5. My crop of wheat this year is 8 % greater than my crop of last year, and I have raised during the two years 5200 bushels; what was my last year's crop ? Ans. 2500 bu. Note 2. — 1.00 + 1.08 = 2.08. Hence, 5200 bu. = 2.08 % of last year's crop. 6. The net profits of a nursery in two years were $6970, and the profits the second year were 5 % greater than the profits the first year; what were the profits each year? Ans. 1st year, $3400; 2d year, $3570. 7. If a number be increased 8 %, and the amount be increased 7%, the result will be 86.67; required the numbez. 173 Note 3. - The whole amount will be 1.08 X 1.07 = 1.155€ times the original number. 8. A produce dealer bought grain by measure, and sold it by weight, thereby gaining 13 % in the number of bushels. He sold at a price 5 % above his buying price, and received $4910.976 for the grain; required the cost. Ans. $4608. 9. B has 6 %, and C 4 % more money than A, and they all have $11160; how much money has A ? Ans. $3600. 10. In the erection of a house I paid twice as much for material as for labor. Had I paid 6 % more for material, and 9 % more for labor, my house would have cost $1284; what was its cost ? Ans. $1200. PROBLEM V. OPERATION. be di 453. Given, the difference and rate, to find the base. 1. What number diminished by 5% of itself, is equal to 342? ANALYSIS. If any number 14.05 = .95 minished by 5% of itself, the dif342 : .95 360, Ans. ference will be .95 of the number. Or, We therefore divide the given differ1 ence, 342, by .95, or jó, and obtain 342 360, Ans. the base, 360, which is the required number. Hence the RULE. Divide the difference by 1 minus the rate. NOTE.-The difference is always a product, of which the base is one factor, and 1 minus the rate the other. 19 1 20 19 20 4 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 $1.37; what is the base ? 3. After taking away 15 % of a heap of grain, there remained 40 bu. 33 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 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. duced 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? SA, $80. Ans. 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. army? A then re 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 %? ANALYSIS. According to $6250 x .03 = $187.50 Prob. I, (449), we multi ply 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 percent OPERATION. age, $187.50. OPERATION. 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 ? ANALYSIS. Ac. 1.00 +.04 = 1.04 cording to Prob. $3796 - 1.01 = $3650, for grain, IV, (452), we di$3796 — $3650 = $146, commission. vide the remittance, $3796, which is 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 1.00 —.05 = .95 Prob. V, (453), we divide $8075 : .95 = $8500, price. the net proceeds, $8075, $8500 – $8075 = $425, com. which is difference, (IV), hy 1 minus the rate of OPERATION. commission, and obtain the base, $8500, which is the price of the property sold; whence by subiraction, 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 33 %? 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 2 %? 7. A dealer in Philadelphia sells hides on commission of 81 %, as follows: 2000 lb. Orinoco @ $.233, 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 $115, 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 26100 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 |