307. Profit and Loss are terms used to express the gains or losses in business transactions. Gains and losses are computed at a certain rate per cent of the cost or the sum invested, and the operations involve the principles already explained in Percentage.

308. The Base is the cost or the sum invested.

309. The Rate % is the rate per cent of profit or loss. 310. The Percentage is the profit or loss.

311 (a). The Amount is the sum of cost and profit, or the selling price.

311 (b). The Difference is the cost less the loss, or the selling price.

CASE I.

312. To find the sum gained, or lost, when the cost and rate % are given.

Oral Exercises

EXAMPLE 1.-A wagon that cost $150 was sold at a gain of 20%. What was the gain?

SOLUTION.-Since the gain was 20%, it was, or of $150,

or $30.

EXAMPLE 2.-A horse that cost $300 was sold at a loss of

27%. What was the loss?

SOLUTION. Since the loss was 27%, it was 2 of $300, or $81.

100

EXAMPLE.What is the gain, when goods are bought for $250 and sold at a gain of 15% ?

the cost by the rate (r), .15. In either case we obtain the same result, $37.50.

313. RULES.-Take such part of the cost as the rate %

Multiply the cost by the rate. (B × r = P.)

PROBLEMS.

1. Sold goods which cost me $1250, at a gain of 121%.

How much did I gain?

Ans. $156.25.

2. How much do I lose by selling a horse, which cost me $542, at a loss of 18% ? Ans. $97.56.

3. I wish to sell my goods at a profit of 20%; how shall I mark calicoes that cost 10? Delaines that cost 40% ? Toweling that cost 124? Silks that cost $3? Broadcloths that cost $4.50? Satins that cost $5? Ans. to last, $6. out my stock, and willing to lose 121% on How should I mark hose that cost 32 ?

4. I am closing

cost of my goods.

Collars that cost 8?

Cloaks that cost $32 ?

CASE II.

Ans. to last, $28.

314. To find the rate % of gain or loss, when the cost and gain, or loss, are given.

Oral Exercises

EXAMPLE.-Bought a shawl for $16, and sold it at an advance of $4. What % did I gain?

SOLUTION. My gain is $4 on $16, or

=

of cost.

Since cost is 100%, my gain is of 100%, or 25%.

PROBLEMS.

1. Bought calico for 89 per yard, and sold it so as to gain

2 on each yard. What % did I gain?

2. Bought shoes at $5, and sold them at $6. What was the gain %?

3. Bought oranges at 3 apiece, and sold them at 5. What is the rate % gain?

4. Bought apples at 3 for 5, and sold them at 4 for 5. What % was the loss?

5. Bought a book for $2, and sold it for $1.50. What was the loss %?

Written Exercises+

EXAMPLE.-Bought a buggy for $360, and sold it for $450.

What was the rate % of gain?

315. RULES.-Take such a part of 100% as the gain or

Divide gain or loss by cost. (P ÷ B = r.)

1. Bought a house for $1750, and sold it for $500. What % is the loss?

Ans. 71%.

2. Bought a farm for $7650, and sold it for $9780. Required the gain %. Ans. 27%. 3. Bought a horse for $160, and sold him for $25. What % did I lose? Ans. 848%. 4. Bought delaines for 20% a yard, and sold them at 371 a yard. Required the rate % gain. Ans. 87%.

5. Bought 100 doz. eggs at 15 a doz.; but 20 doz. were broken in transportation. Sold the remainder at 31 a doz. What did I gain on the investment? Ans. 651%.

6. I buy a horse for $100, and after keeping him at a livery stable for 10 weeks at an expense of $5 a week, I sell him for $120. What is my rate % of loss?

Ans. 20%.

CASE III.

316. To find the cost, when the gain, or loss, and the rate % are given.

Oral Exercises

EXAMPLE.-Sold my horse at an advance of $25, which What was his cost?

was 20% of his cost.

20

SOLUTION. Since 20%, or 10%, or 3, of the cost is $25, §, or the cost, is 5 times $25, or $125.

PROBLEMS.

1. If $20 is 20% of the cost of 16 bbl. of flour, what is the entire cost?

2. If I lose $16 on the price of an ox, my loss amounts to 121% of his value. What is his value?

3. If $10 is 5% of the cost of my fare to San Francisco, what is the whole cost?

4. A lost $450, which was 90% of all he had. How much did he have?

5. A grocer sold some bacon for $250, which was equal to 121% of the value of all he had. What was the entire value?

Written Exercises

EXAMPLE. I sold my farm at a gain of $500, which was equal to 20% of its value. What was its value?