entire stock, will give the gain or loss on each dollar of stock; and each partner's stock, multiplied by the number denoting the gain or loss on $1, will give his share of the entire gain or loss. Or,

As the whole stock is to each partner's stock, so is the whole gain or loss to each partner's gain or loss.

EXAMPLES.

2. Jones, Weston, and Sprague traded in company, with a capital of $10000; Jones put in $ 3000, Weston $ 2000, and Sprague $5000; they gained $4000. What was each man's part of the gain?

Ans. Jones's part, $1200; Weston's part, $ 800; Sprague's part, $2000.

3. Two merchants, C and D, engaged in trade; C put in $6780, and D put in $12000; they gain $2000. What was each man's part?

Ans. C's part, 722.044; D's part, $ 1277.956. 4. Harvey, Blake, and Horsford entered into partnership with a capital of $11000, of which Harvey put in $2500, Blake $3000, and Horsford $ 5500; they lost by trading 5 per cent. on their capital. What was each partner's share of the loss?

5. Elliott, Mayhew, and Griswold engaged together in a speculation. Of the money employed Elliott furnished $ 500; Mayhew $350, and Griswold a cart and two horses; they gained $332.50, of which Griswold's part was $120. What were Elliott's and Mayhew's parts of the gain, and what was the value of Griswold's part of the stock?

Ans. Elliott's gain, $125; Mayhew's gain, $87.50; Griswold's stock, $ 480. ぜ

6. A, B, and C traded in company; A put in $ 5000, B put in $6500, and C put in $7500; they gain 40 per cent. on their capital, but receive the whole amount of their gains in bills, for which they are obliged to allow a discount of 10 per cent. How much was each man's net gain?

Ans. A's gain, $ 1800; B's gain, $ 2340; C's gain, $ 2700. 7. A, B, C, and D are in partnership, with a joint capital of $40,000; on dividing their profits, it is found that A's share is $2000, B's share $4500, C's share $2500, and D's share $1500. What was each partner's stock?

8. A, B, and C were associated in trade; A's part of the general stock was $2000, B's part $ 3000, and C's part $7500. On dividing the profits, it was found that A's and B's gain together amounted to $1000, which was $500 less than C's gain. What was the gain of each?

Ans. A's gain, $ 400; B's gain, $ 600; C's gain, $ 1500. 9. A, B, and C own a ship together, which cost them $30000; of which A paid an unknown sum, B paid 14 as much, and C paid 14 as much. The profits were 25 per cent. of the cost of the ship. What was each man's gain?

Ans. A's gain, $ 2000; B's gain, $3000; C's gain, $2500. 10. Walker, Edwards, and Armstrong are partners, whose respective shares of joint stock are as the fractions 3, 1, and 1. They gain $50000. If, on dividing the profits, Armstrong re linquishes his part of the gain, how much will each of the others receive?

Ans. Walker, $ 28571.42; Edwards, $ 21428.574. 418. To find each partner's share of the profit or loss, when the stock is employed for different periods of time.

Ex. 1. A and B are associated in trade. A has furnished of the joint stock $420 for 5 months, and B has furnished $350 for 8 months; their net profits are $84. What is each man's share of the gain? Ans. A's share, $36; B's, $48.

=

OPERATION.

=

$420 × 5 $2100 $2100 x .01 $36, A's gain. X

$350 X 8 = $2800 $2800 × .01

$4900

=

$48, B's gain.

Proof, $84, entire “

It is evident that $420 for 5 months is the same as $420 X 5 $2100 for 1 month, since $2100 would gain as much in 1 month as $420 in 5 months; and $ 350 for 8 months is the same as $ 350 × 8 $2800, for 1 month. The question then is the same as if A had furnished $2100 and B $ 2800 for equal times. Then, if $ 2100+ $2800 $4900, gain $ 84, $ 1 will gain of $84 - $ 0.015, $36, A's gain; $ 2800 x .01 = gain. The same results may be obtained, as follows,

=

and $2100 X .01

=

BY PROPORTION.

=

=

$4900 $2100::$84: $36, A's gain.

$4900 $2800

:

$84: $48, B's gain.

$48, B's

Proof, $84, entire gain.

RULE. Multiply each partner's stock by the time it was in trade, and divide the entire gain or loss by the sum of the several products; by the quotient multiply the product of each partner's stock and time, and the result will be his share of the gain or loss. Or,

Multiply each partner's stock by the time it was in trade; then, as the sum of these products is to each product, so is the whole gain or loss to each partner's gain or loss.

EXAMPLES.

2. Goodwin commenced business January 1, with a capital of $3200; May 1, he took Blunt into partnership, with a capital of $4200`; and at the end of the year they had gained $240. What was each partner's share of the gain?

Ans. Goodwin's gain, $ 128; Blunt's gain, $112.

