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Place the causes of the first set of quantities on one side of a vertical line, and the effects on the opposite side, and the causes and effects of the second set opposite to the corresponding quantities of the first, supplying the deficient term by a dash. Cancel the like factors on the opposite sides of the lines, and divide the product of the numbers opposite to the dash, by the product in which the dash is included. The quotient will be the term required.


12. How many men, in 6 months, will build a wall that 36 men will build in 8 months?

13. How many bushels of meal will serve 36 persons 12 months, if 10 persons consume 8 bushels in 2 months?

14. If 18 men build a cistern 20 feet long, 12 feet wide, and 10 feet high, in 3 weeks, by working 5 days in a week, and 9 hours a day, how many men, working 6 days in a week, and 12 hours a day, will build a cistern 32 feet long, 16 feet wide, and 15 feet high, in 12 weeks?

15. If $12.00 gain $3.00 in 5 months, how much ought $25.00 to gain in 10 months?

16. If the freight of 900lb. for 56 miles, is $2.50, how far may 2 tons be carried for $40.00?

17. If $1200 will support 24 persons 8 months, how long will $900 support 16 persons?


If $27 buy 4 yards of cloth that is tyd. wide, how many yards of like quality, that is yd. wide, may be bought for $13 ?

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Reducing the mixed numbers to improper fractions, we transpose the denominators, writing them above the causes, then cancel and divide as before.



$5 $5


$ $

Ans. 18-1yd.

18. If 571cwt. of sugar cost $375, what will 18/cwt.


19. If the rent of 19A. 3R. of land is £4 10s., what will be the rent of 24 A.?

20. The shadow of a stick that is 5 feet 6 inches high, measures 3ft. 4in. What is the height of tree whose shadow measures 75 feet at the same time?

21. If the expenses of a family of 8 persons are $40 in 10 weeks, how many persons can be supported 12 weeks for $100?

22. How much wheat, at $1.20 a bushel, must be given in exchange for 90 barrels of flour, at $4.75 per barrel?

23. If 10 compositors, in 4 days of 10 hours, set 663 pages of types, each page containing 45 lines of 50 letters, how many compositors will set 94 pages, each page containing 35 lines of 40 letters, in 5 days of 8 hours? 24. If 293 bushels of wheat yield 1760 bushels in 5 years, how much will 151⁄2 bushels yield in 6 years?

25. A crew of 150 men were supplied with provisions for 9 months, allowing each man 2 pounds per day. When they have been out half the time, they find it will require 6 months to finish their voyage. How much may be allowed to each man, 25 of the crew having been lost?


A French merchant wishes to pay in London a bill of £1500. How many francs must he pay to procure remittances through Russia, Hamburg and Spain, allowing £13=75 roubles, 5 roubles=9 mares of Hamburg; 3 marcs=1 Spanish dollar; and 9 dollars 50 francs?

Merchants often find an advantage in remitting bills circuitously, rather than directly to the place where they are due. The solution of such questions as the above, is called ARBITRATION OF EXCHANGE, and is best determined by THE CHAIN RULE, which is essentially the same as the Rule of Proportion.

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We write the quantities which are equivalent to each other, as antecedent and consequent, or as cause and effect, making each effect of the same denomination with the next cause. The like factors on opposite sides are cancelled, and the products divided as in proportion, to obtain the answer.

The question may be otherwise stated in the following manner: If £13 produce 75 roubles, 5 roubles produce 9 marcs, 3 marcs produce $1.00, and $9.00 produce 50 francs, how many francs will £1500 produce? The second set, or set of demand, contains but a single cause and effect. The first, or given set, contains a number of causes and effects, but they are so connected, that all the terms may be multiplied together, as a single compound term. Thus, if £13 produce 75 roubles, and 5 roubles produce 9 marcs, £13 will produce 5 of 9 marcs, and £13×5 will produce 75×9 marcs. In the same way it may be shown that £13×5×3=$75× 9 × 1, and £13×5×3×9=75×9×1×50 francs. Then, how many francs will £1500 produce?

£13 | 1500£

rou. 5 mar. 3




75 rou.

9 mar.

1 $ 50 fr.

26. A London merchant wishing to pay 1000 milrees in Lisbon, remits as follows: to Amsterdam at 36 schillings 7 groats per £; thence to Cadiz, at 17 groats for 2 rials of plate; thence to Leghorn, at 17 pezze for 100 rials ; thence to Lisbon, at 1497 rees for 2 pezze. How many pounds did he remit?

27. If a merchant of New York remits $5000 to Havre, at 5fr. 35c. for $1.00; thence to London, at 49fr. for £2; thence to Hamburg, at 1 marc for 1s. 6d. ; and thence to St. Petersburg, at 8 roubles for 17 marcs, how many roubles can he pay with his remittance?

