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369. To find each partner's share of the gain or loss, when the stock of each is employed for the same time.

Make each man's stock the numerator, and the whole stock the denominator of a common fraction; multiply the gain or loss by the fraction which expresses each man's share of the stock, and the product will be his share of the gain or loss.

Or, multiply each man's stock by the whole gain or loss; divide the product by the whole stock, and the quotient will be his share of the gain or loss.

PROOF. Add the several shares of the gain or loss together, and if the sum is equal to the whole gain or loss, the work is right. (Art. 284. Ax. 10.).

OBS. 1. This rule is applicable to questions in Bankruptcy, General Average, and all others in which there is to be a division of property in specified proportions.

But since

2. The preceding case is often called Single Fellowship. a partnership is always composed of two or more individuals, it is somewhat difficult to see the propriety of calling it single.

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2. A, B, and C entered into partnership; A put in of the capital, B, and C 10; they gain $4800: what was each man's share of the gain?

3. A, B, and C form a partnership; A furnishes $600, B $800, and C $1000; they gain $480: what is each man's share of the gain?

4. A Bankrupt owes A $1200, B $2300, C $3400, and D $4500; his whole effects are worth $5600: how much will each creditor receive?

5. A, B, C, and D make up a purse to buy lottery tickets; A puts in $30, B $40, C $60, and D $70; they draw a a prize of $2000: what is each man's share?

6. A, B, and C freight a vessel with a cargo worth $30000; of which A owned $8000, B $10000, and C $12000; in a gale the master throws of the cargo overboard: what was each man's loss?

QUEST.-269. How is each man's share of the gain hwen the stock of each is employed for the same time? eration proved? Obs. To what is this rule applicable? times called?

or loss found, How is the opWhat is it some

CASE II.

7. A and B formed a copartnership; A put in $300, and B $200. At the end of 2 months A took out his stock, while B's was employed 6 months; they gained $150: what was each man's just share of the gain?

Note. It is obvious that the gain of each depends both upon the capital he furnished and the time it was employed. (Art. 364.)

Solution. Since A's capital $300 was employed 2mo., his share of the gain is the same as if he had put in $600 for 1mo.; (Art. 365;) for $300×2=$600. Also, B's capital $200 being employed 6 mo., his share of the gain is the same as if he had put in $1200 for 1 mo.; for $200 x6 $1200. The sum of $600 and $1200 is $1800. A's share of the gain must therefore be

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And $150x=$100, B's share. Hence,

370. To find each partner's share of the gain or loss, when the stock of each is employed for different periods.

Multiply each partner's stock by the time it is employed; make each man's product the numerator, and the sum of the products the denominator of a common fraction; multiply the whole gain or loss by each man's fractional share of the stock, and the product will be his share of the gain or loss.

OBS. This Case is often called Compound, or Double Fellowship.

8. A, B, and C enter into business together; A puts in $500 for 4 months, B $400 for 6 months, and C $800 for 3 months; they gain $340: what is each man's share of the gain?

9. A and B hire a pasture together for $60; A put in 120 sheep for 6 months; and B put in 180 sheep for 4 months what should each : pay? ?

QUEST.-370. When the stock of each partner is employed for different periods, how is each one's share found? Obs. What is this case sometimes called?

10. The firm A, B, and C lost $246; A had put in $85 for 8 mo., B $250 for 6 mo., and C $500 for 4 mo. : what is each man's share of the loss?

11. Three men hire a pasture for $75; A put in 8 cows for 5 mo., B 6 cows for 4 mo., and C 10 cows for 4 mo. how much should each pay?

12. A, B, C, and D form a partnership; A advances $2000 for 8 mo., B $2500 for 6 mo., C $3000 for 5 mo., and D $3500 for 4 mo. ; they gain $1800: what is each man's share?

EXCHANGE OF CURRENCIES.

371. The term currency signifies money or the circulating medium of trade.

372. The intrinsic value of the coins of different nations depends upon their weight and the purity of the metal of which they are made. (Art. 203. Obs. 1.)

Note.-1. The standard gold coins of Great Britain are 22 parts of pure gold and 2 parts of copper, i. e. 22 carats fine. The standard silver coins 37 parts of pure silver and 3 parts of copper. A Pound Sterling or Sovereign weighs 123.274 grs., and a shilling, (silver,) 3 pwts. 15

grs.*

2 The present standard for both gold and silver coins of the United States, by Act of Congress, 1837, is 900 parts of pure metal by weight to 100 parts of alloy. The alloy of gold coin is composed of silver and copper, the silver not to exceed the copper in weight. The alloy of silver coin is pure copper.

