30 A regiment of militia containing 830 .nen is to be raised from three towns, A, B, and C. The contingents of A and B are in the proportion of 3 to 5; and of B and C in the proportion of 6 to 7. Required the numbers raised by each.

31. At what time between 6 and 7 o'clock are the hour and minute hands of a watch together?

32. There is a number consisting of two digits, the second of which is greater than the first ; and if the number be divided by the sum of the digits, the quotient will be 4; but if the digits be inverted and that number divided by a number greater by 2 than the difference of the digits, the quotient will be 14. Required the number.

33. There is a fraction whose numerator being tripled, and the denominator diminished by 3, the value becomes ; but if the denominator be doubled and the numerator increased by 2, its value becomes. Required the fraction.

34. A merchant bought a hogshead of wine for $100. A few gallons having leaked out, he sold the remainder for the original sum, thus gaining a sum per cent. on the cost of it, equal to twice the number of gallons which leaked out. How many gallons did he lose?

35. There are two pieces of cloth, differing in length 4 yards; the first is worth as many shillings per yard as the second contains yards; the second is worth as many shillings per yard as the first contains yards; and both pieces are worth £72. 10s. How many yards does each contain ?

36. A merchant bought a piece of cloth for $180, and selling it at an advance of $1 a yard on the cost, he gained 15 per cent. Required the number of yards.

37. There are two rectangular pieces of land, whose lengths are to each other as 3:2, and surfaces as 5:3; the smaller one is 20 rods wide. What is the width of the other?

33. There is a cistern to be filled with a pump, by a man and a boy working at it alternately the man would do it in 15 hours, the boy in 20. They filled it in 16 hours 48 minutes. How long did each work?

39. In a bag of money there is a certain number of eagles, nany quarter eagles, the number of half eagles, together ៖

with dollars sufficient to make up the number of coins equal to of the value of the whole in dollars; and the number of eagles and dollars diminished by 2, is half the number of coins. What is the number of coins of each sort?

40. Suppose a man owes $1000, what sum shall he pay daily so as to cancel the debt, principal and interest, at the end of a year, reckoning it at 6 per cent. simple interest?

41. A merchant bought two pieces of linen cloth, containing together 120 yards. He sold each piece for as many cents per yard as it contained yards, and found that one brought him in only as much as the other. How many yards were there in each piece?

42. A criminal having escaped from prison, travelled 10 hours before his escape was known. He was then pursued so as to be gained upon 3 miles an hour. After his pursuers had travelled 8 hours, they met an express going at the same rate as themselves, who met the criminal 2 hours and 24 min. before. In what time from the commencement of the pursuit will they overtake him?

43. A and B enter into partnership with a joint stock of $900. A's capital was employed 4 months, and B's 7 months. When the stock and gain were divided, A received $512, and B $469. What was each man's stock?

44. A gentleman bought a rectangular lot of valuable land, giving 10 dollars for every foot in the perimeter. If the same quantity had been in a square, and he had bought it in the same way, it would have cost him $330 less; and if he had bought a square piece of the same perimeter he would have had 12 rods more. What were the dimensions of the piece he bought?

45. A and B put to interest sums amounting together to 800 dollars. A's rate of interest was 1 per cent. more than B's, his yearly interest of B's; and at the end of 10 years his principal and simple interest amounted to & of B's. What sum was put at interest by each, and at what rate?

46. Two messengers, A and B, were despatched at the same time to a place 90 miles distant; the former of whom riding one mile an hour more than the other, arrived at the end of his journey an hour before him. At what rate did each travel per hour?

47. A and B lay out some money on speculation. A disposes of his bargain for $11, and gains as much per cent. as B

lays out; B's gain is $36, and it appears that A gains foutimes as much per cent. as B. Required the capital of each?

48. A and B hired a pasture, into which A put four horses, and B as many as cost him 18 shillings a week. Afterwards B put in two additional horses, and found that he must pay 20 shillings a week. At what rate was the pasture hired?

49. A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left. How much wine did he draw each time?

50. Three merchants, A, B, and C, made a joint stock, by which they gained a sum less than that stock by $80. A's share of the gain was $60, his contribution to the stock was $17 more than B's. B and C together contributed $325. How much did each contribute ?

51. A grocer sold 80lb. of mace and 100lb. of cloves for £65; but he sold 60 pounds more of cloves for £20 than he did of mace for £10. What was the price of a pound of each?

