OPERATION. $5 x 20 = 1.00; $5 - $1=$ 4, Ans. If I sell the flour for 20 per cent. loss, I sell it for .20 less than it cost. Therefore, if I subtract from the cost .20 of the cost, the re. mainder will be the price per barrel for which the four must be sold. OPERATION BY PROPORTION. 1.00 .20 .80; 1.00 :.80 :: $ 5 :$ 4, Ans. RULE 1. — Find the percentage on the cost at the given rate per cent., and add it to the cost, or subtract it from the same, according as the selling price is to be that of profit or loss. Or, RULE 2. - As 1 is to 1 with the profil per cent. added, or loss per cent. subtracted, expressed decimally, so is the given price to the price required. EXAMPLES FOR PRACTICE. 3. Bought a hogshead of molasses containing 120 gallons, for 30 cents per gallon, but it not proving so good as was expected, I am willing to lose 10 per cent. on the cost; what shall I receive for it? Ans. $ 32.40. 4. A grocer bought a hogshead of sugar, weighing net 8cwt. 3qr. 5lb., for $ 88; for what must he sell it per pound to gain 20 per cent ? Ans. 12 cents per pound. 5. J. Simpson bought a farm for $ 1728; for what must it be sold to gain 12 per cent., provided he is to wait 8 months, without interest, for his pay? Ans. $ 2012.77+ 6. J. Fox purchased a barrel of vinegar containing 32 gallons, for $ 4; but 8 gallons having leaked out, for how much must he sell the remainder per gallon to gain 10 per cent. on the cost ? Ans. $0.184 per gallon. 7. Bought a horse for $ 90, and gave my note to be paid in 6 months, without interest; what must be my cash price to gain 20 per cent. on my bargain ? Ans. $ 104.84+. 8. H. Tilton bought 7cwt. of coffee at $ 11.50 per cwt., but finding it injured, he is willing to lose 15 per cent.; for how much must he sell the 7cwt. ? Ans. $ 68.42+ 251. To find the cost when the selling price and the gain or loss per cent. are given. Ex. 1. If I sell flour at $ 5 per barrel, and by so doing make 25 per cent., what was the cost of the flour? Ans. $ 4 per barrel.. 250. What is the first rule for finding at what price goods must be sold o gain or lose a given per cent. ? The second rule ? OPERATION. $5.00 • 1.25 =$ 4, Ans. Since the gain is 25 per cent. of the cost, the selling price, $ 5, is equal to the cost increased by 25 per cent. of the cost, or to 1.25 of the cost. Hence, the cost must be as many dollars as 1.25 is contained times in 5, or $ 4. OPERATION BY PROPORTION. 1.00 +.25 = 1.25; 1.25 : 1.00 : : $5 : $4, Ans. 2. If I sell flour at $4 per barrel, and by so doing lose 20 per cent., what was the cost of the flour ? Ans. $5 per barrel. OPERATION. $ 4.00 = .80 = $5, Ans. Since the loss is 20 per cent. of the cost, the selling price, $ 4, is equal to the cost decreased by 20 per cent. of the cost, or .80 of the cost. Hence, the cost must be as many dollars as .80 is contained times in 5, or $ 5. OPERATION BY PROPORTION. 1.00 — .20 = .80 ; .80 : 1.00 : : $4 : $5, Ans. RULE 1. 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 quotient will be the cost. Or, RULE 2. As 1 with the gain per cent. added, or loss per cent. subtracted, expressed decimally, is to 1, so is the selling price to the cost. EXAMPLES FOR PRACTICE. 3. Having used my chaise 16 years, I am willing to sell it for $ 80; but by so doing I lose 627 per cent. ; what was the cost of the chaise ? Ans. $213.331. 4. If I sell wood at $ 7.20 per cord, and gain 20 per cent., what did the wood cost me per cord ? Ans. $ 6 per cord. 5. J. Adams sold 40 cases of shoes for $ 1600, and gained 18 per cent. ; what was the first cost of the shoes? Ans. $ 1355.93+. 251. What is the first rule for finding the cost, when the selling price and the gain or loss per cent. are given ? The second rule ? 6. Sold 17 barrels of flour at $8 per barrel, for which I re ceived a note payable in 3 months. This note I had discounted at the Granite Bank, but, on examining my account, I find I have lost 10 per cent. on the flour ; what was its cost? Ans. $ 148.76+. 252. The selling price of goods and the rate per cent. being given, to find what the gain or loss per cent. would be, if sold at another price. Ex. 1. If I sell flour at $ 5 per barrel, and gain 25 per cent., what should I gain if I were to sell it for $ 7 per barrel ? OPERATION. We find the cost of the flour per barrel, as in Art. 251. Thus, $ 5.00 = 1.25 = $ 4.00, the cost per barrel. We find the gain per cent. on the cost when sold at $ 7 per barrel, as in Art. 249. Thus, $ 7—$ 4=$3 ; 8.004=.75, or 75 per cent. OPERATION BY PROPORTION. 