OPERATION. Since the selling price is to be a gain on the cost of 25 per cent., evidently it $ 4 x 1.25 = $5, Ans. must be 125 per cent. of the cost, or $ 4 X 1.25. RULE. — Multiply the cost price by 1 increased by the gain per cent., or by 1 decreased by the loss per cent., expressed decimally, and the product will be the selling price required. EXAMPLES. 2. If I buy cloth at $ 5 per yard, for what must I dispose of it per yard to lose 20 per cent. ? Ans. $ 4. 3. Bargained for cheese at $ 8.50 per cwt. How must it be sold to gain 10 per cent. ? Ans. $ 9.35 per cwt. 4. Molasses having been bought at 42 cents a gallon, and not proving so good as expected, was sold at a loss of 5 per cent. For what was it sold a gallon? 5. Bought a house and lot for $ 2500; at what price must it be sold to gain 20 per cent. ? Ans. $ 3000. OPERATION 413. To find the cost when the selling price and the gain or loss per cent. are given. Ex. 1. If I sell cloth at $ 5 per yard, and thereby make 25 per cent., what was its first cost? Ans. $ 4 per yard. Since the gain is 25 per cent. of $ 5.00 = 1.25 $ 4, Ans. the cost, the selling price, $5, is equal to the cost increased by 25 per cent. of the cost, or 1.25 of the cost. Therefore, the cost must be as many dollars as 5 contains times 1.25. RULE. — Divide the selling price by 1 increased by the gain per cent., or by 1 decreased by the loss per cent., expressed decimally, and the guotient will be the cost. EXAMPLES. 2. If I dispose of cloth at $ 4 per yard, and by so doing lose 20 per cent., required the prime cost of the goods ? Ans. $5. 3. Sold 10 barrels of four for $ 96, and made 20 per cent. What was the prime cost a barrel ? Ans. $ 8. 4. If 27{cwt. of sugar be sold at $12.50 per cwt., and there is gained 17 per cent., what was the prime cost per cwt. ? 5. Sold wood at $ 6.124 per cord, and by so doing lost 12} per cent. a cord. What was the original cost per cord ? Ans. $ 7.00 414. To find the gain or loss per cent. when the cost and selling price are given. Ex. 1. If I buy cloth at $ 4, and sell it at $5 per yard, what per cent. do I gain? Ans. 25 per cent. OPERATION. $ 5 – $4 = $1; 1.00 = 4= .25, or 25 per cent., Ans. Since the difference between the selling price and the prime cost is $ 1, the gain is of the cost, or, expressed decimally, is .25 of the cost, or 25 per cent. of it. RULE. — Divide the number denoting the gain or loss by that denoting the prime cost, and the quotient, expressed decimally, will be the gain or loss per cent. required. EXAMPLES. 2. Bought cloth at $ 7 per yard, and sold it at $ 6.121. What per cent. did I lose? Ans. 121 per cent. 3. Bought a chaise for $ 200, and sold it for $ 225. What per cent. did I gain ? Ans. 121 per cent. 4. I sell a house that cost me $ 2500 at an advance of $ 500. What per cent. do I gain ? 5. Bought 24 yards of cloth for $64.86434, and sold it at $ 2.50 per yard. What per cent. is the loss ? Ans. 74 per cent. 415. The selling price of goods and the rate per cent. of gain or loss being given, to find what the gain or loss per cent. would be, if sold at another price. Ex. 1. If I sell cloth at $ 5 per yard, and thereby gain 25 per cent., what would have been my gain if I had sold it at $ 7 Ans. 75 per cent. We find the prime $ 5.00 ; 1.25 $ 4; $ 7 $ 4= $ 3. cost of the cloth per 3.00 ; 4= .75, or 75 per cent., Ans. yard, when sold at $ 5, by Art. 413, to be $ 4. We then find what would have been the gain per cent. on the cost, if it had been sold at $ 7 per yard, by Art. 414, and obtain 75 per cent. as the answer. RULE. — Find the prime cost (Art. 413), and then the gain or loss per cent. on this cost at the proposed selling price. per yard? OPERATION. EXAMPLES. 2. If I 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 per cent. should I have gained had I sold it for $1.64714 Ans. 12 per cent. 4. Sold wheat at $ 1.647 iş per bushel, and gained 12 per cent. What per cent. should I have lost had I sold it for $ 1.25 per bushel ? 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 tea, 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 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 14 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. $ 60.7815. 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 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 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 liaving reserved to himself 21 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. 3690. 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 par: titive 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 C's 66 A's stock, $ 2 40 $ 240 x .05 $ 12, A's gain. 3 6 0 3 60 x .05 = 18, B's gain. 480 480 x .05 24, 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 stock will be as many dollars as 54 contains times 1080, or $ 0.05 on every $ 1 of stock. Then, cach 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 : $ 2 40 :: $ 5 4: $ 1 2, A's gain. Proof, $ 5 4, entire gain. |