52. A and B, 165 miles distant from each other, set out with a design to meet. A travels one mile the first day, two the second, three the third, and so on; B travels 20 miles the first day, 18 the second, 16 the third, and so on. In how many days will they meet?

53. A and B engage to reap a field for $20; and as A alone could reap it in 9 days, they promise to complete it in 5 days. They found however that they were obliged to call in C to assist them for the two last days, in consequence of which, B received of a dollar less than he otherwise would have done. In what time could B or C alone reap the field?

54. A mercer bought a piece of silk for $54; and the number of shillings which he paid for a yard was of the number of yards. How many yards did he buy, and what was the price of a yard?

55. The fore wheel of a carriage makes 6 revolutions more than the hind wheel in going 120 yards; but if the periphery of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel in the same space. Required the circumference of each.

56. There are three numbers, the difference of whose differences is 5; the sum of the numbers is 20, and their continual product 130. Required the numbers.

57. From two towns, C and D, two travellers, A and B, set out to meet each other; and it appeared that when they met, B had gone 35 miles more than of the distance that A had travelled; but from their rate of travelling, A expected to reach C in 20 hours; and B to reach D in 30 hours. Required the distance from C to D.

58. Two men, A and B, entered into a speculation, to which B contributed $15 more than A. After four months, C was admitted, who added $50 to the stock; and at the end of 12 months from C's admission they had gained $159; when A withdrawing received for principal and gain $88. What did he originally subscribe?

59. The number of deaths in a besieged garrison amounted to 6 daily; and allowing for this diminution, their stock of provisions was sufficient to last 8 days. But on the evening of the sixth day, 100 men were killed in a sally, and afterwards the mortality increased to 10 daily. Supposing the stock of provisions unconsumed at the end of the sixth day to support 6 men for 61 days; it is required to find how long it would support the garrison, and the number of men alive when the provisious were exhausted.

60. There was a cask containing 20 gallons of brandy; a certain quantity of this was drawn off into another cask of equal size, and this last filled with water, and afterwards the first cask was filled with the mixture. It now appears that if 63 gallons of the mixture be drawn off from the first into the second cask, there will be equal quantities of brandy in each. Required the quantity of brandy first drawn off.

61. From two towns, C and D, which were at the distance of 396 miles, two persons, A and B, set out at the same time, and meet with each other, travelling as many days as are equal to the difference of the number of miles they travelled per day; when it appeared that A has travelled 216 miles. How many miles did each travel per day?

62. A tailor bought a piece of cloth for $200, from which he cut 5 yards for his own use. and sold the remainder for

$175, gaining 75 cents per yard.

How many yards were

there, and what did it cost him per yard?

63. There is a rectangular field containing 10 acres, 1 quarter, 5 rods, and the length of it exceeds the breadth by 12 rods. Required the dimensions of the field.

64. A man travelled 96 miles, and then found that if he had travelled 2 miles faster per hour, he should have been 8 hours less in performing the same journey. At what rate per hour did he travel?

65. A regiment of soldiers, consisting of 900 men, is formed into two squares, one of which has 6 men more in a side than the other. What is the number of men in a side of each square?

66. A and B travelled on the same road and at the same rate from Huntingdon to London. At the 50th mile stone from London, A overtook a drove of geese which were proceeding at the rate of three miles in two hours; and two hours afterwards met a stage waggon, which was moving at the rate of 9 miles in 4 hours. B overtook the same drove of geese at the 45th mile stone, and met the same stage waggon exactly forty minutes before he came to the 31st mile stone. Where was B when A reached London?

67. Two men, A and B, bought a farm consisting of 200 acres, for which they paid $200 each. On dividing the land, A says to B, if you will let me have my part in the situation which I shall choose, you shall have so much more land than I, that mine shall cost 75 cents per acre more than yours. Baccepted the proposal. How much land did each have, and what was the price of each per acre?

68. A person bought two cubical stacks of hay for 41£; each of them cost as many shillings per solid yard as there were yards in a side of the other, and the greater stood on more ground than the less by 9 square yards. What was the price of each?

69. Two partners, A and B, dividing their gain $60 B took $20; A's money was in trade 4 months, and if the number 50 be divided by A's money, the quotient will give the number of months that B's money, which was $100, continued in trade. What was A's money, and how long did B's continue in trade?

END.