1.00+.25 : 1.25; $ 5 : $7: : 1.25 : 1.75 ; 1.75 -1.00 .75, that is, 75 per cent. RULE 1. - Find the cost (Art. 251), and then the gain or loss per cent. on this cost at the proposed selling price. (Art. 249.) Or, RULE 2. As the first price is to the proposed price, so is 1 with the gain per cent. of the first price added, or the loss per cent. of the first price subtracted, to 1 with the gain per cent of the proposed price added, or with the loss per cent. of the proposed price subtracted. NotB. - If the result by the last rule exceeds 1.00, the excess is the gain per cent.; but, if it is less than 1.00, the deficiency is the loss per cent. EXAMPLES FOR PRACTICE. 2. Sold a quantity of oats at 28 cents per bushel, and gained 12 per cent. ; what per cent. should I gain or lose, if I were to sell them at 24 cents per bushel ? Ans. Lose 4 per cent. 3. S. Rice sold a horse for $ 37.50, and lost 25 per cent. ; what would have been his gain per cent. if he had sold him for $ 75 ? Ans. 50 4. S. Phelps sold a quantity of wheat for $ 1728, and took a note payable in 9 months without interest, and made 10 per cent. on his purchase ; what would have been his gain per cent. if he had sold it to James Wilson for $ 2000 cash ? 252. What is the first rule for finding what gain or loss is made by selling goods at another price when the selling price and rate per cent. are given ? The second rule? If the answer exceeds 1.00 what is the excess? If it is less than 1.00, what is the deficiency? per cent. Ans. 33+ per cent. MISCELLANEOUS EXERCISES. 1. A horse that cost $ 84, having been injured, was sold for $ 75.60; what was the loss per cent. ? Ans. 10 per cent. 2. Sold a horse for $ 75.60, and lost 10 per cent. on the cost ; but, if I had sold him for $ 97.44, what per cent. should I have gained on the cost of the horse? Ans. 16 per cent. 3. M. Star sold a horse for $ 97.44, and gained 16 per cent. ; what would have been his loss per cent. if he had sold the horse for $ 75.60, and what his actual loss ? Ans. Loss 10 per cent. $ 8.40 loss. 4. If I buy cloth at $5 per yard, on 9 months' credit, for what must I sell it per yard for cash to gain 12 per cent. ? Ans. $ 5.35+ 5. A. Pemberton bought a hogshead of molasses, containing 120 gallons, for $ 40; but 20 gallons having leaked out, for what must he sell the remainder per gallon to gain 10 per cent. on his purchase ? Ans. $ 0.44. 6. H. Jones sells flour, which cost him $ 5 per barrel, for: $ 7.50 per barrel ; and J. B. Crosby sells coffee for 14 cents per pound, which cost im 10 cents per pound; which makes the greater per cent. ? Ans. H. Jones makes 10 per cent. most. 7. J. Gordon bought 160 gallons of molasses, but having sold 40 gallons, at 30 cents per gallon, to a man who proved a bankrupt, and could pay only 30 cents on the dollar, he disposed of the remainder at 35 cents per gallon, and gained 10 per cent. on his purchase ; what was the cost of the molasses ? Ans. $ 41.45+ 8. D. Bugbee bought a horse for $ 75.60, which was 10 per cent. less than his real value, and sold him for 16 per cent. more than his real value ; what did he receive for the horse, and what per cent. did he make on his purchase ? Ans. Received $ 97.44, and made 285 per cent. 9. A merchant bought 70 yards of broadcloth that was 11 yards wide, for $ 4.50 per yard, but the cloth having been wet, it shrunk 5 per cent. in length, and 5 in width; for what must the cloth be sold per square yard to gain 12 per cent. ? Ans. $ 3.19+ PARTNERSHIP, OR COMPANY BUSINESS. 253. Partnership is the association of two or more persons in business, with an agreement to share the profits and losses. Partners are the persons associated in business. Capital, or Joint Stock, is the money or property invested in the company or firm. The Dividend is the profit or gain on the shares of the capital. 254. To find each partner's share of the profit or loss when each one's stock is employed the SAME TIME. Ex. 1. John Smith and Henry Gray enter into partnership for three years ; Smith puts in $ 4000, and Gray $ 2000. They gain $570. What is each man's share of the gain ? Ans. Smith's gain, $ 380; Gray's gain, $ 190. OPERATION. 66 $ 4 0 0 0, Smith's stock, 4888 $, Smith's part of the stock. $ 2000, Gray's 2008 = }, Gray's part of the stock. $ 6 0 0 0, Whole stock. Then of $570, the whole gain, $ 3 8 0, is Smith's share of the gain. And of $570, = $190, is Gray's share of the gain. Proof, $ 5 70 Since $ 4000 + $ 2000 $ 6000 is the whole stock, Smith's part of the stock is 4000=; and Gray's part, 2888=. Then, since each man's gain must correspond to his stock, z. of $570, or $ 380, is Smith's share of the gain; and f of $570, or $ 190, is Gray's share of the gain. OPERATION BY PROPORTION. $ 6000: $ 4000 : $ 5 70: $ 3 8 0, Smith's gain. 253. What is partnership? What are the persons associated called ? What is the association called? What the property invested? What the profit or loss ? |