year. January 1, Jones put in $1000, but Cotton did not put in any until the 1st of April. What did he then put in to have an equal share with Jones at the end of the year? Ans. $1333.331.

6. S, C and D engage in partnership, with a capital of $4700. S's stock was in trade 8 months, and his share of the profits was $96; C's stock was in the firm 6 months, and his share of the gain was $90; D's stock was in the firm 4 months, and his gain was $80. Required the amount of stock which each had in the firm.

7. P and H engage in trade, and it was mutually agreed that each should receive of the profits in proportion to his stock, and the time it was continued in trade. P put in $ 4000 for 5 months, and H put in $6000 for 8 months, and they gained $680; what was each man's share of the gain?

Ans. P's share $ 200, H's share $480.

8. A, B and C engage in trade. A put in $300 for 7 months, B put in $500 for 8 months, and C put in $200 for 12 months; they gain $85; what share of the gain does each receive? Ans. A $21, B $ 40, and C $24. 9. A and B engage in trade, with $500. A put in his stock for 5 months, and B put in his for 4 months. A gained $10, and B gained $ 12; what sum did each put in?

Ans. A $200, B $300.

10. A and B trade in company; A put in $3000, and at the end of 6 months put in $2000 more; B put in $6000, and at the end of 8 months took out $3000; they trade one year, and gain $1080; what is each man's share of the gain? Ans. A's share is $480, B's $600.

11. Four men hired a pasture for $50. A put in 5 horses for 4 weeks; B put in 6 horses for 8 weeks; C put in 12 oxen for 5 weeks, calling 3 oxen equal to 2 horses; and D put in 3 horses for 14 weeks. How much ought each man to pay?

Ans. A $6.66%, B $ 16.00, C $ 13.33, and D $ 14.00. 12. A, B and C contract to build a piece of rail-road for $7500 dollars. A employs 30 men 50 days; B employs 50 men 36 days; and C employs 48 men and 10 horses 45 days, each horse to be reckoned equal to one man, and he is also to have $112.50 for overseeing the work. How much is each man to receive? Ans. A receives $1875; B $2250; C $3375.

§ XXXVI. PROFIT AND LOSS.

ART. 254. PROFIT and Loss is a rule by which merchants and other traders estimate their gain or loss in buying and selling goods.

The following questions may be performed either by analysis or by proportion.

ART. 255. To find the profit or loss per cent. in buying and selling goods, having the cost and selling prices given. Ex. 1. If I buy flour at $4 per barrel, and sell it at $5 per barrel, what is the gain per cent. ? Ans. 25 per cent.

$5 $4

OPERATION.

= $1; } = 1.00 ÷ 4 = .25, or 25 per cent. By subtracting the cost from the selling price, we find the gain per barrel to be $ 1, or of the cost, which fraction being reduced to a decimal, (Art. 187,) we obtain .25, or 25 per cent., for the gain.

OPERATION BY PROPORTION.

$5-$4=$1; $4: $100::$1: $ 25, that is, 25 per ct. 2. If I buy flour at $5 per barrel, and sell it at $4 per barrel, what is the loss per cent.?

Ans. 20 per cent.

By subtracting the selling price from the cost, we find the loss per barrel to be $ 1, or of the cost, which fraction being reduced to a decimal, (Art. 187,) we obtain .20, or 20 per cent. for the loss.

OPERATION BY PROPORTION.

$5-$4 $1; 85: $100::$1: $20, that is, 20 per cent.

=

RULE I. First find what fractional part the gain or loss is of the cost, by making the gain or loss the numerator of the fraction, and the cost the denominator; and then reduce this fraction to a decimal for the

answer.

Or,

RULE II. As the cost of the goods is to $100, so is the gain or loss to the gain or loss per cent.

NOTE.- Since per cent. is a certain number of hundredths, the figures denoting it can properly occupy only two places; hence those at the right

Art. 255.

What is the
What is the

QUESTIONS. Art. 254. What is Profit and Loss? first rule for finding the profit or loss in buying or selling goods? second rule?

of hundredths are a fractional part of 1 per cent., and may be expressed either as a decimal or vulgar fraction.

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. 1539 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. he gain or lose, and how much per cent. ?

Did

Ans. Lost 6 per cent. 6. A gentleman in Rochester, N. Y., purchased 3000 bushels of wheat, at $1.121 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. 256. To find at what price goods must be sold to gain or lose a given per cent.

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

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 .25 of the cost to itself, it will give the price per barrel for which the flour must be sold; as seen in the operation.

OPERATION BY PROPORTION.

$100 $25-$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. ?

QUESTIONS.-How many places can the figures denoting per cent. occupy? What is the next place below hundredths? How are the figures below hundredths regarded? How may they be expressed?

OPERATION.

$5 X.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 .20 of the cost from itself, it will give the price per barrel for which the flour must be sold; as seen in the operation.

$100 $20

=

OPERATION BY PROPORTION.

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

RULE I. Find the percentage on the cost of the goods at the given rate per cent., and add it to the cost, or subtract it from it, according as the goods are sold at a profit or loss.

RULE II.

Or,

- 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 7cwt. 3qr. 12lb., 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+.

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+.

ART. 257. 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. 256. 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?

OPERATION.

Let 188(1) represent the cost of the flour per barrel; then since $5 is 25 per cent., or more than the cost, it is equal to 188 + 10% 185 of the actual cost. Again, if $5 is 135 of the cost, will be $5÷ 125 $.04, and 188, or the

cost of the flour per barrel, will be $.04 × 100

$100 + $25

OPERATION BY PROPORTION

= $125; $125:$100::$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?

OPERATION.

Ans. $5 per barrel.

Let 188(=1) represent the cost of the flour per barrel; then, since $4 is 20 per cent., or less than the cost, it is equal to 188 100 of the actual cost. Again, if $4 is of the cost. 10 will be $4÷ 80 = = $.05, and 188, or the cost per barrel, will be $.05 × 100 : = $5.00.

OPERATION BY PROPORTION.

$100 $20-$80; $80:$100 :: $4: $5, Ans.

RULE I. — Find what fractional part the selling price is of the cost, by making 100, with the gain per cent. added, or the loss per cent. subtracted, the numerator of a fraction, and 100 the denominator; then divide the selling price by this fraction, and the quotient will be the cost Or,

RULE II. - As $100 with the gain per cent. added or loss per cent. subtracted is to $100, 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 62 per cent.; what was the cost of the chaise ? Ans. $213.33.

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?

QUESTION.

Ans. $1355.93+.

-Art. 257. 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?