EXAMPLES FOR PRACTICE.

1. What number diminished by 10 % of itself is equal to 504? Ans. 560.

2. The rate is 8 %, and the difference $4.37; what is the base?

3. After taking away 15 % of a heap of grain, there remained 40 bu. 34 pk.; how many bushels were there at first?

Ans. 48 bu.

4. Having sold 36 % of my land, I have 224 acres left; how much land had I at first?

5. After paying 65 % of my debts, I find that $2590 will discharge the remainder; how much did I owe in all?

Ans. $7400.

6. A young man having received a fortune, deposited 80% of it in a bank. He afterward drew 20 % of his deposit, and then had $5760 in bank; what was his entire fortune?

Ans. $9000.

7. A man owning of a ship, sold 12 % of his share to A, and the remainder to B, at the same rate, for $20020; what was the estimated value of the whole ship? Ans. $26000.

8. An army which has been twice decimated in battle, now contains only 6480 men; what was the original number in the army?

Ans. 8000.

9. Each of two men, A and B, desired to sell his horse to C. A asked a certain price, and B asked 50 % more. A then reduced his price 20 %, and B his price 30 %, at which prices C took both horses, paying for them $148; what was each man's asking price?

Ans.

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A, $80.

B, $120.

10. A buyer expended equal sums of money in the purchase of 'wheat, corn, and oats. In the sales, he cleared 6 % on the wheat, and 3% on the corn, but lost 17 % on the oats; the whole amount received was $2336. What sum did he lay out in each kind of grain? Ans. $800.

APPLICATIONS OF PERCENTAGE.

454. The principal applications of Percentage, where time is not considered, are Commission, Stocks, Profit and Loss, Insurance, Taxes, and Duties. And since the five problems in Percentage involve all the essential relations of the parts or elements, we have for the above applications the following

GENERAL RULE. Note what elements of Percentage are given in the example, and what element is required; then apply the special rule for the corresponding case.

COMMISSION.

455. An Agent, Factor, or Broker, is a person who transacts business for another.

456. A Commission Merchant is an agent who buys and sells goods for another.

457. Commission is the fee or compensation of an agent, factor, or commission merchant.

458. A Consignment is a quantity of goods sent to one person to be sold on commission for another person.

459. A Consignee is a person who receives goods to sell for another; and

460. A Consignor is a person who sends goods to another to be sold.

461. The Net Proceeds of a sale or collection is the sum left, after deducting the commission and other charges.

NOTE. A person who is employed in establishing mercantile relations between others living at a distance from each other, is called the Correspondent of the party in whose behalf he acts. A correspondent is the agent of those whose custom or patronage he secures to the party in whose interest he is employed.

462. Commission is usually reckoned at a certain per cent. of the money involved in the transaction; hence we have the following relations:

I. Commission is percentage, (445).

II. The sum received by the agent as the price of property sold, or the sum invested by the agent in the purchase or exchange of property, is the base of commission, (446).

III. The sum remitted to an agent, and including both the purchase money and the agent's commission, is the amount, (447). IV. The sum due the employer or consignor as the net proceeds of a sale or collection, is the difference, (448).

EXAMPLES FOR PRACTICE.

1. My agent sells goods to the amount of $6250; what is his commission at 3% ?

OPERATION.

$6250 x .03 = $187.50

ANALYSIS. According to Prob. I, (449), we multiply the sum obtained for

the goods, $6250, which is the base of the commission, (II), by the rate of the commission, .03, and obtain the commission or percentage, $187.50.

2. A flour merchant remits to his agent in Chicago $3796, for the purchase of grain, after deducting the commission at 4 %; how much will the agent expend for his employer, and what will be his commission?

amount, (III), by 1 plus the rate of commission, or 1.04, and obtain the base of commission, $3650, which is the sum to be expended in the purchase. Subtracting this from the remittance, we have $146, the commission.

NOTE 1.-It is evident that the whole remittance, $3796, should not be taken as the base of commission; for that would be computing commission on commission. A person must charge commission only on what he expends or collects, in his capacity as agent.

