25. Find a fourth proportional to 1·34, ·001 and 201.

26. The ages of two persons are related as follows: if to the sum of them 18 be added, the result will be double the age of the elder; if 6 be taken from their difference, the remainder will be equal to the age of Determine their respective ages.

the younger.

27. A and B engage in play; in the first game A wins as much as he had, and 4s. more, and finds he has twice as much as B; in the second game B wins half as much as he had at first, and 1s. more, and then it appears that he has three times as much as 4. What sum had each at first?

28. If copper be worth 1207. 16s. per ton, find the price of 4 cwt. 1 qr. 13 lbs.

29. Reduce 2s. 6d. to the decimal of 5 of 17.

30. A father left his 3 sons, A, B, C, his property; to he gave, wanting 447.; to B he gave 1, and 147. over ; to C he gave the remainder, which was 827. less than the share of B. What was the worth of the father's property?

31. Find the difference between the simple and compound interest of 3,300l. at 3 per cent. for 2 years.

32. A gamester lost at the first game of his money, and 10s. more; at the second game also he lost of his remaining money, and 10s. more, and so on for 5 games; at the end of the fifth game he had 50%. 10s. left. What had he at first?

33. A person investing in the 4 Per Cents. receives 5 per cent. for his money; what is the price of stock?

34. A and B can together do a piece of work in 16 days. They work together for 4 days, when A being called off, B is left to finish it, which he does in 36 days more. Required the number of days in which A or B would do it singly.

35. There are two kinds of gunpowder, one worth 1s. per lb., the other 1s. 3d. How many pounds of each must be taken so that a hundredweight of the mixture may be worth 67.?

36. Divide 10 into three such parts that when the first is multiplied by 2, the second by 3, and the third by 4, the three products may be equal.

37. If a person pay 677. 1s. 8d. income-tax at the rate of 7d. in 17.,

what is his income?

38. If a grocer buy 7 cwt. 3 qrs. 14 lbs. of sugar for 97. 10s. 6d., and retain 1 cwt. 1 qr. 5 lbs. for his own use, at what price per hundred

D

weight must he sell the remainder so as to get his own for nothing?

40. Reduce to their simplest forms—

3+2+43 2+34 × 4
4+91-115 × 1 - 3

41. Find three magnitudes, the products of each two of which are P, q, and r respectively.

42. Reduce to their simplest forms—

3 x 48 3 of 85

+

7 of 4%

43. The reckoning' of a party at a tavern was 37. 12s., but in consequence of two of them having no money, each of the others paid 6d. more than he otherwise would have done; required their number.

44. A person invests 1,000/. in the 3 per cent. Consols at 91ğ, but the price rising to 981, he transfers his money to the 31⁄2 Per Cents. at 971; what will be the increase in his income?

45. If of a house cost 360l. what will 17 of the same cost?

46. If I gain 10 per cent. by selling at 2d. per lb., what do I gain or lose per cent. by selling at 1ąd. per lb. ?

47. A number consists of two digits: the number is equal to three times the sum of its digits, and if it be multiplied by 3, the square root of the result shall be equal to the sum of its digits. Find the number.

48. Straight in a line betwixt two trees stands a statue: that part of it which is level with the bottom of the trees is just 90 feet from the top of each; the one plumbs 54 feet, the other 60 feet. Required the distance between the trees.

50. A clock gains 3 minutes per day; how should its hands be placed at noon that it may give the true time at half-past eleven at night?

51. What two magnitudes are those whose product is a and whose quotient ¿?

52. A person invests 4,8007. in the 4 Per Cents. at 80, and at the end of each year invests the dividend which becomes due in the same stock: supposing the funds to remain at 80 for 3 years, find his dividend at the end of the third year.

53. Find two magnitudes such that the first together with twice the second may be 23, and the sum of their squares 130.

54. How much ought the 3 per cent. Consols to sink below par, in order that a broker may be enabled to obtain 4 per cent. on money ? 55. The population of London in 1831 was 1,471,941, and in 1841, 1,690,084; what was the increase per cent.?

