Find the cost of 278 articles when 1709 cost 231 8 6 76. When the divisor is a concrete quantity, the dividend and divisor must be reduced to the same name. EXAMPLE.-How many chairs can be purchased for £31 1s. 8d., if the cost of 12 is £46 12s. 6d. ? 12 chairs can be purchased. 12 ...... For £46 12s. 6d., 12s. 6d. Hence for £31 1s. 8d. 12x £31 1s. 8d. £46 12s. 6d. " 12 × 7460d. 89520d. 77. We have seen that one sum of money may be divided by another, the quotient being the number of times the second is contained in the first. A third sum may therefore be multiplied by this quotient. EXAMPLE 1.-A gentleman who invests £87 10s. in a mining company receives as five years' profits £21 17s. 6d. What did a person invest who received £58 15s. from the same company for the same period? Here £21 17s. 6d. is the profit on £871 Os. That is, 5244d. Therefore 1d. 20976d. 20976 5244 = 4d. Or the sum invested is four times the profit. EXAMPLE 2.-The rate paid on a house the rent of which is £173 10s. is £4 6s. 9d.: what rate should be paid where the rent is £86 10s.? The rate for £173 10s. rent is £4 6s. 9d. Here the divisor or lower number and one of the upper numbers must be reduced to the same name; thus reducing the £86 10s. and £173 10s. to half-sovereigns we have the rate for £86 10s. rent= £4 6s. 9d. x173 -£2 3s. 3d. The same result would have been obtained if we had reduced the £4 6s. 9d. and £173 10s. to the same name, that is to pence; thus 1041 x £86 10s. 41640 Ex. 53. = £2 3s. 3d. (1) The profit on £160 2s. 14d. is £17 15s. 94d.: calculate at the same rate the profit on £916 14s. 3d., £298 15s. 8d., and £1769 14s. 3d. (2) If each of a number of persons pay £77 19s. 113d., they will raise a sum of £397,092 13s. 11дd.: what sum will they raise if each pays £2 16s. 2d.? (3) The tax on £18,641 5s. 4 d. of income is £716 19s. 51d.: find the tax on 884 guineas of income. What will be gained on £ 8. d. £ S. d. £ 8. d. (4)1768 14 9 when 19 12 33 is the gain on 117 13 10 (5) 8196 17 1 (6) 3186 2 8 (7) 154 4 9 (8) 386 17 6 (9) 2266 0 0 (10) 8154 10 9 12 19 101 90 48 113 (11)16986 11 6 Miscellaneous Questions on the Money Rules. Always preface the working in these exercises with an explanation of the process, as in the examples worked in the previous rules. Ex. 54. (1) What is the worth of 96 tons of coals, when 12 are worth £59 16s.? (2) How much will 17 horses cost, at the rate of 35 for £972 12s. 8d.? (3) A certain sum multiplied by 95 produces £7086 2s. 23d.: what will 36 times this sum amount to? (4) 156 times a certain sum is £5442 15s. 6d.: what number of times this sum will amount to £4221 12s. 91d.? (5) How much more will 75 yds., at the rate of 26 for £17 15s. 3d., cost, than 6 articles at 7 for £52 6s. 6d. ? (6) A gentleman's income for 58 weeks was £5332 14s. 9d.: what will be his income at the same rate for 63 weeks? (7) How many week's income amounted to £3861 12s. 9d. in the above case? (8) How many lbs. of sugar can be bought for £5 18s. 81d., at 2s. 3 d. for 5 lbs. ? (9) A man spends 15s. 8d. a week, and saves £156 13s. in 52 weeks: what is his income for 16 weeks? (10) If 9 bushels of wheat be worth £2 78. 3d., what will 14 bushels of the same quality cost? (11) The rent of 764 acres for years was £71,609 17s. 7d.: how much more rent would a farmer who has 324 of these acres have to pay in the 5 years than a neighbour who has 129 acres ? (12) A gentleman's daily income is £3 12s., and he saves in 7 years enough to purchase 9 houses, each worth £382 4s.: how much does he spend on an average in 4 weeks? (13) How many lbs. of cheese at 10дd. a lb. can be bought for £27 10s. 6d. P (14) A man whose income is £381, pays for income-tax £6 7s.: what tax should another man pay whose income is £185? (15) What is the income tax for every £1 income? (16) What would a man whose income is £235 10s. have after paying income tax at same rate? (17) What is the income of a man who pays £2 10s. 9d. income tax at same rate? (18) What is the income of a man who has £185 12s. 10 d. left after paying the income tax? (19) A merchant exchanged 176 yds. of velvet at 17s. 5d. per yard, for cloth at 8s. 8d. per yard: how many yds. of cloth did he receive? (20) Sugar at 7ąd. per lb. is exchanged for 24 lbs. of tea at 3s. 4d. per lb.: how many pounds of sugar are given? (21) What is coffee worth per lb. when 56 lbs. of it are exchanged for 13 lbs. of tea at 3s. 6d. per lb.? (22) What must be paid for 2 pairs of gloves at the rate of 30 dozen pairs for £69 10s. ? (23) How far does the sum of £3 18s. 8d., £17 19s. 61d., £15 14s. 4d., and £56 14s. 114d. fall short of 19 times £4 15s. 83d.? (24) The wages of 298 men for a week amount to £838 2s. 6d. what are the wages of 138 women, every three of whom receives as much as one man? (25) Find the amount of the following sums: 28 lbs. of tea at 3s. 44d. per lb.; 58 lbs. of coffee at 1s. 3 d. per lb.; 112 lbs. of sugar at 5d. per lb. ; and 288 lbs. of rice at 2s. 3d. for 12 lbs. (26) Two men spend 30s. in eggs at 13 for a shilling, one sells his at 14d. each, the other, after breaking 15, sells his at 1s. 5d. per dozen. Which gains most? How much more does one gain than the other ? (27) A man was engaged to work for 4s. 6d. a day, with the condition that he should pay his employers 1s. 3d. for everyday he was idle. He received £90 8s. when he would have received £95 12s. 6d. if he had worked every day. How many days did he work, and how many was he idle? (28) A tea-dealer sold 9 chests of tea, each containing 38 lbs., at 3s. 8d. a lb. He received in payment £23 10s. 3d. in money and 1824 lbs. of sugar. What was the worth of 19 lbs. of the sugar? (29) A farmer bought 15 oxen for £185 11s. 3d. He kept 2 for himself, and sold the others for 3d. more than the whole cost for how much would 3 oxen be sold at this rate? : (30) Divide £118 12s. 74d. by £6 4s. 104d., and explain the result. (31) The contents of a certain number of purses is £38 7s. 3d. The purses contain 3s. 61d., 5s. 94d., 7s. 11 d. or 15s. 4d., and there is the same number of purses with each of these sums. How many purses are there? (32) A train travelling from Leicester to London, 96 miles, contained 14 carriages, of which 4 were first-class, carrying 28 passengers, and 4 were second with 36 passengers. The amount paid by the passengers was £84 8s., and the rates were, first class 24d. per mile; second class 13d. per mile, and third class Id. per mile. How many third class passengers were there? (33) The carriage of 50 tons of merchandize for a distance of 380 miles cost £2438 6s. 8d.: what should be paid for the carriage of the same goods a distance of 135 miles? |