14 oz. daily per man: what must be the rate of provisions daily if they want to hold out double the time? 66. If 71 lbs. of tea cost £5 10s. 11 d., what ought to be the price of 30 lbs. of the same tea? 67. If 311 sheep sell for £585 1s. 44d., what ought 80 sheep to fetch ? 68. If 12 of a ship be worth £52 10s., what will 3 be worth? 69. If the cost of 13 cwt. be £29 12s. 3d., what will be that of 39 cwt. 1 qr. 10 lbs. at the same rate ? 70. If 7 cwt. cost £27 14s. 8d., what weight ought to be purchased for £748 16s.? 71. If the cost of 46 gallons of wine be £31 12s. 6d., what quantity can be bought for £58 15s. 10d.? 72. If 17 cwt. of barley cost £8 10s., how much may be bought for £6 10s. at the same rate? 73. What is the value of % of a ship, when of the whole is worth £600 ? 74. If 4 yards of cloth cost 7 guineas, how much may be bought for 9 guineas? 75. How much may a person spend in 73 days if he wishes to lay by every year 25 guineas out of an income of £900 ? 76. The carriage for a parcel weighing 2 tous 4 cwt. costs £2 14s.: what will be the charge for 3 other parcels, each weighing 16 cwt. 2 qrs. 7 lbs. ? 77. If 4 oz. Av. cost 8s. 6d., what will 61⁄2 lbs. cost? 78. Paid £6 for 20 weeks' service: how much service will be required for 20 guineas? 79. A coach travels at the rate of 9 miles an hour, and performs its journey in 18 hours; how long would the train take to go the same distance at the rate of 32 miles an hour? 80. If 13 tons cost 250 guineas, what will 14 lbs. cost at the same rate? 81. If it takes 600 bricks 9 inches long to complete certain work, how many bricks 11 inches long would be required? 82. What is the height of a pole whose shadow is 48 ft. 3 in. long, when the shadow of another 12 ft. high is 10 ft. 2 in. ? 83. A besieged town of 20,400 inhabitants has provisions to last 3 weeks: how many must be sent away to enable them to hold out 5 weeks? 84. For how long should £150 be lent if £100 be lent for 121 days? 85. If 120 acres cost £655, what would be the price of 35 acres? 86. If 7 yards cost 6s. 9d., what must be given for 11 yards? 87. The chain for measuring land is 66 ft. long, and divided into 100 links: what is the length of a wall which measures 1,228 links? 88. A bankrupt has assets to the amount of £1,020, and debts to the amount of £2,900; what will his creditors receive in the £? RATIO. E. (a) Ratio is the relation in which one number stands with regard to another, and may be expressed by a fraction, the numerator of which is called the antecedent, and the denominator the consequent of the ratio; thus,— = The ratio of 7: 9 ; the ratio of 19: 619. (b) If the antecedent and its consequent be multiplied or divided by the same number, the value is not altered; thus,7: 9 x 12 = 7 x 12, and 9 × 12 = 84 108 = 1048 = (c) A fractional ratio may always be expressed by whole numbers; thus,— 7 9. 1 Divide £1,213 4s. among A and B in the ratio of 3 22. 16 7 £707 14s., A's share. £505 10s., B's share. The No. of equal parts 2. Divide £98 8s. 2d. among A, B, and C, in the ratio of 12, 11, and 11. .. the No. of equal .. 1 such part parts .. 18 .. 16 .. 15 22 = 18+ 16 + 15 = 49. = of £98 8s. 2d. = £2 Os. 2d. = 16 × £2 Os. 2d. = 15 × £2 0s. 2d. = £36 3s. Od., A's share. = £32 2s. 8d., B's share. = £30 2s. 6d., C's share. Ans. 8 7 9 3. Find the ratio of 8: 10; 3: 7 ; 9 11 4. 5. 3 5 :: :: :: : 345; 7: 63; 8: 78; 43: 311 6. The diameter of a circular pond is 35 yards, and the ratio of the diameter of the circle to its circumference is as 1 : 37: find the circumference. 7. Divide £20 among 56 men and 40 boys, the share of each boy bing to that of each man as 3: 5. 8. At an election for a borough containing 2,400 voters there were 3 candidates-A, B, C,—who were voted for respectively as 1 12 13: what number of votes did each have? 5 9. A bankrupt owes 3 creditors-A, B, and C-£42, £35, and £53, and his assets are £422 10s.: how much does each creditor receive? 