The pupil should reason out a sum of this kind thus :—What number multiplied by 5 will produce 20? Answer 4, found by dividing 20 by 4. Similarly, the fraction required will be found In the same way, the second part of the sum is performed by multiplying 18 by 3 of 31. 18 × 31 of 3 = 38 × 10=15 = 318. (8) What fraction of a mile is of of a mile + of 3 of 2 furlongs + of 4 furlongs + 18 poles? (9) A farmer went to market with £2 in his pocket. He received for wheat sold, £27; for barley, £371; for oats, £17; for poultry, 183s.; for eggs, 3gs. How much did he bring home? (10) A merchant owns of a ship worth £3000, and its cargo worth £27,000. He purchases another person's share, which is of of it. What part of it has he now; and what is its value? (11) A yard measure worn of an inch short is used to find the length of a rope-walk, and gives it as 175 yards. What is the real length of the rope-walk? Since the yard measure is of an inch short, There is an error of in. to each apparent yard, (12) If off of a ship and her cargo is worth £7800; what oss will be experienced by the owner of a share of the ship and cargo, if she goes to the bottom? (13) Add together of a guinea, § of £4, 1% of a half-crown, of a shilling. (14) Simplify + and 121 7-3 (15) Find the value of & of 4s. 8d. + 311⁄2 of £2 6s. — of £5 +of a guinea. (16) Find the value of 110 gallons when the cost of 7 gallons is £iz. This is a Simple Proportion sum, involving fractions. 7: 110 :: 1 Answer. The fourth term of the proportion will be £110 × 13 ÷ 7 = 221 × 15 × = £28 11s. 618d. (17) After taking out of a purse of its contents, of the remainder was found to be 13s. 51d.; what sum did it contain at first? (18) Determine the quantity, in its simplest form, which shall be equivalent to the sum of the magnitudes of of 113; 12 of 3 of; 2 of 4 of (19) If a cask be emptied by 2 taps in 4 and 6 hours respectively, in what time will it be emptied by both of them together, the rates of efflux remaining the same throughout? of the cask. of the cask. = of the cask. In 1 hour the first tap empties In 1 hour the second tap empties .. In 1 hour both taps empty + 1 = .. No. of hours = 1÷=2=22. (20) How many times does the sum of 6% and 4 contain the difference? (21) A. can finish a piece of work in 2 days, and B. in 3 days; if they work together, what portion of the work will they finish in one day? (22) Divide 7 (11 of 3) 9 (232 of 7) by 2 3/ (23) A party having a bill to pay of £12 7s. 1d., one of them pays for himself and three friends the sum of £5 9s. 10d.: how many were there? (24) Simplify 33 + 1} + 13% +18. (25) How many times does the sum of 22 and 13 contain their difference? (26) What would it cost at 4d. per square yard to paint the walls of a room which is 13 ft. 6 in. long, 11 ft. 7 in. wide, and 9 ft. 3 in. high? Length 13 ft.; breadth 117 ft.; height = 9 ft. = = .. Area of each of the longer walls = (1391) sq. ft. = (27 × 37÷9) sq. yd. =111 sq. yd. = 13 sq. yd. .. Area of two longer walls = 133 sq. yd. x 2 = 273 sq. yd. And area of each of the shorter walls .. Total area of walls = (27+23118) sq. yd. = 51111 sq. yd. .. Cost of painting = (51111 × 4) d. = 20613d. = 17s. 212d. (27) What is the value of a quarter of oats, if 17% qr. are worth £334? (28) The product of three numbers is 340; the first is 7, the second is less than first by 16. Find the third number. (29) Express the difference between of £1 and of a guinea as the fraction of half-a-crown. (30) A certain property was to be divided thus: to A., to B., and the rest to C. C.'s share was £1100 13s. 6d. : what was the amount of the whole. |