His expenditure in 3 years is (30 × 26 × 31) guineas,

.. his income in 3 years must be (30 × 26 × 31) guineas + £1719. 18s. = £4586. 8s.

.. (31×364) days: 1 day :: £4586. 8s. : daily income,

whence, daily income = £3. 128.

Ex. 4. Two places, A and B, are distant from each other 324 miles by railway. A train leaves A for B at the same time that a train leaves B for A; the trains meet at the end of 6 hours, the train from A to B having travelled 16 miles an hour more than the other. How many miles did each travel an hour?

Each train is supposed to run with uniform speed: when the trains meet, the whole distance must have been passed over by them.

.. 6 hrs. 1 hr. :: 324 miles: miles passed over by both trains in 1 hr., whence, miles passed over by both trains in 1 hr. = 54.

therefore by question, (54-16)÷2, or 19 miles travelled per hour by one train, and therefore 54-19, or 35 miles travelled per hour by the other.

Ex. 5. A gentleman, after paying an income-tax of 7d. in the £, has £248. 10s. 8d. left, what was his gross annual income?

For every 19s. 5d. which he now has, he had £1. before he paid his income-tax;

.. 19s. 5d.: £248. 10s. 8d. :: £1. required income,

whence, required income = £256.

Ex. LVI.

1. If 4 yards of cloth cost 12s., what will 96 yards of the same cloth cost?

2. If 9 yards of cloth cost £5. 12s., how many yards can be bought for £44. 16s.?

3. If 7 bushels of wheat be worth £1. 16s. 9d., what will be the value of 3 bushels of the same quality?

4. The rent of 42 acres of land is £63, how many acres of the same quality of land ought to be rented for £273 ?

5. If the cost of 72 tons of coals be £55. 168., what will be the cost of 54 tons?

6. How much must be given for 13 articles at the rate of £3. 16s. 6d. for 6 articles?

7. How long will a person be saving £3, if he put by 1s. 6d. per week?

8. Find a number which shall bear the same ratio to 9, which 20 does to 15.

9. If 2 cwt., 3 qrs., 14 lbs. of sugar cost £6. 14s. 2d., what quantity of the same quality of sugar can be bought for £29. 15s.?

10. If 3 cwt., 3 qrs. cost £6. 16s., what will be the price of 2 cwt., 2 qrs.

?

11. Find the value of 23 yds., 1 ft. of cloth, supposing 4 yds., 31 in. of the same quality to cost £3. 15s.

12. What will be the income-tax, at 7d. in the pound, on £257. 10s.? 13. If an income of £185. 10s. pay an income-tax of £5. 8s. 21 d., what ought an income of 1000 guineas to pay?

14. What is the tax upon £302. 3s. 7d., when £429. 8s. 3d. is rated at 13s. 6d. ?

15. If one bushel of malt cost 5s. 10d., how much can I buy for £27. 58. 5d.?

16. Find the price of 2 tons, 3 cwt., 14 lbs. at 8s. 91d. per quarter. 17. A pays half yearly an income-tax of £10. 1s. 3d.; find his income, the tax being 7d. in the £.

18. Find the amount of a servant's wages for 215 days at 2s. 4d. a day?

19. A bankrupt's debts amount to £204. 16s. and his assets to £179. 48.; how much in the pound can he pay?

20. Find the cost of a stone of sugar at the rate of £98. 1fl. 2c. 5m. for 1 ton, 8 cwt., 4 lbs.

21. A bankrupt pays 12s 8d. in the pound and his assets amount to £950.; find the amount of his debts.

22. Find the cost of 1 ton, 4 cwt., 8 lbs. of an article, 3 stone of which are worth 6 fl. 11 c.

23. If 26 yards of butter cost 48s., what must it be sold at per foot, in order to gain 4s. on the purchase?

24. If a farm containing 400 ac., 2 ro., 20 po. be let at £841. 3 fl. 1 c. 23 m. for the year, what is the rent per acre?

25. Find a fourth proportional to the numbers 3, 375, and 40.

26. If 10 men can mow a field in 12 days, in how many days will 15 men mow it?

27. If a man walk 62 miles in 3 days, in how many days will he walk 80 miles ?

28. How many yards worth 3s. 74d. a yard must be given in exchange for 935 yards worth 188. 11d. per yard?

29. A bankrupt pays 5fl. 7c. 5m. in the pound; what sum will be lost on a debt of £11793. 5fl.?

30. Find the price of 2 tons, 16 cwt., 17 lbs. of sugar at 10d. for 21 lbs.

31. If a person travelling 12 hours a day perform a journey in 24 days, in what length of time will he perform the same journey if he travel 16 hours a day?

32. If 35 oz. Avoir. cost 7s., what will 30% lbs. cost?

33. How many men must be employed to finish a piece of work in 15 days, which 5 men can do in 24 days?

34. If 356 ac., 3 ro, 391 po. be rented at £951. 19s. 10d., what is the rent of 2 acres?

35. If the rents of a parish amount to £2514. 7s. 6d. and a rate be granted of £83. 16s. 3d., how much is this in the pound? And how much must be paid by an estate whose rental is £115. 12s. 6d. ?

36. If 27 bus., 2 pks. cost £10. 7s. 24d., what is the price of 163 bus.? 37. How many yards of drugget an ell wide will cover 40 yards of carpet yd. wide ?

