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Examples.

2. If T sell cloth at $ 7 per yard, and thereby gain 75 per cent., do I gain or lose if I sell the same at $ 3 per yard?

Ans. Lose 25 per cent.

3. Sold wheat at $ 1.25 per bushel, and lost 15 per cent. What percent. should I have gained had I sold it for $1,647-^ per bushel? Ans. 12 per cent.

4. Sold wheat at $ l.647Tif per bushel, and gained 12 per cent. What percent. should I have lost had I sold it for $ 1.25 per bushel?

5. I sold a horse for $ 75, and by so doing I lost 25 per cent,; whereas, I ought to have gained 30 per cent. How much was he sold under his real value? Ans. $55.00.

6. When ten, sold at a loss of 25 per cent., brings $ 1.25 per pound, what would be the gain or loss should it bring $ 1.40 per pound? Ans. 16 per cent. loss.

MISCELLANEOUS EXAMPLES.

1. Bought stocks whose par value is $100 per share, and sold the same at a premium of 15 per cent., and thereby gained $ 120. How many shares were there? Ans. 8 shares.

2. Mining stock of a par value of $ 250 per share was bought at 9 per cent, premium, and afterwards sold at a loss of $ 25 per share on the price paid. At what rate per cent, was it sold? Ans. 1 per cent. discount.

3. How much greater income may be realized yearly from $ 19200 invested in 7 per cent. stocks purchased at 96 per cent., than from the same amount in 5 per cent . stocks purchased at 80 per cent.?

4. The par value of the shares in a certain manufacturing company is $ 250 each, and the regular yearly dividends are $ 15 a share. At what price should the shares be bought that the investment may pay 10 per cent, interest?

, Ans. $ 150 each.

5. A broker charges me 1£ per cent, brokerage for purchasing some uncurrent bank-bills 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. 2£ 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. $ 60.78f|.

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. $3.653fJ.

9. Bought a hogshead of molasses for $ 112; but 15 gallons having leaked out, the remainder was sold at $ 2.2162 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 having 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 2^ per cent., cost $ 0135, 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 2£ per cent. on the purchase, which amounted to $ 90, he purchased the iron at $ 95 per ton. Required the sum remitted, and the quantity of iron purchased.

Ans i Sum remittC(1, $3690

(Iron purchased, 37T. 17cwt. 3qr. 14T9?1b.

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 cintion.

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).

417i 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 § 300, and C $ 480. They gain $ 54. What is each man's part of the gain?

OPERATION.

A's stock, $240 $ 2 4 0 X -0 5 =: $ 1 2, A's gain.
B's" 3 6 0 3 6 0 X -0 5 = 18, B's gain.
C's" 4 8 0 4 8 0 X -0 5 = 2 4, C's gain.

Entire stock, $ 1 0 8 0 Proof, $ 5 4, entire gain.

$54.00 H- 1080 = $0.05, gain on $1.

Since the entire stock is $ 1080 and the entire gain $ 54, the gain on every $ 1 of stock 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.

$ 1 0 8 0 : $ 2 4 0 :: $ 5 4 : $ 1 2, A's gain.
$1080:$360 :: $ 5 4 : $ 1 8, B's gain.
$1080 : $480 :: $5 4 : $24, C's gain.

Proof, $ 5 4, entire gain.
Rule. The entire gain or loss, divided by the number denoting the

entire stock; will give the gain or Ions on each dollar of stock; anil 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 ichole 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 $ 35i', 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.

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 1£ as much, and C paid 1J as much. The profits were 25 per cent. of the cost of the ship. What was each man's gain?

Ahs. 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 I. They gain $ 50000. If, on dividing the profits, Armstrong relinquishes his part of the gain, how much will each of the others receive?

Ans. Walker, $28571.42?; Edwards, $ 21428.57f

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, $30; B's, $48.

OPERATION.

$420 X 5 = $2100 $2100X.01f = $3 6, A's gain. $350X8 = $2800 $ 2 8 0 0 X .011 = $ 4 8, B's gain.

$ 4900 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 x S = $ 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 -f $2800 = $4900, gain $84, $1 will gain -^fa of $ 84 = $ 0.014, and $2100 X .014} = $36, A's gain; $2800 X .01} = $48, B's gain. The same results may be obtained, as follows,

BY PROPORTION.

$4900:$2100::$84:$3 6, A's gain.
$4900:$2800::$84:$£8, B's gain.

Proof, $ 8 4, entire gain.

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