Multiply 3.46 by 489. Divide 307-8 by 23.8 to three places of decimals. Divide 8.747 by 413-4 to three places of decimals. Reduce 2 lb. 3 oz. 6 dwt. 5 qrs. to the decimal of a pound troy. Find the least fraction equivalent to '6726. MISCELLANEOUS. N.B.-You are not required to answer any of the following questions; but, if you have time, it will be well for you to do as many as you can. What is a logarithm? What is the ordinary base in use, and what is the peculiar advantage of it? Given log. 2=3010300. log. 3=4771213. 1 Find log. 96 Extract the square root of 406278.76, and of 262 A. has 2,4007. in the 3 per cent. consols; he sells his stock at 824, and buys into a railway at 103, which pays 5 per cent. How is his income affected? What is the true discount on 1,1867, 5s. 11d. due 8 months hence, the rate of interest being 53 per cent. per annum? Find the cube root of 493039. For Competitive Examinations for the WAR DEPARTMENT. Reduce 437. 11s. 93 to farthings. Find the number of ounces in 18 tons 9 cwt. 3 qrs. 15 lbs. How many grains are there in 17 lbs. 3 oz. 7 dwts.? The breadth of a rectangular field is 26 yds. 2 ft. 8 in., and the area is one acre. Find the length. The side of a solid cube is 7 ft. 3 in.; find the content in solid yards, feet, and inches. If the price of one ounce of gold is 37. 10s., what is the price of 14 ingots, each weighing 3 lbs. 7 oz. 14 dwt. 21 grs.? If one yard of cloth cost 15s. 6d. what will be the price of 32 same rate? yards at the Find the price of 56 tons 15 cwt. 2 qrs. 21 lbs. at 247. 6s. 8d. per ton. If 90s. will pay 5 men for 12 days' work, how much will pay 32 men for 24 days' work? Explain the principle of the rule by which you proceed. What should the result be if the efficiency of the second set were half that of the first, and their day's work five-fourths as long? At what rate per cent per annum, simple interest, will 300l. amount to 4147., in 8 years? What will be the amount of 550%. in three years, at 5 per cent. per annum, compound interest? Find the amount of 8751., at the end of 15 months, at 4 per cent. per annum, compound interest, the interest accruing quarterly. Add together, 24, and 13; divide by 13, and subtract the result from 5,7%. Add together guinea. of a pound, and of a of a shilling, of half-a-crown, Find the greatest common measure of 3042 and 3094, and reduce 304 to its lowest terms. Multiply 192-336 by ⚫73307. Divide 16 by ·2, and the result by 0002. What is the rule as to the place of the decimal point in multiplication and division? Express 01056 and 15863 as vulgar fractions in their lowest terms. Explain any rule with which you are acquainted for determining “Equated time of payment," reckoning either simple or compound interest, and apply it to find what sum paid two years hence will be an equivalent for 1007. due one year hence, and 500l. due three years hence, the rate of interest being 5 per cent. If 23 lbs. at 2s., are mixed with 27 lbs. at 3s., and the mixture is sold at 28. 9d. per lb., what is the total gain? and what is the gain per cent. on the money laid out? Extract the square root of 106929; also the square root of 803-7 to two places of decimals. Explain some of the uses of logarithms. Given log. 2=301030 and log. 3=477844, find the logarithms of 5, of 15, and of ⚫15. Explain the meaning of the term local value. Have Roman numerals any local value? It is required to divide the number 34 into two parts, such that the difference between the greater and 18 shall be to the difference between 18 and the less, in the ratio of 2 to 3. Sum the arithmetical progression 1 + 5+ 9 + For Competitive Examinations for the COMMITTEE OF COUNCIL ON EDUCATION. PAPER I. Reduce 15 lbs. 10 oz. 14 grs. troy to grains, and 34677 square yards to acres, &c. The length of a French metre being 39-37 inches, find the number of solid feet and inches in a cube the length of whose side is 2 metres. cwt. be worth 147. 