MISCELLANEOUS EXAMPLES. (Selected from University and other Examination Papers.) 1. Show by an easy example that the division of one whole number by another is equivalent to a series of subtractions. Divide 1.02 by of •144. 2. If the Three per Cents. are at 911, what interest does this give on £100? (Omit brokerage and fractions of a penny.) 3. How many lbs. in •321875 of a ton weight? Convert it into kilograms (omitting fractions), assuming that a cubic decimetre of distilled water weighs 15432-35 grains. 4. Reduce to their simplest forms ~ comma 1175 – 7:63 o and ms 73.5 – 12.1 25-12 + 7:03375 180 – 9:01 5. Convert it into a decimal fraction, and find the vulgar fraction corresponding to the recurring decimal .22297. 6. Show, by proper attention to the value of the figures, in multiplying one number by another, that the order in which the figures of the multiplier are taken is of no importance. Multiply 61·143 by 47.982 correctly to three places of decimals, beginning with the left hand figure of the multiplier, and use as few figures as possible. 7. Extract the square root of 1095.61, and find to three places of decimals the value of $0.75 -1 8. Find the compound interest of £55 for one year, payable quarterly, at 5 per cent. per annum. A person bought into the Three per Cents. at 98, and after receiving three years' interest he sold at 90. How much per cent. on the sum invested did he gain or lose ? 9. Three gardeners working all day can plant a field in 10 days; but one of them having other employment can only work half time. How long will it take them to complete the work ? 10. What fraction of a crown is of 6s. 8d. ? What is the value of of a guinea ? Reduce 112d. to a decimal of a pound, correct to five places of decimals. 11. Reduce the expressions— to + 4 + 4 - , and J{ * + +*). 'N 1- Multiply 4914 by 5076, and add to to the result. Divide (216) – 1 by (218)” + 376. .. 12. A bankrupt's estate amounts to £910. 3s. 1}d., and his debts to £1875. What can he pay in the pound ? and what will a creditor lose on a debt of £57? 13. A person having invested a sum of money in the Three per Cent. Consols received annually therefrom £233, after deducting the income-tax of 7d. in the pound. What is the sum of money? What can the stock be sold for when Consols are at 945 14. Find the value of :003 X.004, and of : 1831 15. 15. Prove the rule for finding the value of a circulating decimal, and divide 4.367 by the circulating decimal .052. Reduce to its simplest form the quantity . 3 + √5 3 - 15 8 - 20 ^8+ 20 16. Three persons, A, B, C, hold a pasture in common, for which they are to pay £30 per annum. A put in 7 oxen for 3 months ; B, 9 oxen for 5 months; and C, 4 oxen for 12 months. How much rent ought each to pay? 17. Calculate to four places of decimals the value of the 006 1 2 5 X expression of of 31416 7.93 18. Find the least common multiple of 16, 24, and 30, and explain the method. 19. What should be the price of English standard silver, 37-40ths fine, in order that the par of exchange between England and France should be 25 fr. 22 c.—200 francs being coined from 1 kilogram of silver, 9-10ths fine? (1 kilog. = 15.434 grains). 20. A person buys 100 shares in a company for £3,500; after receiving four half-yearly dividends of 15s. 4d., 20s. 10d., 30s. 4d., and 38s. 9d. per share, he sells at a profit of 43 per cent.; reckoning the simple interest of money at 4 per cent., how much above that interest has he gained? 21. The price of Three per Cent. Consols is 90%; what sum must be invested in order to purchase £24 per annum; and what is the rate of interest on the money invested ? 22. Three partners in trade contribute respectively the sums of £438, £292, £730, with the agreement that each was to receive 5 per cent. on their respective investments, and that the remainder of the gains of the firm, if any, was to be divided between them in the proportion of the sums originally advanced. The whole gain of the firm was £200. What was each man's share ? 23. If 25 tons of goods are purchased for £37. 10s, and sold at 35s. a ton, what is the gain per ton ? At what rate per ton should the goods have been sold in order to obtain a profit of £9. 7s. 6d. ? 24. Find the value of 1 of £3. 12s. 11}d.; and find the fraction that 3 miles, 2 fur. 100 yards is of 12 leagues, 2 fur. 20 yards. 25. The sum of £9040. 16s. is placed in the Three and a Half per Cents. at 94 ; find the income obtained, allowing on the stock purchased {th per cent. to the broker, and zo per cent for other expenses. 26. Express as a fraction •200123, and express as a recurring decimal •012 ; .00132. 27. By the reduction of the income tax from 7d. in the pound to 5d. a person saves £28. 2s. 6d. a year ; what is his income? 28. If 81 bushels of wheat are consumed by 56 men in 5 days, how long will 16 men take to consume 28 bushels ? 29. Find the square root of .i, and prove that 1.694 = 83. 30. The periods of three planets which move uniformly in circular orbits round the sun are respectively 200, 250, and 300 days. Supposing that their positions relative to each other and to the sun to be given at any moment, determine how many days must elapse before they again have exactly the same relative positions. |