EXAMPLES FOR PRACTICE.

3. Bought 40 yards of broadcloth at $5.40 per yard, and I sell of it at $6 per yard, and the remainder at $7 per yard; what do I gain per cent.? Ans. 159 per cent.

4. A merchant purchased for cash 50 barrels of flour, at $5 per barrel, and immediately sold the same on 8 months' credit, at $5.98 per barrel; what does he gain per cent. ?

Ans. 15 per cent.

5. A grocer bought a hogshead of molasses, containing 100 gallons, at 30 cents per gallon; but 30 gallons having leaked out, he disposed of the remainder at 40 cents per gallon. Did he gain or lose, and how much per cent. ?

Ans. Lost 63 per cent.

6. A gentleman in Rochester, N. Y., purchased 3000 bushels of wheat, at $1.12 per bushel. He paid 5 cents per bushel for its transportation to N. Y. city, and then sold it at $1.37 per bushel; what did he gain per cent. ? Ans. 17 per cent. 7. J. Morse bought, in Lawrence, a lot of land 7 rods square, for $5 per square rod. He sold the land at 5 cents per square foot; what did he gain per cent.?

Ans. 1721 per cent.

ART. 250. To find the selling price when the cost and the gain or loss per cent. are given.

Ex. 1. If I buy flour at $4 per barrel, for how much must I sell it per barrel to gain 25 per cent. ?

OPERATION.

$4 × .25 = $1.00; then $4 + $1

Ans. $5.

It is evident, if I sell the flour for 25 per cent. gain, I sell it for .25 more than it cost. Therefore, if I add to the cost .25 of the cost, the sum will be the price per barrel for which the flour must be sold; as seen in the operation.

$100 + $25

=

OPERATION BY PROPORTION.

$125; $100 $125 :: $4 : $5, Ans.

:

2. If I buy flour at $5 per barrel, for what must I sell it per barrel to lose 20 per cent.?

QUESTION.

Art. 250. Explain how you find the selling price when the cost and the gain or loss per cent. are given.

OPERATION.

$5 × .20 = $1.00; $5 — $1 = $4, Ans.

It is evident, 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 remainder will be the price per barrel for which the flour must be sold; as seen in the operation.

$100

$20

RULE 1.

OPERATION BY PROPORTION.

$80; $100 : $80:: $5 : $4, Ans.

- 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 $100 are to $100 with the profit added or loss subtracted, 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. $0.18 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+: $11.50 per cwt., but per cent.; for how Ans. $68.42+.

8. H. Tilton bought 7cwt. of coffee at finding it injured, he is willing to lose 15 much must he sell the 7cwt. ?

ART. 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.

QUESTIONS. Art. 250. What is the first rule for finding at what price goods must be sold to gain or lose a given per cent.? What is the second rule?

Since the gain evidently 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, as it may be expressed, equal to 1.25 of the cost. Hence, the cost must be as many dollars as the $5 contains times 1.25; and, dividing, we obtain $4, the answer required,

1.00 +.25

OPERATION BY PROPORTION.

=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.

Since the loss evidently 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, as it may be expressed, equal to .80 of the cost. Hence, the cost must be as many dollars as the $5 contains times .80; and, dividing, we obtain $5, the answer required.

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. sub tracted, 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 621 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?

QUESTIONS.

Ans. $1355.93+.

Art. 251. What is the first rule for finding the cost, when the selling price and the gain or loss per cent. are given? What is the second rule?

6. Sold 17 barrels of flour at $8 per barrel, for which I received 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 the cost of it?

Ans. $148.76+.

ART. 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.

The solution of this question involves two principles: First, to find the cost of the flour per barrel. (Art. 251.)

Thus, $5.00 ÷ 1.25 = $4.00, the cost per barrel. Second, to find the gain per cent. on the cost when sold at $7 per barrel. (Art. 248.)

Thus, $7 - $4 = $3; 3.00 ÷ 4

= .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. 248.)

Or,

RULE 2. As the first price is to the proposed price, so is 1 with the profit per cent. added, or the loss per cent. subtracted, to the gain or loss per cent. at the proposed price.

NOTE.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.

12

EXAMPLES FOR PRACTICE.

2. Sold a quantity of oats at 28 cents per bushel, and gained 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 per cent.

4. S. Phelps sold a quantity of wheat for $1728, and took

QUESTIONS. Art. 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? What is the second rule? If the answer exceeds $100, what is the excess? If it is less than $100, what is the deficiency?

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?

Ans. 33+ per cent.

MISCELLANEOUS EXERCISES IN PROFIT AND LOSS.

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 him 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 288 per cent.

9. A merchant bought 70 yards of broadcloth that was 12 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+.