10. A party of three went to an hotel where they agreed to pay the bill in the proportions of 3, 4, and 5. The bill came to £8 4s.; how must they square their accounts? 11. £483 is divided between A, B, and C, so that for every £1 that A gets B gets 15s. and C 11s.; how much does each receive ? 12. Divide £60 between A and B, the share of A being to that of B as 3 5. 13. Divide £7,200 among three men, their shares being as 1: 12: 15. 14. A father died leaving £5,500 to be divided between his three children, their shares being as 3: 5: 6: what was each one's share? 15. A bankrupt owes A, B, and C £126, £105, and £159, and his assets amount to £2,535: how much does each creditor receive? 16. Divide £100 between A and B, so that A gets 3 times as much as B. 7 : 17. Find the ratio of the following: 3: 27, 8: 19, 1, 13:25, 18:33, and 18: 32. 27 11 29 PROPORTION. F.-(a) Proportion.-When two ratios are equal to one another, the four terms composing the ratios are proportional to each other. Thus, : 5 :: 16: 20. .. or 16 is the same as 4 (b) If the first term is more or less than the second, then the third term must be more or less than the fourth. Thus,— } (or 7: 5) = 287; 5:: 28: 20. (c) If either of the antecedents and its consequent (the first and second term, or the numerator and denominator when expressed fractionally) be multiplied or divided by the same number, the proportion is not altered. Thus, 9 3×6= or 18 24: 18 24, 28 144 = or 14 21 42, : 9 : 12. 9: 12. 28: 42. 14÷÷ 7 = , or 2: 3: 28: 42. (d) If the two antecedents or the two consequents (the first and third, or second and fourth terms) be multiplied or divided by the same number, the proportion is not altered. Thus, Ante. multi. , or 2 : 3 :: 4 : 6. x = 8, and Conseq., or 2 3 4 multi. Ante. divided. Conseq. divided. S 20 : :: 2 4 : = 3 = 2, and ÷ 3 = 42: 1 :: 4 : 2. (e) The product of the extremes is equal to the product of the means. Thus,-2 3:: 4: 6. 2 tons, 17 tons, and £50, find a fourth proportional 10 lbs., 150 lbs., and 10s. 9 yds., 36 yds., and 36s. 5 lbs., 1 lb., and 7s. 6d. 4 yds., 18 yds., and 4s. 1 cwt., 215 cwt., and £5 5 tons, 50 tons, and £13 10s. 5s., £40, and 2 yds. 19. 5 cwt., 600 lbs., and 16s. :; 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 4 tons, 7 tons, and £57 8 lbs., 56 lbs., and 5 d. 18 in., 2 yds., 14s. 6d. £12 6s., £50, and £250 10 cwt., 120 lbs., and 9s. 19 oz., 4 lb. 2 oz., and 18s. 6d. 12 lbs., 156 lbs., and 45s. 20 tons, 4 cwt., and £15 36. 18 quarters, 9 yds., and 16s. G.-1. If 2 lbs. of tea cost 9s., what will 36 lbs. cost? 2. If 4 lbs. of coffee cost 8s. 8d., what will 72 lbs. cost? 3. If 8 yds. of cloth cost 19s., what will 160 yds. cost? 4. Bought 3 pairs of boots for £2 5s.: what will 27 pairs cost at the same price? 5. Bought lb. of tea for 1s. 3d.: what will be the cost of 8 lbs. ? 6. Bought 7 lbs. of sugar for 4s. 11d.: what was the price per cwt. ? 7. A person spends £1 18s. 6d. per week, now how much is that per annum? 8. 3 qrs. 12 lbs. of sugar cost £4 15s. 6d. : what is the price per cwt. ? 9. 9s. 31d. will buy 14lbs. of sugar, now how much will 7s. buy? 10. If 24 yds. cost £3 14s. 7d., how much will be given for 2 yds. 3 qrs. ? 11. What is the cost of 5 hogsheads of sugar, each weighing 14 cwt. 2 qrs. 24 lbs., at £2 10s. per cwt.? 12. If for 7s. 8d. I can buy 9 lbs. of raisins, how much can I purchase for £113 12s. ? 13. If 54 men can build a house in 90 days, how many men would it take to do it in 24 days? 14. If 8 horses can subsist on a certain quantity of hay for 4 months, how long would 12 horses subsist on the same quantity ? 15. A bankrupt owes £2484, but can pay only 9s. 6d. in the pound: how much money has he to pay his debts? |