3. A factor sold real estate on commission of 5 %, and returned to the owner, as the net proceeds, $8075; for what price did he sell the property, and what was his commission?

ANALYSIS. According to Prob. V, (453), we divide the net proceeds, $8075, which is difference, (IV), by 1 minus the rate of

commission, and obtain the base, $8500, which is the price of the property sold; whence by subtraction, we obtain the commission, $425.

4. An agent sold my house and lot for $8600; what was his commission at 21% ? Ans. $193.50. 5. A lawyer collects $750.75; what is his commission at 3 %? Ans. $28.15+. 6. My agent in New York has sold 3500 bushels of Indiana wheat @ $1.40, and 3600 bushels of dent corn @ $.74; what is his commission at 24 %?

7. A dealer in Philadelphia sells hides on commission of 8%, as follows: 2000 lb. Orinoco @ $.234, 5650 lb. Central American @ $.22, 450 lb. Texas @ $.23, and 650 lb. city slaughter @$.21; what does he receive for his services? Ans. $162.75.

8. A commission merchant sold a consignment of flour and pork for $25372. He charged $132 for storage, and 6 % commission; what were the net proceeds of the sale?

9. An agent for a Rochester nurseryman sells 4000 apple trees at $25 per hundred, 2000 pear trees at $50 per hundred, 1600 peach trees at $20 per hundred, 1800 cherry trees at $50 per hundred, and 500 plum trees at $50 per hundred; what is his commission at 30 %, and how much should he return to his employer as the net proceeds, after deducting $203.50 for expenses? Ans. Commission, $1041; Net proceeds, $2225.50. 10. A lawyer having a debt of $785 to collect, compromises for 82 %; what is his commission, at 5 %? Ans. $32.185.

11. I purchased in Chicago 4000 bushels of wheat @ $1.25, and shipped the same to my agent in Oswego, N. Y., who sold it @ $1.50; how much did I make, after paying expenses amounting to $415, and a commission of 3 %? Ans. $105.

12. An agent received $63 for collecting a debt of $1260; what was the rate of his commission?

Ans. 5 %.

13. My Charleston agent has charged $74.25 for purchasing 26400 lb. of rice at $4.50 per 100 lb.; required the rate of his commission.

14. A house and lot were sold for $7850, and the owner re

ceived $7732.25 as the net proceeds; what was the rate of commission?

15. A commission merchant in Boston having received 28000 lb. of Mobile cotton, effects a sale at $.12 per pound. After deducting $35.36 for freight and cartage, $10.50 for storage, and his commission, he remits to his employer $3252.89 as the net proceeds of the sale; at what rate did he charge commission? Ans. 5 %.

16. The net proceeds of a sale were $5635, the commission was $115; what was the rate of commission?

17. An agent received $22.40 for selling grain at a commission of 4%; what was the value of the grain sold? Ans. 560.

18. My attorney, in collecting a note for me at a commission of 8 %, received as his fee $6.80; what was the face of the note? 19. Sent to my agent in Boston $255, to be invested in French prints at $.15 per yard, after deducting his commission of 2 %; how many yards shall I receive? Ans. 1666.

20. John Kennedy, commission merchant, sells for Ladd & Co. 860 barrels of flour @ $7.50, on a commission of 2 %. He invests the proceeds in dry goods, after deducting his commission of 1% for purchasing; how many dollars' worth of goods do Ladd & Co. receive? Ans. $6195.81+.

21. A commission merchant, whose rate both for selling and investing is 5 %, receives 24000 lbs. of pork, worth 6 cents, and $3000 in cash, with instructions to invest in a shipment of cotton to London. What will be his entire commission? Ans. $280.

22. A speculator received $3290 as the net proceeds of a sale, after allowing a commission of 6%; what was the value of the property? Ans. $3500.

23. The net proceeds of a shipment of 500 tons of pressed hay, after deducting a commission of 3 %, and $500 for other charges, were $6290; what was the selling price per ton?

24. I send a quantity of dry goods into the country to be sold at auction, on commission of 9 %. What amount of goods must be sold, that my agent may buy produce with the avails, to the value of $3500, after retaining his purchase commission of 4 %?