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3. Suppose the distance between London and Edinburgh is 360 miles, and that one traveller starts from Edinburgh and travels at the rate of 10 miles an hour, while another starts at the same time from London and travels at the rate of 8 miles an hour: it is required to know where they will meet.

4. Find two numbers whose difference is 4, and the difference of their squares 112.

5. A sum of 24 shillings is received from 24 people; some contribute 9d. each, and some 13 d. each: how many contributors were there of each kind?

6. Divide the number 48 into two such parts that one part may be three times as much above 20 as the other wants of 20.

7. A person has £98; part of it he lent at the rate of 5 per cent. simple interest, and the rest at the rate of 6 per cent. simple interest; and the interest of the whole in 15 years amounted to £81: how much was lent at 5 per cent.?

8. A person lent a certain sum of money at 6 per cent. simple interest; in 10 years the interest amounted to £12 less than the sum lent: what was the sum lent?

9. A person rents 25 acres of land for £7. 12s.; the land consists of two sorts, the better sort he rents at 88. per acre, and the worse at 5s.: how many acres are there of each sort?

10. A cistern could be filled in 12 minutes by two pipes which run into it; and it would be filled in 20 minutes by one alone: in what time could it be filled by the other alone?

11. Divide the number 90 into four parts such that the first increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2 may all be equal.

12. A person bought 30 pounds of sugar of two different sorts, and paid for it 198.; the better sort cost 10d. per lb., and the worse 7d.: how many pounds were there of each sort?

13. Divide the number 88 into four parts such that the first increased by 2, the second diminished by 3, the third multiplied by 4, and the fourth divided by 5, may all be equal.

14. If 20 men, 40 women, and 50 children receive £50 among them for a week's work, and 2 men receive as much as 3 women or 5 children, what does each woman receive for a week's work?

15. Divide 100 into two parts such that the difference of their squares may be 1000.

16. There are two places 154 miles apart, from which two persons start at the same time with a design to meet; one travels at the rate of 3 miles in two hours, and the other at the rate of 5 miles in 4 hours: when will they meet?

17. Divide 44 into two parts such that the greater increased by 5 may be to the less increased by 7, as 4 is to 3.

18. A can do half as much work as B, B can do half as much as C, and together they can complete a piece of work in 24 days: in what time could each alone complete the work?

19. Divide the number 90 into four parts such that if the first be increased by 5, the second diminished by 4, the third multiplied by 3, and the fourth divided by 2, the results shall all be equal.

20. Three persons, whose powers for work are as the numbers 3, 4, 5, can together complete a piece of work in 60 days: in what time could one alone complete the work ?

21. Divide the number 36 into two parts such that one part may be to the other as 5 to 7.

22. A general on attempting to draw up his army in the form of a solid square finds that he has 60 men over, and that he would require 41 men more in his army in order to increase the side of the square by one man: how many men were there in the army?

23. Divide the number 90 into two parts such that one part may be to the other as 2 is to 3.

24. A person bought a certain number of eggs, half of them at 2 a penny, and half of them at 3 a penny; he sold them again at the rate of 5 for two pence, and lost a penny by the bargain: what was the number of eggs?

25. A and B are at present of the same age; if A's age be increased by 36 years, and B's by 52 years, their ages will be as 3 to 4: what is the present age of each?

26. For 1lb. of tea and 9 lbs. of sugar the charge is 88. 6d.; for 1 lb. of tea and 15 lbs. of sugar the charge is 12s. 6d. what is the price of 1 lb. of sugar?

27. A prize of £2000 was divided between A and B, so that their shares were in the proportion of 7 to 9: what was the share of each ?

28. A workman was hired for 40 days at 3s. 4d. per day, for every day he worked; but with this condition that for every day he did not work he was to forfeit 1s. 4d.; and on the whole he had £3. 3s. 4d. to receive: how many days out of the 40 did he work?

29. A at play first won £5 from B, and had then as much money as B; but B, on winning back his own money and £5 more, had five times as much money as A: what money had each at first?

