8.7 1 a minute ? If it were filled with oil at $18.75 a hektoliter, what would the contents be worth ? XIV. WESLEYAN UNIVERSITY, MIDDLETOWN, CT. Examination for Admission, June, 1883. \ 3 ,5 1. Express the value of - - - - - - exactly as a decimal. 2. What was the amount due January 15, 1883, on a note for 175, dated April 1, 1882, bearing 5 per cent interest ? 3. A merchant sold \ of a certain lot of goods at a gain of 18 per cent, * at a loss of 5 per cent, and the re- mainder at half cost. Did he lose or gain? What per cent ? 4. Extract the square root of 0.01952, carrying the result to four places of decimals. ARITHMETIC. 85 5. What is the cost of digging a cellar 3 dkm wide, 5 dkm 4 m long, and 2 m 6 dcm deep, at the rate of 50 cents a stere ? 6. Two men undertake to do a piece of work for $6.00. One could do it alone in 5 days, the other in 8 days. With the assistance of a boy, they finish it in 21 days. How should the money be divided ? XV. CORNELL UNIVERSITY, ITHACA, N.Y. Entrance Examination, June, 1882. 1. Define : an abstract number, the prime factors of a number, a quotient, a mixed number, cube root, percentage, bank discount, compound interest. 2. Get the sum of five, five-tenths, thirty-seven thousandths, one-thousand millionths, XIX, MDCCCLXXXI, o.is. 3. Find all the common divisors of 225, 2025, 8100. 4. Divide A of 91 by -^ of 637. 5. What is the amount, at compound interest, of $500 for 2 years 6 months, at 7 per cent ? 6. Get the square root of 530 to three decimal places, and give the reasons for the several steps in the work. 7. Give the common and the metric tables for liquid meas- ure ? 8. How many liters in 10 gallons, 3 quarts, 1 pint, 3 gills, the gallon being 231 cubic inches, and the meter 39.37 inches? 86 EXAMINATION PAPERS. XVI. STEVENS INSTITUTE OF TECHNOLOGY, HOBOKEN, N.J. /Specimen Entrance Examination Paper. 1. What is a prime number? 2. Find the L.G.M. of 36, 48, and 72. Why can it not be found by first dividing by 36 ? 3. Find the G.C.D. of 120, 228, and 720. 4. If John sells a book for 110 cents, and thereby loses 12 per cent, what did the book cost him ? 5. Find the square root of 0.4 to three places. 6. Find the cube root of 0.8. 7. Multiply 3 hundredths by 300 -thousandths. 8. Divide 300 thousandths by 3 hundred-thousandths. XVII. MADISON UNIVERSITY, HAMILTON, N.Y. Entrance Examination, June, 1882. 7 1515 21 5 85 4 002 1. From - subtract ' - - - , obtaining the result to three places of decimals. 2. Extract the square root of 102.002 to two places of decimals. 3. What is the interest on 51584 for 1 year, 2 months, and 20 days at 7 per cent ? ARITHMETIC. 87 XVIII. VASSAR COLLEGE, POUGHKEEPSIE, N.Y. Specimen Examination Paper for Admission. 1. Find the greatest common divisor of 256, 480, and 1296. 2. What is the value of (^^- + 16 ~ ' 8 - |) X 7 T V ? 3. What is the sum of ' f ^ and f-^A? 4. Divide two thousand five hundred one and four-tenths by four thousand one hundred twenty-five ten- millionths. Divide 1.29136109 by 184.3, and write the quotient in words. 5. A gentleman bought a yacht for $3500, and sold it at a loss of 20 per cent ; the buyer sold it at a gain of 25 per cent ; what did the latter receive for it ? 6. What sum of money, at 10 per cent compound interest, will amount to $8651.50 in three years? 7. A cistern is 4 m long, 24 dm wide, and 80 cm deep. How much water will it hold in cubic meters? In liters? 8. The longitude of St. Petersburg is 39 19' east ; of New York 74 41' west; when it is one o'clock in the afternoon at St. Petersburg, what time is it at New York? 9. Extract the square root of 4.932841. 88 EXAMINATION PAPERS. XIX. COLLEGE OF NEW JERSEY, PRINCETON, N. J. Examination for Admission, Sept., 1883. 2. State and demonstrate a rule for finding the greatest common divisor of any set of integers ; and make use of it to find the greatest common divisor of 847, 1331, and 1573. 3. Prove that any circulating decimal may be reduced to a rational fraction. To what fraction is the circu- lating decimal 0.57 equal ? 