9. A house, which ordinarily lets for £80 a-year, is leased for a term of four years, at a rent of £20, a certain sum being paid in addition at the time of letting. Find this latter amount. 10. What is the present value of a freehold which produces a clear rental of £50, but which cannot be entered upon for two years, reckoning interest at 5 per cent. ? 11. Find the annuity which in four years, at 4 per cent., will amount to £100. 12. A corporation borrows a sum of £3000 at 4 per cent. What annual payment will clear off the debt in ten years ? (Give the result correct to four places of decimals.) £100 X 8 5 X 12 Profit and Loss. 52. All questions involving the loss or gain per cent. by any transaction belong to this rule, and may be generally worked by Proportion. Ex. 1.—A man buys goods at 5s. and sells them at 5s. 8d. Find his gain per cent. The actual gain upon 5s. is 8d., and we are required to find the gain upon £100. Now 5s. : £100 :: 8d. : gain upon £100, £13, 13. Ex. 2.-By selling goods at 6s. 3d. there is a gain of 25 per cent. What will be the selling price to gain 10 per cent. ? Now, selling price of goods which cost £100, so as to gain 25 per cent, is £125, and that to gain 10 per cent. is £110. Hence £125 : £110 :: 6s. 3d. : selling price required ; from which, selling price required = 5s. 6d. Ex. 3.–Find the cost price when articles sold at ls. 9d. entail a loss of 121 per cent. Now, articles which cost £100 when sold at a loss of 127 per cent. must sell for £874. Hence £874 : ls. 9d. :: £100 : cost price required; from which, cost price = 2s. Ex. XXII. 1. Find the cost price of goods which are sold at a loss of 10 per cent. for 4s. 10_d. 2. Goods which are sold for 7s. 11d. entail a loss of 5 per cent. What should be the price to gain 30 per cent. ? 3. A tradesman reduces his goods 71 per cent. What was the original price of an article which now fetches £1. 78. 9d. ? 4. In what proportion must tea at 4s. 2d. be mixed with tea at 6s. a pound, so that a grocer may sell the mixture at 58. 6d. and gain by the sale 10 per cent. ? 5. A quantity of silk, after paying a duty of 121 per cent., cost £54. Find the original cost price. 6. An innkeeper buys 37 gallons of brandy at 14s. a gallon, and adds to it sufficient water to enable him to sell it at the same price and gain 12 per cent. How much water does he add ? 7. By selling goods at 8s. 2d. a tradesman gains 16; per cent. What will be the gain or loss per cent. by selling at 6s. 14d. 8. A company has a capital of £750,000, and the working expenses for the year have been £42,123. 12s. 6d. What must have been the gross receipts in order that the shareholders may receive a dividend of 4 per cent. ? 9. If stock which is bought at 91} is immediately sold at 91%, what is the gain per cent. ? 10. A person buys goods at 6 months' credit and sells them for cash at the nominal cost price immediately. What is his gain per cent.? (Interest 5 per cent.) 11. Goods are marked at a ready-money price and a credit price allowing 12 months. The credit price is £4. 9s. 3d., what is the ready-money price ? 12. Goods are now being sold at 10 per cent. loss. How much per cent. must be put upon the selling price in order that they may be sold at 20 per cent. gain ? Square Root and Cube Root. 53. To avoid unnecessary repetition, the student is referred to the articles on Involution, Algebra, stage I., where the arithmetical principles and methods are explained. Estimates. 54. The following specimens will give the student an idea of what he may expect to meet with under the head of Estimates. It is usual, in ordinary transactions, to use certain abbreviations; as cub. for cubic measure, sup. for superficial measure, run. for running or lineal measure. Builders, too, are in the habit of calling twelfths of a foot—whether it be cubical, superficial, or lineal measure—by the name of inches. The names yards, feet, inches, are often written thus : yds., ', ". Ex. 1.—DIGGER, BRICKLAYER, AND MASON. 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 1 of •144. 2. If the Three per Cents. are at 91}, 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. 11.75 1-63 4. Reduce to their simplest forms and 13.5 - 12-1 35.12 + 9-03375 280 - 5.01 5. Convert ita 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 4 places of decimals the value of 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? |