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PROFIT AND LOSS.

272. Profit and Loss are commercial terms, used to express the gain or loss in business transactions, which is usually reckoned at a certain per cent on the prime or first cost of articles.

The operations in Profit and Loss involve the same principles as those of Percentage. The cost corresponds to the base; the per cent of profit or loss to the rate per cent; the profit or loss to the percentage, and the selling price to the amount or difference.

EXAMPLES.

273. To find the amount of profit or loss, when the cost and the gain or loss per cent are given. 1. A man bought a horse for $135, and afterwards sold him for 20% more than he gave. How much did he gain?

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RULE.-Multiply the cost by the rate per cent expressed decimally. Or,

Reduce the per cent to a common fraction, and take that fractional part of the cost.

2. A grocer bought a hogshead of sugar for $84.80, and sold it at 121% profit. What was his gain?

3. A miller bought 500 bushels of wheat at $1.15 a bushel, and he sold the flour at 163% advance on the cost of the wheat. What was his gain? Ans. $95.831. 4. I bought 76 cords of wood at $3.621 a cord, and sold it so as to gain 26%. What did I make ?

5. A hatter bought 40

them at a loss of 144%.

hats at $1.75 apiece, and sold What was his whole loss?

6. A sloop, freighted with 3840 bu. of corn, encountering a storm, threw 371% of her cargo overboard. was the loss, at 62 cents a bushel?

What

Ans. $900 loss.

7. A grocer bought 3 barrels of sugar, each containing 230 pounds, at 81 cents a pound, and sold it at 182% profit. What was his whole gain, and what the selling price per pound?

Ans. Gain, $10.35; price per lb., 94 cents.

8. A man bought a carriage for $160, and after paying 10% for repairs, sold it at 121% profit. What was his gain?

9. What is the profit on 6 doz. pairs of gloves, bought at $12 a doz. and sold at a gain of 50% a pair?

10. I bought two houses for $2500 each, and sold one at an advance of 331% and the other at a loss of 331%. What did I gain or lose on both ?

11. A merchant pays $6840 for a stock of spring goods, and sells them at an advance of 261% on the purchase price. After deducting $375 for expenses, what is his gain?

274. To find the gain or loss per cent when the cost and selling price are given.

1. Wool bought at 32 cents a pound, was sold for 40 cents a pound. What per cent was gained?

OPERATION.

40% - 324 84; 8÷32 =

SOLUTION.

=

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Since the gain on 32 cents is 40 328 cents, the whole gain is of the purchase money; and reduced to a decimal is 25 hundredths, equal to 25 per cent.

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RULE.-I. Find the difference between the cost and selling price which will be the gain or loss.

II. Make the gain or loss the numerator, and the cost the denominator; reduce to a decimal, and the result will be the per cent.

2. A man bought a pair of horses for $275, and sold them for $330. What per cent did he gain? Ans. 20%. 3. If a merchant buys cloth at $.60 a yard, and sells it for $.75 a yard, what per cent does he gain?

4. A speculator bought 108 barrels of flour at $4.62 a barrel, and sold it so as to gain $114.884. What per cent profit did he make? Ans. 23%.

5. Sugar bought at 8 cents a pound, was sold for 9 cents a pound. What per cent was gained?

Ans. 144%.

6. A drover bought 150 head of cattle for $42 per head, and sold them for $5400. What was his loss per cent? 7. If I sell for $15 what cost me $25, what do I lose?

per Ans. 40%.

cent

8. Paper bought at $2 per ream, was sold at 25 cents a quire. What was the gain?

Ans. 150%.

9. If I sell of an article for of the cost of the

article, what per cent is gained?

Ans. 50%.

10. If of an article is sold for what of the article Ans. 37%.

cost, what is the loss per cent ?

11. If I sell 3 pecks of clover-seed for what 1 bushel cost me, what per cent do I gain? Ans. 331%.

12. A, having a debt against B, agreed to take $.871 on the dollar. What per cent did A lose?

13. A grocer bought 7 cwt. 20 lb. of sugar, at 7 cents a pound, and sold 3 cwt. 42 lb. at 8 cents, and the remainder at 84 cents. What was his gain per cent? Ans. 18%.

14. A grain dealer bought corn at $.55 a bushel, which he sold at $.66, and wheat for $1.10, which he sold for $1.37. Upon which did he make the greater per cent? Ans. 5% upon the wheat. 15. If I buy a piano for $650 and sell it for $400, what per cent do I lose?

275. To find the selling price, when the cost and the gain or loss per cent are given.

1. A horse was bought for $136. must he be sold to gain 25% ?

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For how much

SOLUTION. Since $1 of cost sells for $1.25, $136 of cost will sell for 136 times $1.25, which equals $170, the selling price.

RULE.-Multiply $1 increased by the gain or diminished by the loss per cent by the number denoting the cost. Or, Take such a part of the cost as is equal to 100 increased or diminished by the gain or loss per cent.

2. If 12 hundred-weight of sugar cost $140, for how much must it be sold per pound to gain 25%?

3. I bought a hogshead of molasses for 30 cents a gallon, and paid 163% on the prime cost for freight and cartage. What must I sell it for, per gallon, to gain 331% on the whole cost? Ans. $.463.

4. For what price must I sell coffee that cost 101 cents a pound, to gain 171% ?

5. If I am compelled to sell damaged goods at a loss. of 15%, how should I mark goods that cost me $.621? $1.20? $3.87? Ans. $.531; $1.02; $3.293. 6. A man, wishing to raise some money, offers his house and lot, which cost him $3240, for 18% less than cost. What is the price for which he offers it?

7. C bought a farm of 120 acres, at $28 an acre, paid $480 for fencing, and then sold it for 121% advance on the whole cost. What was his whole gain, and what did he receive an acre? Ans. $480 gain; $36 an acre. 8. A merchant bought 15 pieces of broadcloth, each piece containing 23 yards, for $840, and sold it so as to gain 18%. What did he receive a yard?

PRAC. AR. - -17

276. To find the cost, when the selling price and the gain or loss per cent are given.

1. A merchant sold cloth for $4.80 a yard, and by so doing made 331%. How much did it cost?

OPERATION.

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1.00 +.33} = 1.33}; $4.80 ÷ 1.33 $3.60, Ans.

SOLUTION. Since the gain is 33% of the cost, the selling price must be 100% + 33 % = 1331% of the cost. If $4.80 is 1.33} of the cost, the cost must be $4.80 ÷ 1.33, which is $3.60.

If the rate per cent is loss, subtract it from 100 per cent, instead of adding it. RULE. Divide the selling price by 100% increased by the gain or diminished by the loss per cent, expressed decimally, or in the form of a common fraction, and the quotient will be the cost.

2. By selling sugar at 8 cents a pound, a merchant lost 20%. What did the sugar cost him? Ans. 10 cents. 3. I sold flour for $6.12 per barrel, and lost 12%. What was the cost? Ans. $7.00. 4. A grocer, by selling tea at $.96 a pound, gains 28%. What did it cost him? Ans. $.75. 5. A quantity of flour was sold for $1881, which was 18% more than it cost. What did it cost?

6. I sold 25 barrels of apples for $69.75, and made 24%. What did they cost me per barrel?

7. A man sold 94 cwt. of sugar at $8 per cwt., and thereby lost 12%. What was the whole cost?

8. Having used a carriage six months, I sold it for $96, which was 20% below cost. What would I have received had I sold it for 15% above cost? Ans. $138. 9. A grocer sold 4 barrels of sugar for $24 each; on 2 barrels he gained 20%, and on the other 2 he lost 20%. Did he gain or lose on the whole ? Ans. Lost $4

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