3. Three men hire a pasture in common, for which they are to pay $26.40. A put in 24 oxen for 8 weeks, B put in 18 oxen for 12 weeks, and C put in 12 oxen for 10 weeks. What ought each to pay?

4. Barclay, Hickman, and Oliver are partners. Barclay furnishes of the capital $300 for 5 months, Hickman $ 400 for 8 months, and Oliver $500 for 3 months; they gain $200. After paying $50 for advertising and $50 for agency, what will be each partner's share of the net profits?

Ans. Barclay's share, $24.1911; Hickman's, $51.61; Oliver's, $ 24.191.

5. A, B, and C engaged in partnership, with a joint capital of $1000, A putting in stock for 7 months, B for 8 months, and C for 12 months. Of the profits A's part was $ 21; B's, $ 40; and C's, $24. Required the capital each put in.

་

Ans. A, $300; B, $500; C, $ 200.

6. White and Daniels traded in company, with a joint stock of $6300. White's money having been employed 12 months, and Daniel's 8 months, on dividing profits, each had gained exactly the same sum. How much of the capital did each furnish?

7. Three men engage in partnership for 20 months. A at first put into the firm $4000, at the end of four months he put in $500 more, and at the end of 16 months he took out $1000; B at first put in $3000, at the end of 10 months he took out $1500, and at the end of 14 months he put in

$3000; C at first put in $ 2000, at the end of 6 months he put in $ 2000 more, at the end of 14 months he put in $2000 more, and at the end of 16 months he took out $1500; they had gained by trade $ 4420. What is each man's share of the gain?

Ans. A's gain, $1680; B's gain, $ 1260; C's gain, $1480. 8. Grover and Thorndike are associated in trade, Grover contributing of the capital $12000, and Thorndike $18000. At the end of 6 months they reduce the joint stock $ 5000, by each withdrawing an equal sum. 3 months afterwards Thorndike withdraws $6000, and Grover $1000. The business proving a losing one, they dissolve copartnership at the end of the year. Required what part of the stock then remaining, which was only $15000, belonged to each of the partners?

Ans. To Grover, $7276.69; Thorndike, $7723.30-10. 9. John Jones, Samuel Eaton, and Joseph Brown formed a partnership, under the firm of Jones, Eaton, & Co., with a capital of $10,000; of which Jones put in $4000, Eaton put in $3500, and Brown put in $ 2500; but at the end of 6 months Jones withdrew $2000 of his stock, and at the end of 8 months Eaton withdrew $1500 from the firm; but at the end of 10 months Brown added $2000 to his stock. At the end of 2 years they found their gains to be $1041.80. What was the share of each man?

Ans. Jones's gain, $ 300.5143; Eaton's gain, $300.511; Brown's gain, $440.76.

10. James Bradshaw commenced trade, January 1, 1856, with a capital of $10000, and after some time formed a partnership with John Parkman, who contributed to the joint stock $ 2800. In course of time they admitted into the firm Joseph Delano, with a stock of $3600. On making a settlement, January 1, 1857, it was found that Bradshaw had gained $2250; Parkman, $ 420; and Delano, $405. How long had Parkman's and Delano's money been employed in trade, and what rate of interest per annum had each of the partners gained on their stock?

Ans. Parkman's, 8 months; Delano's, 6 months. Gained 22 per cent. interest.

BANKRUPTCY.

419. BANKRUPTCY refers to business failures and inability to meet pecuniary liabilities.

A bankrupt, or insolvent, is one who fails or becomes unable to pay his debts.

An assignee is a person selected to take charge of the property and effects of a bankrupt, to convert the same into cash, and, after deducting the necessary expenses of settling, to divide the net proceeds, as the law requires, among the creditors. The distribution is generally made pro rata, each creditor receiving according to his respective demand, or just claim.

420. To find each creditor's dividend or share of the net proceeds of an insolvent estate.

Ex. 1. A bankrupt owes to A $500, to B $1200, and to C $ 4300; and the net cash proceeds of his estate amount to only $1500. How much does he pay on $ 1, and what dividend does each creditor receive?

Ans. 25 cents on a dollar. A receives $125; B, $ 300;

RULE.

= $1075, C's share.

Proof, $1500, entire proc❜ds.

$ 0.25, or 25 cents on $1.

·Divide the net proceeds of the insolvent estate by the number denoting the total amount of its indebtedness, to find the sum it pays on each dollar of the debts.

Multiply each man's claim by the sum the estate pays on a dollar, to

obtain each man's dividend.

EXAMPLES.

2. Clarke, Soule, & Co. have failed. Their liabilities are $63500, their assets have a cash value of $52384, and the expenses of settling are $1584. How much can they pay on a dollar, and what dividend should John Dayton receive, whose claim is $8361.55? Ans. 80 cents on a dollar; $6689.24.