APPLICATIONS.

508. Profit and Loss, Commission, Insurance, Stocks, Taxes, and Duties, are applications of Business Problems VIII, IX, X, XI. The rate in these subjects is usually a per cent. Hence, for convenience in expressing rules, we denote the quantities by letters as follows:

1. B represents the Base, or number on which the percentage is reckoned.

2. R represents the Rate per cent expressed decimally.

3. P represents the Percentage, or the part of the Base which is denoted by the Rate.

4. A represents the Amount, or sum of the Base and Percentage. 5. D represents the Difference, or Base less the Percentage.

Formulæ, or Rules for Percentage.

509. Prob. VIII., P=B× R. Read,{

The percentage is equal to the base multiplied by the rate. The base is equal to the percentage divided by the rate. The rate is equal to the percentage divided by the base. The base is equal to the amount

divided by 1 plus the rate. The base is equal to the diff'nce divided by 1 minus the rate.

513. Refer to the problems on pages 222 to 226 inclusive, and answer the following questions regarding these formula: 1. What is meant by B× R, and why is P=B×R? Illustrate your answer by an example, giving a reason for each step.

2. Why is PR equal B? Give reasons in full for your

answer.

3. If R is 135%, which is the greater, P or B, and why?

4. If R is 248%, how would you express R without the sign %?

5. Why is R equal to P÷B, and how must the quotient of P÷B be expressed to represent R correctly?

6. What is meant by A? How many times R in P (502) ? How many times 1 in B? How many times 1+ R must there be in A and why?

7. How many times R in P (502)? D is equal to B minus how many times R (501)?

8. Why is B equal to D÷ (1 – R)? Give reasons in full for your answer.

PROFIT AND LOSS.

514. The quantities considered in Profit and Loss correspond with those in Percentage thus:

1. The Cost, or Capital invested, is the Base.

2. The Per cent of Profit or Loss is the Rate.

3. The Profit or Loss is the Percentage.

4. The Selling Price when equal the Cost plus the Profit is the Amount, when equal the Cost minus the Loss is the Difference.

515. 1. A firkin of butter was bought for $19 and sold at

a profit of 16%. What was the gain?

Formula P = B x R. Read, Profit or Loss = Cost × Rate %.

Find the profit on the sale

2. Of 320 yd. cloth bought @ $1.50, sold at a gain of 17%. 3. Of 84 cd. wood bought @ $4.43, sold at a gain of 20%. 4. Of 873 bu. wheat bought @ $1.25, sold at a gain of 14%. Find the loss on the sale

5. Of 180 T. coal bought @ $7.85, sold at a loss of 81%.

6. Of 124 A. land bought @ $84.50, sold at a loss of 21%. 7. If a farm was bought for $4860 and sold for $729 more than the cost, what was the gain per cent?

Formula BP÷R. Read, Rate % Gain = Profit ÷ Cost.

8. A piece of cloth is bought at $2.85 per yard and sold at $2.10 per yard. What is the loss per cent?

Ans.

9. If of a cord of wood is sold for 2 of the cost of 1 cord, what is the gain per cent? Ans.

10. Find the selling price of a house bought at $5385.90, and sold at a gain of 18%.

Formula A=B× (1+R). Read, Selling Price Cost × (1+ Rate % Gain).

Χ

11. Corn that cost 65 ct. a bushel was sold at 20% gain. What was the selling price? Ans. 78 ct. a bu. 12. A grocer bought 43 bu. clover seed @ $4.50, and sold it in small quantities at a gain of 40%. What was the selling price per bu. and total gain?

13. Sold 184 barrels flour for $1380, losing 91%. What was the cost or buying price?

Formula D B (1-R). Read, Cost = Selling Price x (1-Rate % Loss).

14. Flour was bought at $8.40 a barrel, and sold so as to lose 15%. What was the selling price?

15. C. Baldwin bought coal at $6.25 per ton, and sold it at a loss of 18%. What was the selling price?

16. Sold a house at a loss of $879, which was 15% of the cost. What was the cost?

Formula BP÷R. Read, Cost Profit or Loss Rate %.

17. A grain merchant sold 284 barrels of flour at a loss of $674.50. which was 25% of the cost. and selling price per barrel?

What was the buying

18. A drover wished to realize on the 236 sheep $531, which is 30% of the cost. head must he sell the flock?

sale of a flock of At what price per

19. Two men engaged in business, each having $4380. A

gained 331% and B 75%. How much was B's gain more than A's?

20. If I buy 72 head of cattle at $36 a head, and sell 33% of them at a gain of 18%, and the remainder at a gain of 24%, what is my gain?

21. A grocer sells coffee that costs 13 cents per pound, for 10 cents a pound. What is the loss per cent?

22. Fisk and Gould sold stock for $3300 at a profit of 33%. What was the cost of it?

23. A man bought 24 acres of land at $75 an acre, and sold it at a profit of 81%. What was his total gain?

24. A merchant sold cloth for $3.84 a yard, and thus made 20%. What was the cost price?

25. Bought wood at $3.25 a cord, and sold it at an average gain of 30%. What did it bring per cord?

26. If land when sold at a loss of 121% brings $11.20 per acre, what would be the gain per cent if sold for $15.36.

27. Bought a barrel of syrup for $20; what must I charge a gallon in order to gain 20% on the whole?

COMMISSION.

516. A Commission Merchant or Agent is a person who transacts business for another for a percentage.

517. A Broker is a person who buys or sells stocks, bills of exchange, etc., for a percentage.

518. Commission is the amount paid a commission merchant or agent for the transaction of business.

519. Brokerage is the amount paid a broker for the transaction of business.

520. The Net Proceeds of any transaction is the sum of money that is left after all expenses of commission, etc., are paid.

521. The quantities considered in commission correspond with those in percentage thus:

1. The amount of money invested or collected is the Base.

2. The per cent allowed for services is the Rate.

3. The Commission or Brokerage is the Percentage.

4. The sum invested or collected, plus the commission, is the Amount, minus the commission is the Difference.

EXAMPLES FOR PRACTICE.

522. Let the pupil write out the formula for each kind of examples in commission in the same manner as they are given in Profit and Loss.

What is the commission or brokerage on the following:

1. The sale of 85 cords of wood @ $4.75, commission 31%? 2. The sale of 484 yds. cloth @ $2.15, commission 13%? 3. The sale of 176 shares stocks at $87.50 a share, brokerage 3% ?

4. The collection of $3462.84, commission 24% ?

What is the rate of commission on the following:

5. Selling a farm for $4800, commission $120 ?

6. Collecting a debt of 7500, commission $350 ?

7. Selling wheat worth $1.80 a bu., commission 4 ct. a bushel?

What is the amount of the sale in the following:

8. The commission is $360, rate of commission 24%? 9. The brokerage is $754.85, rate of brokerage 1%? 10. The commission is $26.86, rate of commission 15%? Find the amount of the sales in the following:

Observe, that the commission is on the amount of the sales. Hence the formula for finding the amount of the sales when the net proceeds are given is (506)

Amount of sales

=

Net proceeds (1 − Rate %).

11. Net proceeds, $8360; rate of commission, 3%.