4. Two bodies let fall at different instants from the same point are found, \|-^ - seconds after the latter of \ 981 them started, to have fallen, the one 25 m , the other 100 m . These distances being to one another as the squares of the times during which the bodies have been falling, how many seconds must the one body have started before the other ? 5. What per cent is 3 of 6 ? What is the number to which if 2 per cent of itself be added the sum is 516 ? 6. The amount of a certain principal at a certain rate of interest for 6 months is $949.76, and for 1 year at the same rate is $1003.52. Required the rate per cent and principal. 7. The dimensions of a room are, length 4 m l dm , breadth 3 m 2 cm , and height 3 m l mm . Find its cubical contents (in kilosteres) and the area of its walls (in centares), ARITHMETIC. &9 XX. JOHN C. GREEN SCHOOL OF SCIENCE, PRINCETON, N. J. Entrance Examination, Sept., 1883. 1. Simplify ||f. 2. Find the G.O.M. of 252, 315, 420, and 504. 3. Find the square root of 0.434 to three decimals. 4. If I sell goods at 4 per cent commission, and receive $60, what amount have I sold? 5. Find the edge of a cubical can which will hold 27.57 kg of sulphuric acid, whose specific gravity is 1.8. XXI. UNIVERSITY OF PENNSYLVANIA, PHILADELPHIA, PA. Examination for Admission, June, 1882. i. n a- r* 5i-0.042-2. 2. Simplify - 3. Simplify 0.6 of 3.3 + -of 17+0.4 of 5.75- 2-625 2.095238 4. Extract the square root of 5683 to four places of decimals. 5. A rectangular piece of ground is 32 m 7 dm long, and 19 5 cm broad. Find the cost of enclosing it with a path l m 5 dm broad, at 3 francs 5 centimes a square meter. (i.) Path outside of the ground ; (ii.) path part of ground. 6. A house cost $5000, and rents for $25 a month, with $25 to pay annually for repairs and $50 for taxes ; what is the difference in the income from this and. from the same money invested in 6 per cent stock at 96? 90 EXAMINATION TAPERS. XXII. UNIVERSITY OF MICHIGAN, ANN ARBOR, MICH. Examination for Admission, June, 1883. 1. Reduce - - to a simple fraction, and state the pro- (> cess and principles. 2. Reduce 2 years 5 months 12 days to years and decimals of a year. 3. Extract the square root of 0.4. 4. Give the denominations used in linear measure in the metric system. 5. How are the measures of capacity and of weight in the metric system related to the linear measures ? XXIII. LAKE FOREST UNIVERSITY, LAKE FOREST, ILL. Entrance Examination, June, 1882. 1. Add ten thousand and one millionth ; four hundred thousandths ; ninety-six hundredths ; forty -seven millions sixty thousand and eight billionths. 2. Define integer, compound number, the power of a num- ber, a fraction. How many classes of fractions ? 3. Find the interest of $375.75 for 4 years 5 months and 25 days, at 4? per cent. 4. If the wages of 72 men for 5 days is $450, how many men may be hired for 12 days for $540? 5. A can build a wall in 18f. days, B in 3H days; how long will it take both together to build it ? ARITHMETIC. 91 6. What is the present worth of $3471.50, due 3 months and 9 days hence, at 7 per cent ? 7. What is the interest at 4J per cent of $360.45, from July 4, 1873, to November 3, 1875, allowing a credit of $75, paid October 5, 1874? 8. Reduce to equivalent fractions, having a common denominator, f of f , 2f , 5f , f of of 3 J. 9. On what principal at 7 per cent, in 1 year and 3 months, will the interest be $15.40? 10. Extract the cube root of 225,866,529. XXIV. EDUCATION DEPARTMENT, ONTARIO. Examination for Admission to High Szhools, June, 1883. 1. What is the object of division ? Write down the rela- tion connecting the divisor, dividend, quotient, and remainder. Divide one hundred and eight billion four hundred and nineteen million seven hundred and sixteen thou- sand and one, by eighteen million seven hundred and forty-eight thousand and five. 2. Find, by " casting out nines," whether the following is correct: 349,751 X 28,637 = 10,015,819,397. Find the weight of 500,000 bricks at 4 pounds, 2 ounces each, and the cost, in dollars and cents, at 27s. Qd. a thousand, allowing 4s. 2d. to make a dollar. 