PARTNERSHIP

ORAL EXERCISES.

775. 1. If John has 10 marbles, William 15 marbles, and Charles 25 marbles, what part of the whole has each ?

2. Two men bought a barrel of flour for $9, the first paying $4 and the second $5. What part of the flour belongs to each?

3. Three men bought 108 sheep, and as often as the first paid $3, the second paid $4, and the third $5. How many sheep should each receive?

4. If $45 be divided between two persons, so that of every $5, one receives $2, and the other $3, how many dollars does each receive?

5. Two men hired a pasture for $36; one put in 2 horses for 3 weeks, the other 3 horses for 4 weeks. What should each pay?

DEFINITIONS.

776. Partnership is the association of two or more persons under a certain name, for the transaction of business with an agreement to share the gains and losses.

777. A Firm, Company or House is any particular partnership association.

778. The Capital is the money or property invested by the partners, called also Investment, or Joint-Stock.

779. The Resources of a firm are the amounts due it, together with the property of all kinds belonging to it; called also Assets, or Effects.

780. The Liabilities of a firm are its debts.

781. The Net Capital is the excess of resources over liabilities.

WRITTEN EXERCISES.

782. To apportion gains or losses according to capital invested.

1. A and B engage in trade; A furnishes $400 capital, B $600. They gain $250; what is the profit of each ? 1ST OPERATION. (By Fractions.)

$1000 (whole cap.): $400 (A.'s inv.): : $250 (whole gain): A.'s share. $1000 (whole cap.): $600 (B.'s inv.) : : $250 (whole gain) : B.'s share.

3D OPERATION. (By Percentage.)

$250 gain is 250

=

1000

25% of the whole capital.

$400 × .25 $100, A.'s gain; $600 × .25 = $150, B.'s gain.

ANALYSIS.—(1st Method.) Since $400, A.'s investment, is 4000 or, of the whole capital, he is entitled to of the gain, or $100; and B is entitled to of the gain, or $150.

2d Method. The ratio of $1000, the whole capital, to $400, A.'s investment, is equal to the ratio of $250, the whole gain, to A.'s share of the gain. Hence the proportions, etc.

3d Method. Since the gain is 25% of the whole capital, each partner is entitled to 25% of his investment as his share of the gain. The third method (by dividend) is that generally adopted by jointstock companies having numerous shareholders.

2. At the end of the year, Norton, Smith & Co. take an account of stock, and find the amount of merchandise, as per inventory, to be $8400; cash on hand, $4850; due from sundry persons, $5273. Their debts are found to amount to $4223. S. Norton's investment in the business is $5000; R. Smith's, $4000; and C. Woodward's, $2000. Make a statement showing the resources, liabilities, net capital, and net gain; and find each partner's share of the gain.

PROOF.-$1500+ $1200+ $600 $3300, total gain.

=

RULE 1. Find what fractional part each partner's investment is of the whole capital, and take such part of the whole gain or loss for his share of the gain or loss. Or,

2. State by proportion, as the whole capital is to each partner's investment, respectively, so is the whole gain or loss to each partner's share of the gain or loss. Or,

3. Find what per cent. the gain or loss is of the whole capital, and take that per cent. of each partner's investment for his share of the gain or loss, respectively.

3. A furnishes $4000, B, $2700, and C, $2300, to purchase a house, which they rent for $720. What is each one's share of the rent?

4. Four persons rent a farm of 230 A. 64 P. at $71 an acre. A puts in 288 sheep, B, 320 sheep, C, 384 sheep, and D, 648 sheep; what rent ought each to pay?

5. Prime & Co. fail in business; their liabilities amount to $22000; their available resources to $8800. They owe A $4275, and B $2175.50: what will each of these creditors receive?

6. Four persons engage in manufacturing, and invest jointly $22500. At the expiration of a certain time, A's share of the gain is $2000, B's $2800.75, C's $1685.25, and D's $1014. How much capital did each put in? 7. An estate worth $10927.60 is divided between two heirs so that one receives more than the other. does each receive ?

What

8. Three persons engage in the lumber trade with a joint capital of $37680. A puts in $6 as often as B puts in $10, and as often as C puts in $14. Their annual gain is equal to C's stock. What is each partner's gain?

9. Ames, Lyon & Co. close business in the following condition: notes due the firm to the amount of $24843.75, cash in hand, $42375.80, due on account, $26500, merchandise per inventory, $175840. Notes against the

firm, $14058.75, due from the firm on account, $12375.80. Ames invested $60000, Lyon, $40000, and Clark $25000. Make a statement showing the total amount of resources, liabilities, investments, net capital, net gain, and each partner's share of the gain.

783. To apportion gains or losses according to amount of capital invested, and time it is employed.

1. Three partners, A, B, and C, furnish capital as follows: A, $500 for 2 mo.; B, $400 for 3 mo.; C, $200 for 4 mo. They gain $600; what is each partner's share?

ANALYSIS.-The use of $500 for 2 mo. is the same as the use of $1000 for 1 mo. ; the use of $400 for 3 mo. is the same as that of $1200 for 1 mo. ; and the use of $200 for 4 mo. is the same as that of $800 for 1 mo. Therefore the whole capital is the use of $3000 for 1 mo. ; and as A's investment is $1000 for 1 mo., it is of the capital, and hence he should receive } of the gain, or $200. For the same reason, B should receive, and C of the gain, or $240 and $160, respectively.

The other methods of operation may be applied by considering the products of investment and time as shares of the capital. Thus, $600 is 20% of $3000; and 20% of $1000, $1200, and $800 will give $200, $240, and $160, respectively, the shares of gain required.