The same result would have been obtained if we had reduced the £4 6s. 9d. and £173 10s. to the same name, 1041 x £86 10s. 41640 that is to pence; thus 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. 84d., 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. 114d.: what sum will they raise if each pays £2 16s. 24d.? (3) The tax on £18,641 5s. 41d. of income is £716 19s. 51d.: find the tax on 884 guineas of income. What will be gained on £ S. d. £ S. d. £ S. 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 (11)16986 11 (12) 885 14 3 29 16 7 12 19 101 90 48 11 135 6 6 160 2 1 285 19 9 710 14 03 (14) 8888 0 0 215 7 7 239287 8 23 (13) 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 12 tons of coals, when 96 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. 2d.: 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 ease? (8) How many lbs. of sugar can be bought for £5 18s. 81d., at 2s. 3 d. for 5 lbs. P (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 7s. 3d., what will 14 bushels of the same quality cost? (11) The rent of 764 acres for 5 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 104d. 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. 6 d., £15 14s. 43d., 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. 34d. per lb.; 112 lbs. of sugar at 54d. per lb. ; and 288 lbs. of rice at 2s. 3 d. 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 P (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. 10d., and explain the result. (31) The contents of a certain number of purses is £38 78. 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 1 d. 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? (34) For what should 35 tons be carried 380 miles ? (35) How many tons would be carried 380 miles for £487 13s. 4d. ? (36) A sum of £40 19s. 41d. was paid in farthings, halfpence, pence, threepenny-pieces, fourpenny-pieces, sixpences, shillings, and half-sovereigns, and the same number of each how many were there of each? (37) A parish contains 850 acres, and the whole rent is £14,237 10s.: what proportion of the rent should be paid by a farmer who holds 176 acres? (38) If the whole rate in the above parish is £444 18s. 54d. what is the rate for every pound of rent? (39) What rate should be paid by a farmer who rents 120 acres in the above parish? (40) A bankrupt owes £2768 18s. 3 d. and his possessions are worth £2001 13s. 11d.: how much can he give for every pound he owes ? (41) How much will a creditor get to whom he owes £188 10s.? (42) How much will another creditor to whom he owes £295 12s. 6d. lose? (43) A workman who is paid at the rate of 38s. a week, made full time for 26 weeks in the year, one day over-time for each of 12 weeks, half-time for 8 weeks, and for the rest of the year he was unable to work. How much did he receive in the year? (44) A person has 373 sovereigns. He gives to each of 48 persons as many as he can, so that all shall have the same number. He then changes the remainder for shillings, and gives to each of the 48 as before. He then changes the remaining shillings into pence, and distributes as before. How many pence has he left? (45) At a post-office £10 6s. 6d. was taken for stamps in one week. There were sold 78 sixpenny, 126 fourpenny, 72 twopenny, and a number of penny stamps. How many penny stamps were sold? (46) If a news-agent gain d. on every paper sold for 1d., and the same rate for other prices, what will he gain in a week if he sell 825 copies of the Daily Telegraph, 454 of the Standard, 402 of the Morning Star, 56 of Punch (3d.), 26 of All the Year Round (2d). ? WEIGHTS AND MEASURES. 78. The various weights and measures are used in order to enable us to compare magnitudes differing in extent or kind. 79. The various kinds of magnitudes are the following; namely, those of weight, length, surface, solidity or volume, value, and time. 80. Before we can compare two magnitudes we must determine upon a certain unit or standard of measurement. The unit of measurement must be of like kind with the magnitude which is to be measured. Thus, it would be impossible to tell the extent of a piece of land if we had no other unit than that used in estimating the weight of a sack of coals. 81. Magnitudes of the same kind differ widely in extent, some being large and others small. It is found convenient therefore to have several units of measurement, varying in extent for each kind of magnitude. 82. The relation of the units of like kind to one another is shown in the various TABLES OF WEIGHTS AND MEASURES. These may be classified as follows: Units of ( Units of Avoirdupois Units of Liquid tons, cwts., qrs., lbs., lbs., oz., dwts., grs. lbs., oz., drs., scrs., grs. Capacity. Dry Commodities} galls., qts., pts., etc. 83. Of units of the same kind, that which is the greater is said to be of the higher name or denomination; thus 1 ton and 1 lb. are of the same kind, but 1 ton and 1 acre are not of the same kind. Of the ton and the pound the former is of the higher denomination; similarly, square yard is of a higher denomination than a square foot, but of a lower denomination than an acre. a |