30. Divide 100 into two parts, such that the square of their difference may exceed the square of twice the less part by 2000.

31. A cistern has two supply pipes, which will singly fill it in 4 hours and 6 hours respectively; and it has also a leak by which it would be emptied in 5 hours: in how many hours will it be filled when all are working together?

32. A farmer would mix wheat at 48. a bushel with rye at 2s. 6d. a bushel, so that the whole mixture may consist of 90 bushels, and be worth 3s. 2d. a bushel: how many bushels must be taken of each?

T. A.

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33. A bill of £3. 1s. 6d. was paid in half-crowns, and florins, and the whole number of coins was 28: how many coins were there of each kind?

34. A grocer with 56 lbs. of fine tea at 5s. a lb. would mix a coarser sort at 3s. 6d. a lb., so as to sell the whole together at 4s. 6d. a lb.: what quantity of the latter sort must he take?

35. A person hired a labourer to do a certain work on the agreement that for every day he worked he should receive 2s., but that for every day he was absent he should lose 9d.; he worked twice as many days as he was absent, and on the whole received £1. 19s.: find how many days he worked.

36. A regiment was drawn up in a solid square; when some time after it was again drawn up in a solid square it was found that there were 5 men fewer in a side; in the interval 295 men had been removed from the field: what was the original number of men in the regiment ?

37. A sum of money was divided between A and B, so that the share of A was to that of B as 5 to 3; also the share of A exceeded five-ninths of the whole sum by £50: what was the share of each person?

38.

sons.

A gentleman left his whole estate among his four The share of the eldest was £800 less than half of the estate; the share of the second was £120 more than one-fourth of the estate; the third had half as much as the eldest; and the youngest had two-thirds of what the second had. How much did each son receive?

39. A and B began to play together with equal sums of money; A first won £20, but afterwards lost half of all he then had, and then his money was half as much as that of B: what money had each at first?

40. A lady gave a guinea in charity among a number of poor, consisting of men, women, and children; each man had 12d., each women 6d., and each child 3d. The number of women was two less than twice the number of men; and the number of children four less than three times the number of women. How many persons were there relieved?

41. A draper bought a piece of cloth at 3s. 2d. per yard. He sold one-third of it at 4s. per yard, one-fourth of it at 3s. 8d. per yard, and the remainder at 3s. 4d. per yard; and his gain on the whole was 14s. 2d. How many yards did the piece contain?

42. A grazier spent £33. 7s. 6d. in buying sheep of different sorts. For the first sort, which formed one-third of the whole, he paid 9s. 6d. each. For the second sort, which formed one-fourth of the whole, he paid 11s. each. For the rest he paid 12s. 6d. each. What number of sheep did he buy?

43. A market woman bought a certain number of eggs, at the rate of 5 for twopence; she sold half of them at 2 a penny, and half of them at 3 a penny, and gained 4d. by so doing what was the number of eggs?

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44. A pudding consists of 2 parts of flour, 3 parts of raisins, and 4 parts of suet; flour costs 3d. a lb., raisins, 6d., and suet 8d. Find the cost of the several ingredients of the pudding, when the whole cost is 2s. 4d.

45. Two persons, A and B, were employed together for 50 days, at 5s. per day each. During this time A, by spending 6d. per day less than B, saved twice as much as B, besides the expenses of two days over. How much did A spend per day?

46. Two persons, A and B, have the same income. A lays by one-fifth of his; but B by spending £60 per annum more than A, at the end of three years finds himself £100 in debt. What is the income of each?

47. A and B shoot by turns at a target. A puts 7 bullets out of 12 into the bull's eye, and B puts in 9 out of 12; between them they put in 32 bullets. How many shots did each fire?

48. Two casks, A and B, contain mixtures of wine and water; in A the quantity of wine is to the quantity of water as 4 to 3; in B the like proportion is that of 2 to 3. If A contain 84 gallons, what must B contain, so that when the two are put together, the new mixture may be half wine and half water?

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