20. A farmer hired a labourer for 40 days, at 3s. 4d. per day, for every day he worked; but for every day he played he was to forfeit 16d.: at the end of the time he received £3. 3s. 4d. How many days did he work, and how many did he play? Ans. He worked 25 days, and played 15. 21. Two merchants, A and B, entered into partnership with a joint stock of £500, by which they gained £160; of this A received £32 more than B. Required each person's stock. Ans. A's stock £300, and B's £200. 22. A person bought a certain number of oranges at five for two pence, and afterwards sold one half of them at two for a penny, and the remainder at three a penny, and by so doing gained four pence. How many oranges were bought? Ans. 240. 23. What two numbers are in the proportion of 3 to 4, and whose sum is to the sum of their squares as 7 to 50 ? Ans. 6 and 8. 24. A draper sold a certain quantity of cloth for £33. 7s. 6d.; for one third of the whole he received 9s. 6d. per yard, for one fourth of the whole he received 11s. per yard, and for the remainder he received 12s. 6d. per yard. How many yards did he sell? Ans. 60 yards. 25. A certain sum of money put out to interest amounted to £297. 12s. in eight months, and to £306 in fifteen months. Required the sum and rate per cent. Ans. £288, at 5 per cent. 26. Four merchants, A, B, C, and D, entered into partnership, by which they gained a certain sum; of G the gin 15s. per gallon; and he paid £4. 10s. more for the brandy than for the gin. Required the content of each cask in gallons. Ans. 20 gallons of brandy, and 34 of gin. 14. The perimeter of a triangle is 35 chains; the base is 7 chains longer than one side, and 3 chains longer than the other. Required the length of each side. Ans. 15, 12, and 8. 15. A contributed 15s. more than B towards the relief of the poor, and if 25s be added to three quarters of B's money, the sum will be equal to A's money. How much did each contribute? Ans. A 55s., and B 40s. 16. A merchant sold two pieces of cloth, by one of which he gained 15s. more than by the other, and his whole gain was £2. 5s. less than four times the less gain. How much did he gain by each piece? Ans. 45s. and 30s. 17. Ten years ago, A's age was in proportion to B's as 2 to 3, but they now find that the proportion is as 3 to 4. Required each person's age. Ans. A's 30, and B's 40. 18. A cistern, which holds 945 gallons, is filled in half an hour by 3 pipes; the second conveys four-fifths as many gallons as the first, and the third three-fourths as many gallons as the first and second together, per minute. How much flows through each pipe per minute? Ans. 10, 8, and 13} gallons. 19. Divide the number 44 into two such parts, that the greater increased by 5, and the less by 7, their sums will be in the proportion of 4 to 3. Ans. 27 and 17. 20. A farmer hired a labourer for 40 days, at 3s. 4d. per day, for every day he worked; but for every day he played he was to forfeit 16d.: at the end of the time he received £3. 3s. 4d. How many days did he work, and how many did he play? Ans. He worked 25 days, and played 15. 21. Two merchants, A and B, entered into partnership with a joint stock of £500, by which they gained £160; of this A received £32 more than B. Required each person's stock. Ans. A's stock £300, and B's £200. 22. A person bought a certain number of oranges at five for two pence, and afterwards sold one half of them at two for a penny, and the remainder at three a penny, and by so doing gained four pence. How many oranges were bought? Ans. 240. Ans. 6 and 8. 24, A draper sold a certain quantity of cloth for £33. 7s. 6d.; for one third of the whole he received 9s. 6d. per yard, for one fourth of the whole he received 11s. per yard, and for the remainder he received 12s. 6d. per yard. How many yards did he sell? Ans. 60 yards. 25. A certain sum of money put out to interest amounted to £297. 12s. in eight months, and to £306 in fifteen months. Required the sum and rate per cent. Ans. £288, at 5 per cent. 26. Four merchants, A, B, C, and D, entered into partnership, by which they gained a certain sum; of G which, A had £800 less than one half of the whole, B £120 more than one fourth of the whole, C half as much as A, and D only two thirds as much as B. How much had each? Ans. A £2200, B £1620, C £1100, and D £1080. 27. A charitable person gave twenty-four shillings amongst some poor men, women, and children; each man received twelve pence, each woman nine pence, and each child three pence. Now, if there had been two women more, there would have been twice as many women as men; and had there been four children more, their number would have been equal to three times the number of women. Required the number of each. Ans. 7 men, 12 women, and 32 children. 28. Two persons, A and B, received each five shillings per day for their labour; A saved six pence per day more than B, and at the end of 50 days, the amount of his savings was double B's, and two day's expenses over. What did each person spend per day? Ans. A spent 4s. 2d., and B 4s. 8d. 29. A mercer bought a quantity of silk at 3s. 2d. per yard, and retailed one third of it at 4s. per yard, one quarter of the whole at 3s. 8d. per yard, one fifth of the whole quantity at 3s. 6d. per yard, and the remainder at 3s. 4d. per yard, and by so doing gained 15s. 2d. How many yards did he buy? Ans. 30. 30. A and B began to play with equal sums of money; A won 20 sovereigns; B afterwards won half the money A had; he then found that he had twice as much money as A. How much had each permoney son at first? Ans. 60 sovereigns. 31. A person being asked the hour of the day, answered, that if three eights of the hours remaining till midnight be multiplied by 4, the product will as much exceed 12 hours, as half the present time from noon is below 4. Required the hour of the day. Ans. 2 o'clock, P. M. 32. A bill of £36. 5s. was paid in half guineas and crowns, and the number of pieces used of both sorts was 90. How many were there of each ? Ans. 50 half guineas, and 40 crowns. 33. Two persons, A and B, have each the same annual income; A saves one fifth of his yearly, and B, by spending £60 per annum more than A, at the end of three years finds himself £100 in debt. Required each person's income and expenditure. Ans: £133. 6s. 8d. yearly income; A spends £106. 13s. 4d., and B £166. 13s. 4d. 34. Divide 36 into three such parts, that one half of the first, one third of the second, and one fourth of the third may be equal to each other. Ans. 8, 12, and 16. 35. What number is that, which being divided into three equal parts, and also into four equal parts, whose continued product, in each case, is the same? 36. After A had been dispatched 16 hours on his journey from Leeds to London, a distance of 192 miles, B started to overtake him; in order to do this, he found that his rate of travelling must be to A's as 3 to 2. How many miles did each person travel per hour? Ans. A 4 miles, and B 6 miles. 37. A draper bought a quantity of cloth for £62 10s., after parting with 10 yards to a friend, he sold |