The present legal weight of the eagle is 258 grs. standard gold; that of the dollar 412 grs. of standard silver; that of the cent 168 grs. of pure copper. For their original standard weight and purity by Act of Congress, 1792, see Art. 203.

373. The relative value of foreign coins is determined by the laws of the country. Thus by Act of Congress, 1842,

QUEST.-371. What is currency? 372. On what does the intrinsic value of the coins of different countries depend? 373. How is the relative value of foreign coins determined? What is the value of a Pound Sterling? Of a guinea? A franc? Five-franc piece? A doubloon? *Hind's Arithmetic,

378. Hence, to reduce Federal money to either of the State currencies.

Multiply the given sum by that fraction of a pound, which is equal to $1 in the required currency; the product will be the answer in pounds and decimals of a pound. The decimals should be reduced to shillings, &c. (Art. 201.) 12. Reduce $378 to New England currency. 13. Reduce $465.45 to New York currency. 14. Reduce $640 to Pennsylvania currency. 15. Reduce $1000 to Canada currency.

16. Reduce £15, 7s. 6d., N. E. currency,,to Federal money.

Solution. £15, 7s. 6d. £15.375. (Art. 200.) Now, since £3make $1, N. E. cur., £15.375 will make as many dollars as is contained times in 15.375; and 15.375-51.25. Ans. $51.25.

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The other State currencies may be reduced to Federal money in a similar manner. Hence,

379. To reduce the State currencies to Federal money.

Set down the pounds as whole numbers, and reduce the shillings, pence, and farthings, to the decimal of a pound; (Art. 200;) then divide the sum by that fraction of a pound, which in the given currency is equal to $1; the quo

tient will be the answer in dollars and cents.

17. Reduce £48, 15s., N. E. cur., to Federal money. 18. Reduce £73, 4s., N. E. cur., to Federal money. 19. Reduce £100, 18s., N. Y. cur., to Federal money. 20. Reduce £256, 5s., N. Y. cur., to Federal money. 21. Reduce £296, 12s., Penn. cur., to Federal money. 22. Reduce £430, 8s., Penn. cur., to Federal money. 23. Reduce £568, 10s., Ga. cur., to Federal money. 24. Reduce £1000,15s., Canada cur., to Federal money.

QUEST.-378. How is Federal money reduced to the State currencies ? 379. How are the several State currencies reduced to Federal money?

3. What is the value of £100 in Federal money? 4. What is the value of £275, 15s. in Federal money? 5. What is the value of £450, 7s. 6d. in Federal money?

6. What is the value of £900, 2s. 6d. in Federal money?

7. Change $27.467 to Sterling money.

Solution. Since there is £1 in $4.84, in $27.467 there are as many pounds as $4.84 is contained times in it; and $27.4674.84-5.675; that is, £5.675. Reducing the decimal .675 to shillings and pence, (Art. 201,) we have £5, 13s. 6d. for the answer. Hence,

376. To reduce Federal to Sterling money. Divide the given sum by $4.84. (the value of £1,) and point off the quotient as in division of decimals. (Art. 194.) The figures on the left of the decimal point will be. pounds; those on the right, decimals of a pound, which must be reduced to shillings, pence, and farthings. (Art. 201.)

8. Change $486.42 to Sterling money. 9. Change $1452 to Sterling money. 10. Change $4840 to Sterling money.

877. Previous to the adoption of Federal money in 1786, accounts in the United States were kept in pounds, shillings, pence, and farthings. At the time of its adoption, different States assigned to the dollar different values in their own currency. Its value was fixed

In the N. E. States, Va., Ky., and Tenn., at 6s. or £1. In New York, North Carolina, and Ohio, at 8s. or £. In New Jersey, Penn., Del. and Md., at 7s. 6d. or £. In South Carolina and Georgia, at 4s. 8d. or £%•

In Canada and Nova Scotia,

11. Reduce $45 to New England currency.

Solution. $45x=13.5.

(Art. 201.) Hence,

at 5s.

or £1.

Ans. £13.5; or £13, 10s.

QUEST.-376. How is Federal money reduce d to Sterling? 377. Previous to the adoption of Federal money, in what were accounts kept?

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