6s., what will be the value of If If £3 of a ton? 20 thalers; 25 thalers = 93 francs; and 62 francs 25 gulden: find how many gulden are equivalent to one pound sterling. The population of Great Britain in 1851 was 21,121,967: and the increase during the previous half century had been 93.5 per cent. the population in 1801? What was Find by the method of practice the price of 8 cwt. 1 qr. 12 lbs. at 47. 12s 5}d per quarter. A person who has £2954 in the 3 per cents at 803, transfers his capital into the 4 per cents at 98; find the alteration in his income. A person's average annual expenditure from the year 1833 to 1853, inclusive, is 2937 17s. 4d. He finds that in 1833 he spent 2837. 17s, 10d., and in 1854 3657. 14s. 1d.; what was his average annual expenditure from 1834 to 1854 inclusive? If 20 horses and 196 sheep can be kept 18 days for 1517. 10s., what sum will keep 15 horses and 72 sheep for 8 days, supposing 5 horses to eat as much as 76 sheep? Find how many yards of paper of a yard wide, will paper a room whose length is 26 ft. 4 in., its breadth 18 ft. 8 in., and its height 12 ft. 3 in. If 20 lbs. 4 oz. of tea at 5s. 10d. per pound be mixed with 46 lbs. 6 oz. at 4s. 3d., and 35 lbs. 6 oz. at 6s. 8d., and the mixture be sold at 6s. per pound, what will be the gain or loss, and what the gain or loss per cent? Find the amount of 13,333l. 6s. 8d. for four years at five per cent compound interest. At what rate per cent will 6517. 13s. 4d. amount to 7487. 12s. 0d in 31 years, at simple interest? Find the discount on 1261. 13s. 4d. due 8 months hence at 4 per cent simple interest. What would be the amount of error in this case if interest were taken instead of discount, and in whose favour would the error be? Reduce to their simplest forms the expressions→→→ Find the sum of 375 of a guinea +2∙1875 of a crown +3 of 7s. 6d. (a) Multiply 2.7 by 27, and their product by 027. (b) Divide 17.28 by 0144, and 42-0463 by 136. Extract the square roots of 531441 and of 321. If £110 florins 100 cents 1000 mils: show how the addition of £896 5f. 4c. 7m., £23 9c. 6m., would be performed. Explain the nature and use of logarithms, and the advantages of selecting the number 10 as the base of tabular logarithms. Having given log. 6.234 =· 794767, and log. 6 235794836, find log. 623472, and the number whose logarithm is 2.794800. PAPER II. N.B. It is strongly recommended that no candidate who finds that he can employ his time advantageously on the other paper should attempt any question in this. Divide 759197. 11s. 7d. by 7. Divide 6113601. 5s. 8d. by 623. Write in figures (1) ninety thousand and forty, (2) three hundred and four millions forty thousand and four. There are two mountains such that if 126 feet are added to four times the height of the lower one, the sum is half the difference between their heights; given that the lower one is 441 feet high, find the height of the other. What is the length of the longest day at a place where the sun rises on that day at 3 hrs. 49 min. 51 sec.? How many entire days have elapsed since the opening of the Great Exhibition in Hyde Park? MISCELLANEOUS PAPERS FOR VARIOUS EXAMINATIONS. REDUCTION. Reduce 375 cwt., 2 qrs., 1 st., 13 lbs., to ounces. Reduce 36 miles, 3 furlongs, 36 poles, 5 yards, to feet. How often will a wheel 34 yards in circumference turn between London and York, the distance being 198 miles ? How many pounds of silver are there in 270 spoons, each of which weighs 1 oz., 13 dwts., 8 grs.? How many seconds are there in 35 days, 8 hrs., 48 min., 29 sec.? How many square yards, feet, and inches are there in the top of a table the sides of which are 21 ft. 7 in., and 19 ft. 5 in.? How many solid yards, feet, and inches, are there in 175,983 solid inches? PROPORTION. If 597. 