3. A merchant received from England the following in- voice in sterling : 92 EXAMINATION PAPERS. 375 tons iron plates, at 8 15s. Grf. ; 107& tons bar iron, at 11 14s. ; 10 tons bulb iron, at 10 10s. ; 17 tons T iron, at 15 10s. ; 48 tons steel, at 18 7s. 6 d. ; 15 tons rivets, at 11 1 s. Find the amount of this invoice in Canadian currency, allowing the shilling sterling to be equal to 24-^ cents. 4. At $1.75 per rod, what will it cost to fence a piece of land 63.5 rods long, and 27.75 rods wide ? 5. Simplify 1 - 1 + J - drtv + THfcr = J and 5.81 2.5^ 441 of 32 of 0.45 3760* 6. Gunpowder is composed of nitre, charcoal, and sulphur, in the proportion of 15, 3, and 2. A certain quan- tity of gunpowder is known to contain 20 cwt. of charcoal ; find its w r eight, and also the weight of nitre and of sulphur it contains. 7. Bought 360 gallons of wine at 2.60 a gallon ; paid for carriage, 17.20, and for duties, $86.50. If -^ of it be lost by leakage, at what price must the remainder be sold to gain $50 on the whole transaction? 8. Find the interest on a note for $257.81, dated January 3, 1883, and paid April 6, 1883, at 8 per cent per annum. 9. The length of a second's pendulum is 39.37079 inches ; if 64 French meters are equal to 70 yards, by what decimal of an inch will the length of a second's pen- dulum differ from one meter ? 10. At what times between 4 and 5 o'clock are the hands of a clock (i.) coincident? (ii.) at right angles? ARITHMETIC. 93 XXV. EDUCATION DEPARTMENT, ONTARIO. Examination of Third Class Teachers, July, 1883. 1. Add together -f- of 13, of -^ of f of 2 12s., and '0f9rf. Reduce 13s. 4J c?. to the decimal of 19s. Gel. 2. Find by practice the value of 8596 pounds, at 10 18s. *l\d. each. 3. A person borrows 500 on April 10, and on June 22 pays his debt with $510.20. At what rate per cent' per annum was he charged interest? 4. A man having a certain sum of money to invest has an opportunity of purchasing 7 per cent stock at 95, but delays until it has risen to 110. What per cent is his income less than if he had purchased at the fipst price ? 5. At an international exhibition, one country was awarded 5 gold, 9 silver, and 11 bronze medals; and an- other, 4 gold, 15 silver, and 10 bronze. Find a ratio of values for such medals that these countries may be regarded as equally fortunate. 6. In a box there is a certain number of- sovereigns, three times as many guineas, and twice as many marks (13s. 4 and 3 i- 6. Subtract 9^ from 10 T J^. 7. Multiply 6^j- by ff 8. Divide 31$ by Iff. 9. Add together 371.87001, 0.0031, 0.00631, and 5786.44321. 10. Subtract 185.939131 from 186.847. 11. Multiply 323.211 by 0.20343. 12. Divide 343.5777 by 0.525 to three places of decimals. 13. What fraction of a sovereign is 0.345 of 1 4s. ? 14. Reduce 3 quarters 7 bushels 1 gallon to pints. 15. The market price of wheat being 3 4s per quarter, what will be the value of 11 bushels and 3 pecks? 16. Find (by practice) the dividend on 3760 15s. at 17s. Qd. in the pound. 17. Find the amount of 4096 in 3 years at 1J per cent compound interest (neglecting fractions of a penny). 18. Add together 5|i, , 3o 4 T , and 1^. 19. Subtract -j^ from T 7 ^. 20. Multiply together 5-^, ^, ff , and 1^. 21. Divide | by 6|. ARITHMETIC. 125 22. Add together 11.431, 0.00101, 243.734, 400, and 1.3743. 23. Subtract 876.315 from 1000.01. 24. Multiply 7.3406 by 0.00437. 25. Divide 0.003634 by 0.0632. 26. Find the value of 0.0625 of an acre. 27. Reduce 1 mile 7 furlongs 5 perches 2J- yards to inches. 28. If 49 men can empty a reservoir in 65 days, pumping 8 hours a day, how many hours a day must 196 men pump to empty it in 26 days? 29. Find (by practice) the value of 7719 articles at 1 7s. 6d. per dozen. 