28. If 33 copecks are equal to 5 English pence, 11 English pence are equal to 3 piasters, 13 piasters are equal to 1 florin, and 5 florins are equal to 29 francs, how many francs are equal to 9000 copecks?

29. If a man receives $30 for building 8 rods of wall, and he can purchase 3 barrels of flour for $14, and 3cwt. of sugar for 4 barrels of flour, and 21lb. of tea for 2cwt. of sugar, how many pounds of tea could he purchase by building 17 rods of wall?

30. If $1000 gain $111 in 80 days, how much will $2500 gain in 120 days, at the same rate?

31. If 13 days' work will purchase 1 hogshead of molasses, and 2 hogsheads of molasses are worth 5 tons of hay, and 3 tons of hay are worth 4 bags of coffee, how many bags of coffee can be bought with 39 days' labour?

32. If a man, by walking 3 miles an hour, for 6 hours a day, can accomplish a journey in 12 days, in how many days would a man walk the same distance, at the rate of 2 miles an hour, for 9 hours a day?

33. If 42 bushels of corn, that weighs 514 pounds a bushel, can be bought with 23 bushels of wheat, that weighs 56 pounds a bushel, how much corn, weighing 60 pounds a bushel, would be equivalent to 100 bushels of wheat that weighs 54 pounds a bushel ?

34. If a man travels 240 miles in 8 days, when the days are 12 hours long, how many miles will he travel in 24 days, when the days are 16 hours long?

35. If the freight of 2T. 6cwt. for 28 miles, is $14.50, what will be the freight of 9T. 4cwt. for 96 miles?

36. If 4 men in 3 days of 8 hours, build 40 rods of wall, how many rods will 18 men build in 5 days of 9 hours?

37. If I pay $9.75 for carrying 23 tons 37 miles, how much ought I to pay for carrying 7T. 3cwt. 2qr., 45 miles.

38. How many men, in 24 days of 16 hours, will do three times as much work as 18 men can perform in 36 days of 12 hours?

39. If $495 will support a family of 7 persons, 11 months and 6 days, how much will maintain a family of 9 persons, for 13 months and 10 days?

40. How many persons may be supported a year, with $1014, if $140.25 will support 11 persons 8 weeks? ·

41. If $973.16 yields an interest of $91.25 in 13 months, what will be the interest of $2801 for 173 months, at the same rate?

42. If 3 tons are carried 87 miles for $151, how far may 23 tons be carried for $27.75 ?

43. If 11 men reap 16 acres of grain in 3 days, how many acres can 7 men reap in 15 days?

44. If 14 men, in 5 days, by working 8 hours a day, reap 38 acres of grain, how many men will reap 37 acres in 63 days, by working 9 hours a day?

45. If 12 men dig a trench 124yd. long, 4ft. wide, and


2ft. deep, in 6 days, by working 10 hours a day, how long a trench that is 7ft. wide, and 4ft. deep, will 45 men dig in 21 days, working 7 hours a day?

46. If 14 yards of cloth, that is yd. wide, cost $29. 50, what should be the price of 21 yds. of similar quality, that is lyd. wide?

47. If 300 tiles that are 9in. long and 6in. wide, will pave a court-yard, how many tiles would be required that are 6in. long and 4in. wide?

48. What is the weight of 16 iron bars, each 7ft. long, ɓin. wide, and 3 in. thick, if a bar 2ft. long, 2in. wide, and lin. thick, weighs 18 pounds?

49. How many men will build a wall 240yd. long, 6ft. high, and 3ft. thick, in 8 days of 9 hours, if 7 men can build a wall 40yd. long, 4ft. high, and 2ft. thick, in 32 days of 7 hours?

50. If 70 braces of Venice are equal to 75 braces of Leghorn, and 7 braces of Leghorn are equal to 4 yards, how many yards are there in 79.375 braces of Venice?

51. A merchant in New York orders £500 sterling, due him in London, to be sent by the following circuit: to Hamburg, at 15 marcs banco per £; thence to Copenhagen, at 100 marcs banco for 33 rix-dollars; thence to Bourdeaux, at 3 rix-dollars for 18 francs; thence to Lisbon, at 125 francs for 18 milrees; and thence to New York, at $1.25 per milree. What was the arbitrated value of a dollar by this remittance?

52. If the freight of 11 boxes of sugar, each weighing 7cwt. 3qr. 11lb., is $37.50 for 90 miles, what must be paid for the freight of 34 boxes, each weighing 818cwt., for 75 miles?

53. How much wheat, that weighs 607b. per bushel, would be required to supply a garrison of 1400 men 9 months, if 2800 bushels, weighing 581b. per bushel, supply 800 men 3 months?

54. How many hours a day must 15 men work, to dig a trench 400ft. long, 6ft. wide, and 3ft. deep, in 187 days, if 72 men can dig a trench 250ft. long, 8ft. wide, and 4ft. deep, in 314 days, by working 7 hours a day?

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