38. A borrowed of B 400 guineas for 6 months, afterwards A would requite B's kindness by lending him £910; how long should he lend it?

39. A field is 121 yds. long, and 86 yds. broad; what will be its value at £80. an acre?

40. If the price of 1 lb. of sugar be 5625 fl., what is the value of '75 of a cwt.?

41. If 31 shares in a mine cost £11. 5s., what will 28 shares cost? 42. If 34 yards of cloth cost £12. 7s. 11ğd, how many yards can be bought for £3. 19s. Oąd.?

43. Find the rent at 30s. an acre of a rectangular field whose sides are respectively 50 chains 40 links, and 56 chains 25 links.

44. In what time will 25 men do a piece of work which 12 men can do in 3 days?

45. If 3 of 45 cwt. cost £11. 5 fl. 5c., what is the price per lb.?

46. A piece of gold at £3. 17s. 101d. per oz. is worth £150; what will be the worth of a piece of silver of equal weight at 54s. 6d. per lb.?

47. If a piece of building land 375 ft. 6 in. by 75 ft. 6 in. cost £118. 28. 61d., what will be the price of a piece of similar land 278 ft. 9 in. by 151 feet?

48. A servant enters on a situation at 12 o'clock at noon on Jan. 1, 1854, at a yearly salary of 35 guineas, he leaves it at noon on the 27th of May following; what ought he to receive for his services?

50. 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?

51. A person, after paying 7d. in the £. for income-tax on his income, has £1632. 18s. 10d. remaining; what had he at first?

52. If a person's estate be worth 3000 guineas a year, and the landtax be assessed at 2s. 91d. in the £., what is his annual income?

53. A watch is 10 minutes too fast at 12 o'clock (noon) on Monday, and it gains 3'. 10′′ a day; what will be the time by the watch at a quarter past 10 o'clock A.M. on the following Saturday?

54. The circumference of a circle is to its diameter as 3·1416 : 1; find (in feet and inches) the circumference of a circle whose diameter is 221 feet.

55. A bankrupt's estate amounts to £455. 1s. 63d., and his debts to £937. 10s. What can he pay in the £? and what will a creditor lose on a debt of £114?

56. If the carriage of 3 cwt. cost 10s. for 40 miles, how much ought to be carried for the same price for 25 miles?

57. If I spend 20 guineas in a fortnight, what must my income-be that I may lay by £200. in the year 1855?

58. The house-tax upon a house rated at 175 guineas is £6. 17s. 9ąd., what will be the tax upon one rated at £120 ?

59. A silver tankard, which weighs 1 lb., 10 oz., 10 dwts. cost £6. 38. 9d., what is the value of the silver per ounce ?

60. A man, working 71⁄2 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?

61. If a pound of silver costs £3. 6s., what is the price of a salver which weighs 7 lbs., 7 oz., 10 dwts., subject to a duty of 1s. 6d. per ounce, and an additional charge of 1s. 10d. per ounce for the workmanship?

62. How much did a person spend in 63 days, who with an annual income of £818. is 90 guineas in debt at the end of a year

?

63. If 15 men, 12 women, and 9 boys, can complete a piece of work in 50 days, what time would 9 men, 15 women, and 18 boys take to do four times as much, the parts done by each in the same time being as the number 3, 2, and 1?

64. A person possesses £800. a-year, how much may he spend per day in order to save £48. 2 fl. 5 c. after paying a tax of £5. on every £100. of income?

65. If 3 cows or 7 horses can eat the produce of a field in 29 days, in how many days will 7 cows and 3 horses eat it up?

66. How many yards of carpet yard wide will cover a room whose width is 16 feet, and length 27 feet?

67. 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 by selling them at the rate of 5 for 2d.?

68. A church-clock is set at 12 o'clock on Saturday night; at noon on Tuesday it is 3 minutes too fast: supposing its rate regular, what will be the true time when the clock strikes four on Thursday afternoon?

69. A person after paying a poors' rate of 10d. in the pound has £728. 68. 8d. remaining, what had he at first?

70. If a piece of work can be done in 50 days by 35 men working at it together, and if, after working together for 12 days, 16 of the men were to leave the work; find the number of days in which the remaining men could finish the work.

71. A regiment of 1000 men are to have new coats; each coat is to contain 2 yards of cloth 14 yards wide; and it is to be lined with shalloon of a yard wide; how many yards of shalloon will be required?

72. If 5 ounces of silk can be spun into a thread two furlongs and a half long, what weight of silk would supply a thread sufficient to reach to the Moon, a distance of 240,000 miles?

73. How many revolutions will a carriage-wheel, whose diameter is 3 feet, make in 4 miles? (See Ex. 54).

74. If 8 oz. of sugar be worth 5625s., what is the value of 75 of a ton?

75. The price of '0625 lbs. of tea is 45838., what quantity can be bought for £61. 12s.?

76. Two watches, one of which gains as much as the other loses, viz. 2′. 5′′ daily, are set right at 9 o'clock a. M. on Monday; when will there be a difference of one hour in the times denoted by them?

77. How many yards of matting, 2:5 feet broad, will cover a room 9 yards long, and 20 feet broad?

78. A person bought 1008 gallons of spirits for £640.; 48 gallons leaked out at what rate must he sell the remainder per gallon so as not to lose by his bargain?