10s. will buy 25 cwts. 2 qrs. of sugar, what quantity will 67. 14s. 2d. buy? If the penny loaf weighs 5 ounces when wheat is at 62 shillings the quarter, what ought it to weigh when wheat is 64 shillings the quarter? If by paying down 70l. 17s. 6d. a person becomes entitled to 21. 9s. 7d. a year, what income should he gain by paying 2,1517. 17s. 8d. in the same way? If a tax on an income of 1,1327. amount to 125l. 1s. 57d., what is that in the pound? If the carriage of 107 cwt. 10 lbs. cost 371. 9s. 71⁄2d., what would the carriage If 24 men working 8 hours a day can build a house in 70 days, in how many days might it be built by 42 men working 10 hours a day? PRACTICE. Find the value of 373 at 21. 16s. 104d. What is the rent of 67 acres of land for 2 years, 9 months, 11 days, the yearly rent of an acre being 21. 5s.? Find the value of 9 tons, 4 cwt. 3 qrs. 21 lbs., at 147. 15s. 9d. per ton. What is the price of 329 yds. 3 qrs. 2 nls. at 5s. 2 d. per quarter? INTEREST. Find the interest, on 12577. 15s. for 5 years at 4 per cent per annum. Find the interest on 1947. at 5 per cent per annum, from the 3rd of March to the 18th of December following. At what rate per cent. simple interest, will 9517. 7s. 6d. amount to 1,1417. 13s. in five years? Find the discount on 5947. 14s. 9d, due 8 months hence, at 53 per cent, simple interest. When the Three per Cents are at 851. 17s. 6d., what is the rate of interest? Find the amount of 2251. for 3 years, at 4l. per cent, compound interest. VULGAR FRACTIONS. Add together, 4, 4, and, of 74, and subtract the result from 3. What number multiplied by will give 153 as the product? If of a quarter of wheat cost 54s., what will be the price of of a bushel? What fraction of half-a-crown is of 6s. 8d.? Add together 3 pounds, 9 shillings, and 24 pence. DECIMAL FRACTIONS. Add together 130055, 900, 57·1, 1334, and 00000397, and subtract the result from 1314·9. Multiply 95376 by⚫ 0283. Divide 16 by 2, and the result by · 0002. Express as a decimal. Reduce 8/11 d. to the decimal of a guinea. Add together 3211 of a guinea, of a crown, and 6925 of a shilling, ex pressing the result as a decimal of a pound. REDUCTION. Reduce 5277. 16s. 8d. to farthings. Reduce 47 cwt. 1 qr. 16 lbs. 2 oz. to drams. Reduce 13 lbs. 7 oz. 16 grs. to grains. How many square yards, &c., are there in a table 6 ft. 8 in. long by 4 ft. 9 in. broad? In 1,847,638 inches, how many miles, &c.? Reduce 138,297 cubic inches to yards. PROPORTION. Find the amount of income tax on 875l. 15s. at 14d. in the pound. If a rental of 8,050l. per annum be charged with a land tax at 117. 5s. per 1007., what will be the net income? A coach goes from London to Liverpool, at the rate of 9 miles per hour, in 24 hours, in what time would the distance be traversed by a train moving at the rate of 32 miles per hour? A besieged town containing 22,400 inhabitants has provisions for 3 weeks; how many must be sent away that they may be able to hold 7 weeks? If 5 men receive 187. 15s. wages for 12 weeks, what will be the wages of 16 men for 20 weeks? If 6 iron bars 4 ft. long, 3 in. broad, and 2 in. thick, weigh 288 lbs., how much will 15 weigh each 6 ft. long, 4 in. broad, and 3 in. thick? Find the value of 373 at 9/7d. PRACTICE. Find the value of 821 at 13/10 d. Find the value of 3 lbs. 5 oz. 14 dwts. 12 grs. at 17/6d. per oz. What is the dividend on 24687 at 15s. 6d. in the pound? What is the expense of digging a ditch of which the solid content is 5755 cubic yards, at the rate of 15/72d. per yard? Find the value of 136 at 17. 7s. 2d. Find the interest on 4,000l. for 9 months at 5 per cent, less income tax at 14d. in the pound. Find the interest on 11587. 17s. 6d. for 1 year 115 days, at 24 per cent. |