30. At what rate per cent will 461 10s. amount to 611 9s. in 13 years at simple interest? 31. Add together f , &, Iff, and |f 32. Subtract 12^- from 15^. . 33. Multiply together T 7 , 3^-, l-fa, and ^. 34. Divide 5f by 35. Add together .1.001 of a cwt. and 0.039 of a quarter, and give the answer in ounces and the decimal frac- tion of an ounce. 36. Subtract 0.335 of a gallon from 12.51 of a quart, and give the answer in pints and the decimal of a pint. 37. Multiply 0.003631 by 200.001. 38. Divide 28.028 by 4900. 39. Reduce 13s. Qd. to the decimal of 3. 120 EXAMINATION PAPERS. L. CIVIL SERVICE OF GREAT BRITAIN. Competitive Examination for the Excise, Dec., 1876. Higher Arith- metic. Time allowed, 3 hours. 1. An estate is divided among three persons, A, B, C, so that A has -f of the whole, and B has twice as much as C. It is found that B has 27 acres more than C. How large is the estate ? 2. 2 cwts. 1 quarter 3 pounds of an article is bought for 15s., and 17 pounds is sold for Is. 3d. What profit is made per cent ? 3. What fraction of 300 yards is 1 furlong 2 poles 6 yards 2 feet ? Express the answer as a decimal. Express as a fraction of an acre the ground taken up by a path 3 feet broad round a house, the front of which is 57 feet, and side 37 feet long. 4. Extract the square root of 30,789^^-, and the cube root of 2,326,203.125. 5. How many ounces of silver are there in a piece of plate costing 59 10s., the price of silver being 0.255 of 1 per ounce, and the cost of manufacture -J- the value of the silver used ? 6. Explain what is meant by the L.C.M. of two or more numbers? Find the L.C.M. of 3696, 286, 19,656. 7. Find the value of 1.72 of 0.276 of 15. 8. How much must a man invest in 3-J- per cents at 91 in order to receive 590 per annum, after paying 4 d. in the pound income tax ? ARITHMETIC. 127 9. The difference between 'the discount and interest on a debt due a year and a quarter hence, at 4 per cent, is 5s. What is the debt? 10. A tradesman's prices are 12 per cent above cost price. If he allows 1 6s. 3d. discount on a bill of 21, what profit does he make per cent ? 11. A man rents a house from the first of January at 142 per annum, payable half-yearly. He sublets it for 160 per annum, payable quarterly. Allowing simple interest at 4 per cent, what will he make by the transaction in- 3 years ? 12. A cistern containing 600 gallons measures externally 7 feet in length, 2 feet 1.1 inches in breadth, and 5 feet 6 inches in height. The sides being H inches thick, what is the thickness of the bottom ? (A cube foot of water contains 6-^- gallons.) 13. The map of a country is drawn on the scale of ^ of an inch to a mile. What area on the map will represent a lake 4000 acres in extent ? 14. A fast train leaves a place A for another place B at the same moment that a slow train leaves B for A. The fast train takes 2 hours on the journey, and, if the slow train kept its time, they would meet at a distance from B equal to -| the whole distance from A to B. Instead of this, the place where they meet is at a distance from B equal to -J the distance from A to B. How much behind time will the slow train be when it arrives at A ? 15. A round column stands on a cubic pedestal of the same material, whose edge is 6 feet. The column is hol- low, the external and internal diameters measuring 5 feet and 4 feet, respectively. If the weight of the column be the same as that of the pedestal, what is its height ? 128 EXAMINATION PAPERS. LI. CIVIL SERVICE OF GREAT BRITAIN. Open Competitive Examination for Clerkships of the Superior Class in the India Office, 1879. Elementary Arithmetic. Time allowed, 2j hours. 1. Reduce 6 tons 3 cwts. 2 quarters 14 pounds to ounces. 2. What must be given for a piece of silver weighing 73 pounds 5 ounces 15 pennyweights, at the rate of 5s. 9 d. an ounce ? 3. Find (by practice) the value of 1 ton 3 cwts. 1 quarter 14 pounds at 3 10s. per ton. 4. Find the simple interest on 840 15s. for 6-| years at 3 per cent per annum (neglecting fractions of a penny). 