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5. A broker charges me 11 per cent. brokerage for purchasing some uncurrent bank-bilis at 20 per cent. discount Of these bills four of $ 50 each become worthless, but the remainder I dispose of at par, and thus make by the operation $ 364. What was the amount of the bills ?

Ans. $ 3000. # 6. A commission merchant sold a consignment of cotton for $ 5640, and after deducting his commission, and $ 76.50 for freight, storage, &c., remitted to his consignor $ 5422.50 as the net proceeds. What per cent. was his commission ?

Ans. 21 per cent. 7. A horse which I bought for 30 per cent. less than his real worth, having become injured, I sold him for 25 per cent. less than what he cost, and thereby lost $ 55 of his original value. What did I get for the horse ?

Ans. $ 60.7815. 8. A watch, which cost me $30, I have sold for $ 35, on a credit of 8 months. What did I gain by the bargain?

Ans. $ 3.65311 9. Bought a hogshead of molasses for $ 112; but 15 gallons having leaked out, the remainder was sold at $ 2.2163 a gallon. What per cent. is the loss?

Ans. 5 per cent. 10. A hogshead of molasses was bought for a certain sum ; but 15 gallons having leaked out, the remainder was sold at $ 2.216 a gallon, and thereby the loss was 5 per cent. on the cost. What was the cost ?

Ans. $ 112. 11. Bought 50 barrels of flour at $ 9.00 per barrel, but a part of it baving been damaged, half of it was sold at a loss of 10 per cent., and the remainder at $ 9.50 per barrel. How much was lost by the operation ?

Ans. $ 10. 12. My agent purchases flour for me, which, with his commission at 24 per cent., cost $ 6135, and I dispose of it at 20 per cent. advance upon the price he paid. What did I make by the operation, allowing freight and storage to have been $ 31.63 ?

13. I have remitted to my correspondent a certain sum of money, which he invested in iron; and having reserved to himself 24 per cent. on the purchase, which amounted to $ 90, he purchased the iron at $ 95 per ton. Required the sum re. mitted, and the quantity of iron purchased.

Ans.

Sum remitted, .
Iron purchased, 37T. 17cwt. 3qr. 14 lb.

{, . . .

PARTNERSHIP, OR COMPANY BUSINESS.

416. PARTNERSHIP is the association of two or more persons in business, with an agreement to share the profits and losses in proportion to the amount of the capital stock, or the value of the labor and experience of each.

Partners are the persons associated in business.

Company, or Firm, is the general name of the business asso ciation.

Capital, or Joint Stock, is the money or property invested in the company or firm.

Dividend is the profit or loss on the shares of the capital, or joint stock.

NOTE. — Partnership is an application of the principle of distributive or partitive proportion (Art. 339).

417. To find each partner's share of the profit or loss, when there is no regard to time.

Ex. 1. Three men, A, B, and C, enter into partnership for two years, with a capital of $ 1080. A puts in $ 240, B $ 360, and C $ 480. They gain $ 54. What is each man's part of the gain ?

OPERATION,

B's

66

A's stock, $ 2 40 $ 240 x .05 = $ 1 2, A's gain.

3 60 3 60 x .05 = 18, B's gain. C's

480 480 x .05 2 4, C's gain. Entire stock, $1080

Proof, $ 5 4, entire gain. $ 54.00 ; 1080 = $ 0.05, gain on $1. Since the entire stock is $ 1080 and the entire gain $ 54, the gain on every $ 1 of stocle will be as many dollars as 54 contains times 1080, or $ 0.05 on every $ 1 of stock. Then, each man's stock multiplied by .05 gives his part of the entire gain. The same result also may be obtained, as follows,

BY PROPORTION.

$1080: $ 240 :: $ 5 4: $ 1 2, A's gain.
$ 1080 : $360 :: $ 5 4:$ 18, B's gain.
$1080 : $ 480 :: $ 5 4: $ 2 4, C's gain.

Proof, $ 54, entire gain.
The entire gain or loss, divided by the number denoting the

RULE.

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.

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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 ; Gris

wold's stock, $ 480. 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 11 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 }, }, and }. 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, $ 28571.424 ; Edwards, $ 21428.577. 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 x 5 = $2100 $ 2100 X.01$= $36, A's gain. $ 3 5 0 X 8 $ 2800 $ 2 800 X .01$ $ 48, B’s gain. $ 4900

Proof, $ 84, entire 6 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 x 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 a dog of $ 84

$ 0.015, and $ 2100 x .01 $36, A's gain; $ 2800 x .01€ = $ 48, B's gain. The same results may be obtained, as follows,

BY PROPORTION,

$ 4900: $ 2100 :: $8 4: $3 6, A's gain.
$ 4900 : $2800 :: $8 4: $ 48, B’s gain.

Proof, $ 8 4, 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 procluct of each partner's stock and time, and the result will be his share of the gain or loss.

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.

Or,

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, $ 51.611;

Oliver's, $ 24.19}i: 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

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