(7.) The price of beef is 11d. per lb., and that of mutton 9d. What is the ratio of the price of beef to that of mutton, and of mutton to that of beef? (8.) If 4 lbs. of mutton is of the same value as 6 lbs. of fish. Compare the prices of mutton and fish. (9.) A person buys 19 yds. for 5s., and again 21 yds. for 7s. Compare the prices of the two kinds of cloth. PROPORTION. Terms to be explained-Proportion, terms, means, extremes, simple rule of three, compound rule of three, direct proportion, inverse proportion. LIV. (1.) Do the numbers 3, 9, 5, and 8 constitute a proportion? If not, what must the fourth term be to form a proportion? what the third? the first? the second ? (2.) If 6 and 8 are the means, and 12 one of the extremes, what is the other? (3.) If 9 and 12 are the extremes, and 2 one, of the means, what is the other? (4.) What number has the same ratio to 9 as 15 to 20 ? (5.) What number has the same ratio to 12 as 20 to 16? Supply the omitted terms in the following proportions : : (6.) 8 12 (7.) 7:21:9 : (). (8.) 16: 12 :8: (). (9.) 32: 20 :: 28: (). (10.) 17:30 :(): 19. (11.) 11:33: (): 19. 6: (). Ans. 9. (12.) 25 : 15 : : () : 12. (17.) () : 6 × 3 : : 7 × 8 : 16 × 9. Ans. 7. Ans. 24. (20.) 8 × 3 × 2:7 × 6 × 16 :: 2 × 6: (21.) 4 × 15 × 7 : 10 × 21 × 3 : 17 : (). (22.) 8 X 21 : (). × 45: 16 X 7 X 9::5 × 8 × 6: (). (23.) 17 × 6 × 3 × 2 12 × 34 × 2 :: 3 : (). (24.) 36 × 7 × 8 × 6 48 X 7 X 16 X 9 : 21 : (). (25.) 13 × 14 × 7 × 3 7 × 9 × 26 × 4 :: 49 : (). : (26.) 25 × 16 X 18 X 14 : 30 × 8 × 36 × 7 :: 56: (). (27.): (). (31.) 41 : 63 : : 9 : ( ). (32.) 11: 224 : : 93: (). (36.) 6:111: : 151⁄2 : (). (37.) 11 × 8: 14 × 12: : 94 : (). Ans. 17181. (38.) 155 × 85 : 108 × 551 :: 11† : (). (39) 12 × 8 × 65 : 36 × 811 × 16 : : 17 : (). (40.) 113 × 7 × 6 × 13: 10 (41.) 6 18 × 32 × 6 × 3 :: 14 : (). :£4, 10s. : (). Ans. £13, 10s. (42.) 14: 3 :: £5, 15s. : (). (43.) 31: 26: 5s. 9d. : (). (44.) 4 × 3 × 5 : 10 × 9 × 4 : : £1, 6s. 8d. : (). (45) 6 × 9 × 3 : 9 × 12 : : £4, 6s. 9d. :(). : 3 × 34 × 17 : : £1, 3s. 114d. : (). (46.) 7 × 4 (50.) 5d. : 2d. : : £6, 15s. : (). Ans. £3, 7s. 6d. (51.) 2s. 6d. : 5s 9d. :: £2, 10s. : (). (52.) 4s. 11 d. : 3s. 24d. : : £4, 11s. 6d. : (). (53.) 3s. 4d. × 5 × 3 : 2s. 6d. × 4 × 2 : : 7s. 6d. : (). (54) 2s. 4d. × 6 × 9: 3s. 7d. × 5 × 4 :: £1, 10s. : (). (55.) ls. 1 d. × 4 × 21: 2s. 42d. × 3 × 2:: £2, 15s. :( ). RULE OF THREE. LV. (1.) If 5 lbs. of tea cost 15s., what will 19 lbs. cost? Ans. £2, 17s. (2.) If 18 lbs. of coffee cost £1, 16s., what will 11 lbs. cost? Ans. £1, 2s. (3.) If 17 ounces of silver be sold for £4, 5s., what will be the price of 31 ounces? (4.) If a farmer buy 7 oxen for £126, what should be given for 4? (5.) If the expense incurred by keeping 3 horses for a week be £1, what will it cost to keep 24 horses for the same time? (6.) If I travel by coach 9 miles for 4s., what shall I have to pay if I travel 27 miles ? (7.) If 9 days' wages for one man be £1, 4s., what will be the wages of 11 men for 4 days? (8.) A person bought 9 dozen of eggs for 12s., and sold 6 dozen of them without profit. How much was paid for the 6 dozen? (9.) A bookseller bought 39 copies of a new book and sold 17 of them for £2, 11s., what will he get for the rest if he sell them at the same rate? (10.) If a man walk 242 miles in 11 days, how far will he walk in 17 days? (11.) If 9 men can perform a piece of work in 35 days, in what time will 5 men do the same? (12.) If 3000 men in a besieged city consumed a stock of provisions in 150 days, how long would the provisions have lasted if they had received at the beginning