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5. If a man travels 145 miles in 5 days, when he travels 12 hours a day, how many days will it take him to travel 435 miles, if he travels only 6 hours a day?

6. If a bin that is 9 feet long, 6 feet wide, and 9 feet deep, holds 320 bushels of wheat, how many bushels will a bin hold that is 15 feet long, 8 feet wide, and 12 feet deep?

7. If 18 men, working 10 hours, finish a task in one day, how many days will it require for 10 men to do the same work, by working 9 hours a day?

8. If 32 men have enough provisions to last them 40 days, how long will twice the quantity last 75 men?

9. If a regiment of 1,000 soldiers consume 10,400 pounds of bread in 16 days, how many pounds will 5 regiments of the same size consume in 10 days?

10. If a five-cent loaf of bread weigh 12 ounces, when flour is $8 a barrel, how much should a three-cent loaf weigh when flour is $9 a barrel ?

11. If 10 yards of muslin, 1 yards wide, cost $1.30, what is the cost of 12 yards of the same quality 1 yards wide?

12. If 24 men can build 40 rods of wall in 16 days, in what time can they build, 64 rods, if 10 men quit work when 20 rods are finished ?

13. If 8 horses eat 42 bundles of hay in 30 days, how many bundles will 16 horses eat in 28 days?

14. If it takes 3 men 24 days to lay a pavement 40 feet long and 3 yards wide, how long will it take 5 men to lay a pavement 50 feet long and 2 feet wide ?

15. If 24 men, working 10 hours a day, build a wall 180 feet long, 2 feet wide and 8 feet high, how many men, working 12 hours a day, will it take to build a wall 144 feet long, 1 foot wide and 8 feet high in the same time?

16. If 10 men excavate a cellar 12 feet long, 10 feet

wide and 5 feet deep, in 3 days, how many men will be required to excavate a cellar 18 feet long, 12 feet wide and 5 feet deep in 2 days?

17. If a bicyclist rides 360 miles in 4 days of 9 hours each, how many miles will he ride in 6 days of 8 hours each ?

18. If a man walk 84 miles in 4 days of 12 hours each, how many miles will he walk in 18 days of 10 hours each ?

19. If 6 men dig a ditch in 12 days of 10 hours each, in how many days of 9 hours each will 8 men perform the same work?

20. If 6 acres will pasture 8 cows for 21 days, how long will 9 acres pasture 12 cows?

21. If 2,000 bricks, each 8 inches long and 4 inches wide, will make a pavement, how many flags of stone, each 3 feet long and 1 foot 6 inches wide, will be required to make a pavement of the same dimensions?

22. If 3 men build a fence 40 rods long and 4 rails high in 2 days, working 8 hours a day, how long will it take 4 men to build a fence 50 rods long, 5 rails high, working 10 hours a day.

23. A contracted to build a wall 500 feet in length in 20 days; 20 men built 300 feet in 15 days: how many additional men must be employed to complete the wall in the required time?

24. If 24 men, working 9 hours a day, build a stone wall 33 yards long, 2 feet wide and 6 feet high, in 8 days, how many men, working 12 hours a day, can build a wall 2 rods long, 1 feet wide and 8 feet high, in 6 days?

25. Illustrate by an original problem the method of solving questions in Compound Proportion.

Partnership.

ART. 419.-Partnership is the association of two or more persons with a joint capital, for the transaction of business.

ART. 420.-The Capital consists of the money or property invested by the partners, and constitutes the Interest or Joint Stock.

ART. 421.-The Resources or Assets of a firm are the property which it owns, and the debts due it.

ART. 422.-The Liabilities of a firm are its debts.

ART. 423.-The Net Capital is the excess of the resources over the liabilities.

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1. A, B and C engaged in business with a capital of $12,000, of which A invested $3,000, B $5,000, and C $4,000. At the end of a year they had gained $3,000: how should it be divided among them?

Process.

A invested 3000, or of the capital, and was therefore entitled to of $3,000 = $750.

B invested, or of the capital, and was therefore entitled to of $3,000 = $1,250.

C invested 4000

120009

or of the capital, and was there

fore entitled to of $3,000 = $1,000.

2. Suppose A put in $3,000, and at the end of 6 months added $1,000 to his investment; B put in $5,000, and at the end of a year withdrew $1,000; C put in $4,000, and at the end of a year and 4 months withdrew $500. At the close of two years they had gained $5,800: how should the gain be apportioned among the partners?

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gained $5,800; or $1 for 1 mo. gained 5888 = $.02.

5800 290000

$.02 × 90,000 = $1,800, A's share of the gain.
$.02 × 108,000

=

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2,160, B's

66

66

66

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Analysis. In problem 1, the capital of each partner was invested for the same time. The division of profits or losses, therefore, is based simply on the amount of each one's capital.

In problem 2, the investments are for different times. A's $3,000 for 6 months should earn the same as $18,000 for 1 month, and his $4,000 for 18 months is the same as $72,000 for 1 month. Hence, A's investment is equivalent to $90,000 for 1 month.

In like manner, B's capital is equivalent to an investment of $108,000 for one month, and C's to an investment of $92,000 for

1 month.

The investments being now reduced to investments for the same time, that is, for 1 month, the gain is divided as in problem 1.

ART. 424.-Rule for Partnership.-Distribute the gains or losses in proportion to the amount of each one's capital, multiplied by the time it was invested.

3. A, B, C and D form a partnership, A contributing $3,000; B $2,500; C $3,500; D $1,000. At the end of a year they had lost $3,000: how should it be apportioned?

4. A, B and C associated themselves in business. A invested $4,000; B, $6,000 and C was allowed a fifth interest for managing the business. The year's balance sheet showed they had gained $2,500: what was each one's share?

5. Messrs. Brown, Jones and Robinson formed a partnership in the wholesale grocery business. Brown put in $3,000 and added $1,500 more at the end of the first year; Jones put in $5,000 and at the end of 8 months withdrew $1,000; Robinson invested $4,000 and at the end of a-year-and-a-half withdrew $800. At the close of two years they found they had gained $8,556: how should it be apportioned ?

5. A man failing in business owed C $1,500, D $1,800, and E $2,000; his assets were $2,650: how much did each receive?

7. A and B hired a pasture together, for $40; A put in 20 cattle for 3 months, and B 30 cattle for 4 months: what should each pay?

8. Button Brothers find themselves obliged to sus.. pend with liabilities amounting to $25,000, while their resources foot up only $15,000. They owe A $4,000, B $3,000, C $6,400, D $6,500: what did each creditor receive?

9. A, B and C went into the coal business, A investing $6,000, B $5,000 and C $4,000. At the close of the year they sold out for $13,365 cash: what was each one's share?

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