5. Add together fj, 4J-, |f, and 1^. 6. Subtract 7f< T from 12^. 7. Multiply SA by 2&. 8. Divide 3-^ by 2Jf 9. Add together 3106.8157, 0.0624, 0.00441, and 43.2875. 10. Subtract 84.937658 from 100.3062431. 11. Multiply 947.36 by 0.00423. 12. Divide 950.562 by 19.56 to three places of decimals. 13. Reduce 0.0016395 of a pound Troy to grains and the decimal of a grain. 14. Reduce 8,868,097 square feet to acres, roods, perches, and yards. ARITHMETIC. 129 15. If 10 men' can build a wall 65 feet long and 5 feet high in 3^ days, in how many days will 6 men build a wall 80 feet long and 4 feet high ? 16. Find (by practice) the dividend on g236 10s. at 4s. 7 d. in the pound. 17. Find the amount of 7205 in 3 years at 6 per cent compound interest (neglecting fractions of a penny). 18. Add together -J-, T V, &, and 4 i- 19. Subtract 1 from 3^. 20. Multiply together -f , -f-, If, and 1-J. 21. Divide 10J- by 1-^, 22. Add together 16.41215, 9.376, 0.00403, 177.42, and 27.03067. 23. Subtract 17.2398 from 27.06. 24. Multiply 46.2375 by 0.00743. 25. Divide 92.3784 by 0.623 to four places of decimals. 26. Find the value of 1.025 of 1 13s. 4d. 27. In 406,395 pints how many bushels, pecks, gallons, etc.? 28. If the 6d. loaf weigh 4 pounds, when wheat is at 36s. a quarter, what should the \d. loaf weigh when wheat is at 48s. a quarter? 29. Find (by practice) the value of 17 ounces 10 penny- weights 12 grains at 1 13s. 4d. an ounce. 30. At what rate per cent will 2100 amount to 5250 in 3 years? 31. Add together 5f , -3J-, f , and |f. 32. Subtract 8-J from 130 EXAMINATION PAPERS. 33. Multiply together 10-J-, 2, f and 3^. ' 34. Divide 10|- by 13. 35. Add together 3.062 of a day and 1.5347 of an hour, and give the answer in minutes and the decimal fraction of a minute ? 36. Subtract 5.017 of a furlong from 1.358 of a mile, and give the answer in yards and the decimal fraction of a yard ? 37. Multiply 34.0069 by 0.005006. 38. Divide 0.038452 by 0.1005 to three places of decimals. 39. Reduce 1.00065 to farthings and the decimal of a farthing. LII. CIVIL SERVICE OF GREAT BRITAIN. Open Competitive Examination for Clerkships of the Superior Class in the India Office, 1879. Higher Arithmetic. Time allowed, 3 hours. 1. If 26 sheep be worth 5 oxen, 2 oxen be equal in value to 3 horses, and 7 horses can be purchased for 91 guineas, find the value of 1 sheep. 2. Simplify the following, and express the results as deci- mals : (i.) (2-H)x(3- r-\ 2J- of 3 U of _ ( 1L ' 3frf2 ~ 4 of 2 " 2} + I (iii.) 0.16 -f- 0.0027. 3. Divide 987,654,321 by 3509, and 0.00321 by 0.000011. Find the value of 2.0136 of 2 1 s. 3d. 4. Explain what is meant by the G.C.M. and the L.C.M. of several arithmetical quantities. ARITHMETIC. 131 Find the G.G.M. of 5049, 4301, 3553. The driving-wheel of a locomotive engine is 27|- feet in circumference, and the fore-wheel 16 feet. Two particular spokes, one in each wheel, are observed pointing vertically upwards. How far will the engine travel before the same two spokes are again simultaneously in the same direction, and how often will this happen in 9 miles ? 5. What is the present worth of 1866 16s., payable 2 years hence at 3 per cent per annum? 6. The area of a rectangular piece of ground is 87 acres 1 rood 26 perches. What is its length, its breadth being 462.5 links? 7. A block of granite is 17.7 feet broad, 9.4 thick ; what length must be cut off so as to contain 554.6 cubic feet? 8. Find the square root of 1,874,161. Extract to 4 places of decimals the cube root of 0.002. What must be the side of a cubical cistern which is to contain 1000 gallons of water, if a gallon contains 277.164 cubic inches? 9. A grocer mixes 2 kinds of sugar at 4d. and 61 d. per pound, taking 3 pounds of the first to 2 of the sec- ond. At what price per pound must he sell the mixture to gain a profit of 20 per cent ? 10. Divide 144 10s. among 3 persons in the proportions of 0.3, 0.33, and 0.3. 