a reinforcement of 4000 men? (13.) If 16 men can build a wall in 54 days, how many men would be required to do it in 36 days? (14.) If the wages of 17 men for a certain time amount to £5, 2s., how many men would earn £9, 12s. in the same time? (15.) If the expenses of a family of 9 persons be £12 a month, what will be the expenses of a family of 5 persons at the same rate? (16) Nine men undertake to dig a trench in 51 days; how many men could do it in 27 days? (17.) If 11 men can build 39 yards of wall in a certain time, how many yards could 25 men build in the same time? (18.) How many lbs. of tea at 15 lbs. for £2, 5s. are equal in value to 150 lbs. at 4 lbs. for 8s. ? (19.) John lent James 26 marbles for 12 days; for how long must James lend John 48 marbles to return the favour? (20.) A merchant buys 200 lbs. of tea at 2s. 6d. per lb., but one box containing 25 lbs. was lost. At what price per lb. must he sell the rest to have a profit of £10 on his first outlay? (21.) A says to B, for every 6s. you give toward defraying the expenses of our new library, I will give 2s. 6d.; B gave £3, 3s., how much will A require to give? (22.) If, when income-tax is 5d. per £, a man's clear income is £470, what will it be when the tax is 6d. per £? (23.) A gentleman after paying 6d. per £ of income-tax has £444, 12s. left; what was his gross income? (24.) The poor's-rates on a rental of £450 are £6, 10s. ; what is the rental, of which the rates are £715 ? (25.) The rental of a parish is £45950, 10s. £ must be levied to realise £670, 2s. 2}d. ? (26.) A bankrupt can pay 15s. 3d. in the £, and his debts amount to £3645, 10s. What are his assets? (27.) A bankrupt's assets are £4412, 16s. 3d., and he owes £15690. What can he pay per £? per What sum (28.) A creditor receives a dividend of 13s. 6d. per £ on a debt of £780, and again a dividend of 2s. 6d. per £ on the deficiency. What was his loss? (29.) A person owes £3240, 15s., and his assets are £2160, 10s. What will be received on a debt of £18, 10s.? (30.) What is the interest on £650 at 5 per cent. ? From this example deduce a general rule for the following: (31.) Find the interest on £250, 10s. at 32%; £780, 15s. at 4%; £89, 16s. 7 d. at 33 %. (32.) If 23 yards cost £13, what will 45 yards cost? (33.) If £6 be paid for 14 yards, what will be the price of of a yard? (34.) If 6 tons of coal cost £43, what will be the price of of a ton? (35.) If £15 equal of a sailor's prize money, what will of it be? (36.) If 23 lbs. cost 3 s., what will 5 lbs. cost? (37.) If I pay 43s. for travelling 35 miles, what must I pay for travelling 94 miles? (38.) If 95s. be the price of 16 yards, what will be the price of of 24 yards? (39.) If 27 shares in a certain speculation cost £108, what is the price of 31 shares? (40.) If 28 men can do a piece of work in of a day, how many men will be required to do it in 13 days? COMPOUND RULE OF THREE. LVI. (1.) If it cost £75 to keep a family of 5 persons for 25 weeks, how much will it take to keep a family of 9 persons for 52 weeks? Ans. £280, 16s. (2.) If 27 men earn £150 in 5 weeks, in how many weeks will 36 men earn £200 ? (3.) If 9 men can mow 12 acres in 2 days, how many acres will 40 men mow in 21 days? (4.) If a ship's crew of 10 men use 6 bags of biscuits when the bag contains 120 biscuits, each weighing 2 ounces, in 12 days, how many bags of biscuits will a crew of 15 men consume during a voyage of 60 days, when each bag contains 200 biscuits, each weighing 3 ounces? (5.) If 15 cwt. be carried 70 miles for 7s., what should be charged for carrying 25 cwt. 130 miles? |