56. A dealer sold 60 bullocks and 80 sheep for 1,0607.; but he sold 42 more of the latter for 907. than he did of the former for 45l. Find the price of each bullock and each sheep.

57. Bought 69 gallons of brandy and 57 gallons of rum, all at 8s. 6d. per gallon; the brandy is sold at 10s. 2d.; at what must the rum be sold to gain 20 per cent. on the whole?

58. Solve the following equation :—

59. Add together 7 √63 +2√252 + 11 √28.

60. If a piece of building land 375 ft. 6 in. by 75 ft. 6 in. cost 1187. 2s. 6d., what will be the price of a piece of land 278 ft. 9 in. by 151 ft.?

61. Extract the square root of 1821 as far as 3 places of decimals. 62. A exchanged with B 60 yards of silk worth 7s. 3d. a yard for 48 yards of velvet; what was the price of the velvet a yard ?

63. Extract the cube root of the following cube number: 000004913.

64. A person buys 100 eggs at the rate of 2 a penny, and 100 more at the rate of 3 a penny; what does he gain or lose at the rate of selling them 5 for 2d.?

65. Extract the cube root of 62359 to 3 places of decimals.

66. The population of London in 1851 was 2,361,640, and that of Great Britain and Ireland was 27,452,262; what per centage is the population of London of the entire population?

68. A ball 12 inches in diameter weighs 30lbs.; what will a ball weigh whose diameter is 28 inches?

69. Express

23+5·27
23 of 5

of 51. as a fraction of

3.7 of 2.25
4.4583+7.16

of 41.

70. Extract the square root of 44533-6609.

71. A was owner of of a vessel, and sold of of his share for

12

10007.; what was the value of

of of the vessel ?

41

33

72. Extract the square root of 1000 as far as 3 places of decimals. 73. A man working 7 hours a day does a piece of work in 9 days; how many hours a day must he work to finish it in 4 days?

74. Extract the cube root of 100 to 3 places of decimals.

75. A person after paying a Poor rate of 10d. in the pound, has 7281. 6s. 8d. remaining; what had he at first?

76. If silver is worth 5s. 2d. per oz., what profit per cent. is gained by coining 66s. from 1 lb. of silver?

77. There are a certain number of ships; at one time the square root of half the number sailed, at another time of them, and then 2 remained; how many were there at first?

78. Reduce 3567. 11s. 8d. to United States currency, the course of exchange being 4 dollars 84 cents for 17. sterling.

80. A gentleman has two elliptical ponds; the area of one is 3 acres 2 'roods; of the other, 1 acre 2 roods 20 poles; he wants a square pond three times as large as both required the length of its side.

SECTION III.-GEOMETRY. 1.

1. ANALYSE the word "Geometry," and give a fuller account of the study than the name would imply.

2. Define exactly "point," "line," "superficies," "solid ;" and state what a point possesses positively.

3. Lines are of various kinds; define a straight line, also define parallel lines.

4. Figures (i.e. surfaces) are different according to their containing lines; name a figure contained by one line only, and accurately define it also by two.

5. Define "triangle ;" name a figure contained by three lines which is not a triangle.

6. Show that triangles are of three kinds, according to the equality of their lines, and name the three kinds.

7. What name is given to a four-sided figure, the sides of which are neither parallel nor equal? define accurately "square," "rhombus," oblong," "rhomboid," and state what quality they possess in common 8. Name all the figures contained by equal lines from five to twelve. 9. What are the boundaries of a solid? Name a solid contained by one boundary only; having two surfaces only; three; four; and five. 10. Geometrical figures depend not only upon the sides but also upon the angles; define a plane angle, also a solid angle.

11. State how plane angles are generally read, and read them in the following figures (1) singly; (2) two together; (3) three together; (4) all together.