11. A merchant invests half of a sum of money in the 3 per cents at 92, and the other half in the 3-^ per cents at 98. Which is the better investment? If he receives 44 as income, what is the amount of the sum? 134 EXAMINATION PAPERS. 22. A ditch has to be made 360 feet long, 10 feet wide at the top and 3 feet wide at the bottom, the angle of the slope of each side being 45. Find the number of cubic yards to be excavated. 23. A circular pond has an area of 346|- square yards. Find to the nearest penny the cost of fencing it round at 4s. 6c?. per lineal yard. 24. A cubical block contains 1 cubic yard, 2 cubic feet, 541 cubic inches. Find the cost of covering the entire surface with lead at Is. C>d. per square foot. 25. A hemispherical punch-bowl is 5 feet 6 inches round the brim. Supposing it to be half full, how many persons may be helped from ifc in hemispherical glasses If inches in diameter ? LIV. CIVIL SERVICE OF GREAT BRITAIN. Open Competitive Examination for Admission to the Royal Indian Engineering College, July, 1880. Time Allowed, 3 hours. 1. Add together 4fl, 7^, If |f , and l|f 2. Subtract 2-f$ from 3^. 3. Multiply together 1^, 17|, l^f, 1-^, and 2^. 4. Divide 7-& by 5. Add together 17.429, 0.0173, 1156.8, and 0.0001723. 6. Subtract 60.25738 from 356.17. 7. Multiply 7.18 by 0.0919. 8. Divide 331.8553 by 55.3. 9. Express 1 peck 1 gallon 3 quarts as the decimal of a quarter. ARITHMETIC. 135 10. Add together |f , ^, and 11. Subtract 19JL- from 20^- 12. Multiply together 2-J, 1-g^, 1^, and -^ 13. Divide 7{| by l|f . 14. Add together 2.25 of a cwt. and 5.76 of an ounce, and give the answer in quarters and the decimal of a quarter. 15. Subtract 18.75 dwts. from 2.12875 pounds, and give the answer in grains arid the decimal of a grain. 16. Multiply 42.317 by 10.075. 17. Divide 48 by 0.144. 18. Reduce 19.062 furlongs to inches and the decimal of an inch. 19. A steel plate is 11 feet 6 inches 5' long, 3 feet 2 inches 8' wide, and 1 inch 3' thick. Find, by duodecimals, the number of cubic feet, cubic inches, etc., it con- tains. 20. Two circular courts measure 40 and 50 feet in diam- eter. The paving of the former costs 74 16 s. 8 d. Find the cost of paving the latter at the same rate. 21. A rectangular room has its length, breadth, and height as 7, 6, 5, respectively. Its walls were decorated at a cost of 2s. 6d. per square yard, and its ceiling finished at the same rate. The bill for the whole was 86. What will be the expense of covering the floor with carpet at 7 s. per square yard ? 22. Find the cost of constructing a hemispherical dome of stone, the internal diameter of which is 45 feet, and , uniform thickness 18 inches, at 4s. \d. per cubic foot of masonry. 136 EXAMINATION PAPERS, 23. The diameters of a conical frustum of marble are 17^- and 10-|- inches, and the height 24 feet. Find its volume. 24. A and B receive 1GOO cabbages to plant, but of these 10 prove worthless. A plants 5 while B plants 4, and the rows are equal. After some hours they have, not sufficient between them to complete an- other row, A having 45 to spare and B 6. A then finds he has planted three rows more than B. How many did each plant, and how many cabbages in a row? 25. A fast train, travelling at the rate of 36 miles per hour, leaves Dover for London, 79 miles distant, at 8 A.M., and is shortly after followed by a slow train whose speed is 24 miles per hour. The former train meets at 8.45 the express from London, which covers 48 miles in the hour ; and the slower train from Dover meets the express 12-|- minutes later. Find at what time the express leaves London and the slow train Dover, supposing both trains to travel uniformly between Dover and London. LV. CIVIL SERVICE OF GREAT BRITAIN. Competitive Examination of Candidates nominated for Appointments in the India Forest Department, Jan., 1880. Elementary Arith- metic. Time allowed, 2% hours. 1. Eeduce 4 tons 1 cwt. 11 pounds to ounces. 2. If 1 pound 2 ounces 5 pennyweights of gold cost 69 9s. 4-|-