13. A sold two city lots, which cost the same price, to B, at a loss of 15%; B sold them to C, gaining 20% on one, and losing 25% on the other; what did each cost A, if B received $765 more for one than the other? Ans. $2000. 14. Mr. Brown bought a horse and carriage, the horse costing twice as much as the carriage, but afterwards sold the carriage for 331% more, and the horse for 10% less than he gave, and received for both $705; what was the cost of each? Ans. Carriage, $225; horse, $450. 15. Mr. Oakley, when stocking his farm, spent equal sums in cows, sheep, and hogs; on the sale of which he made 2% on the cows, lost 9% on the sheep, and gained 121% on the hogs; if he received for all $1833, and bought 120 sheep, 15 cows, and 150 hogs, what did he pay per head? Ans. Sheep, $5; cows, $40; hogs, $4. 16. A man invested a certain sum in several different stocks; on of his investment he gained 25%, and on the remainder lost 15%; his whole profit was $260; had he gained 15% on 1⁄2 and lost 25% on the remainder, would he have gained or lost, and how much? Ans. Lost $100. CASE III. 530. Given, the cost and the profit or loss, or the selling price, to find the rate. 1. A man bought a boat for $560, and sold it at a gain of $140; what was the gain per cent.? SOLUTION. Since $560, the base, multiplied by the rate, equals $140, the rate must equal $140 divided by $560, which we find to be .25, or 25%. OPERATION. $140 $560.25 Rule I.-Divide the profit or loss by the cost, to find the rate. Rule II.-Divide the difference between the cost and the selling price by the cost, to find the rate. 2. Calico was bought at 183 cents a yard, and sold for 25 cents a yard; what was the gain per cent.? Ans. 33%. 3. If I buy at 10% off and sell at 15% on, what % profit do I make? what if I buy at 20% off and sell at 20% on? Ans. 27%; 50%. 4. I marked calicoes 15 and sold them at 121; what do I lose per cent., if I marked them 20% above cost? 5. A street car fare in Philadelphia was 7 cents, but 4 tickets were sold for a "quarter;" what per cent. did I save by buying a package? Ans. 10%. 6. If of the cost equals the selling price, what is the loss per cent.; and if of the selling price equals the cost, what is the gain per cent.? Ans. Loss, 16%; gain, 20%. 7. A grocer bought melons for 25% more than 12 cents each, and sold them for 25% less than 12 cents each; what was the loss per cent.? Ans. 40%. 8. A farm was offered for sale at 25% advance on its cost, but finding no purchasers at that price, it was finally sold at 25% less than was first asked; what was the gain or loss per cent.? Ans. Loss, 61%. 9. I marked plaid Nainsooks 621, and gained at that rate 25%; if I sell them for 6 cents more than the marked price, what is my gain per cent.? Ans. 37%. 10. Mr. Walker was offered $3500 for his house, but declined to sell, as he would thereby lose 121%; a few months later he sold for $4800; did he gain or lose, and what per cent.? Ans. Gained 20%. 11. Mr. Fawcett bought a quantity of broadcloth @ $5.25, and marked it r.bw, his key being "be smart now;" what was the gain per cent. at the marked price? Ans. 16%. 12. Mr. Howard bought 25 building lots for $11250 and sold 20 of them for what he paid for all of them; what was his gain per cent. on the investment? Ans. 25%. 13. Miss Martin sold her diamond breastpin for $560, and thereby cleared 121% of this money; what would she have gained per cent. by selling it for $600? Ans. 2233%. 14. Mr. Bechtel sacrificed 37% on his library by selling it for $1500; if he had sold it for 20% more than he did, what would he have lost per cent.? Ans. 25%.. 15. If a druggist gives me a lb. Troy of washing soda instead of a lb. Avoirdupois, what is my loss and his gain per cent.? Ans. Loss, 17%; gain, 21%. 16. I ride on two street railway lines, making exchanges, and get an exchange ticket for 9 cents; what per cent. more would it cost to use a ticket on each car, and what per cent. more to pay single fares? Ans. 388%; 555%. 17. A news agent bought 50 copies N. Y. Tribune, and 60 copies N. Y. Herald @31, sold @ 4; 50 Harpers' Weekly at 7, sold @ 10, 12 Independent @ 6, sold @ 10; 12 Lippincott's Magazine @ 274, sold @35; 8 Harpers' Magazine @28, sold @ 35; what was the average per cent. of profit? Ans. 29137%. COMMISSION. 531. Commission is a percentage paid to a commission merchant, agent, or factor, for the transaction of business. 532. A Commission Merchant, Agent, or Factor, is a person who transacts business for another. 533. The Base in commission is the actual amount of the sale, purchase, collection, or exchange. 534. The Net Proceeds is the sum left after the commission and charges have been deducted from the amount of a sale or collection. 535. The Entire Cost is the sum obtained by adding the commission and charges to the amount of a purchase. 536. The Quantities considered are: 1. The Amount sold, bought, etc.; 2. The Rate of Commission; 3. The Commission; 4. The Entire Cost or Net Proceeds. The goods forwarded to be sold on commission are called a consignment; the person sending them is called the consignor; and the person to whom they are sent, the consignee, or factor. An agent residing at a great distance from his employer, is often called a correspondent; the person for whom an agent does business is called the principal. CASE I. 537. Given, the base and the rate, to find the commission, or the net proceeds, or the entire cost. 1. An agent sold goods to the amount of $2560; required his commission at 21%. SOLUTION.-The commission is .024 times $2560, which equals $57.60. OPERATION. $2560×.02 $57.60 = Rule I.-Multiply the base by the rate, to find the commission. Rule II-Multiply the base by 1 minus the rate, to find the net proceeds; or by 1 plus the rate, to find the entire cost. 2. I sold on commission 540 barrels of flour, @ $8.25, and 75 barrels of cider, 35 gallons each, @ 37 cents; what is my commission at 21% ? Ans. $135.98. collect, compro 3. A lawyer, having a debt of $6500 to mises for 97%; his commission is 21%; how much does he remit to his employer? Ans. $6194.91. 4. A speculator sells $7452.50 worth of dry goods through a factor who charges 21% commission and 21% for insuring payment; what does the factor remit? Ans. $7079.871. 5. An agent sold a consignment of flour for $5657.25, and afterward bought 2500 bushels of grain at 87 a bushel; his commission is 24%; what sum did he remit to his employer? Ans. $3306.02. 6. I sell on commission 1500 bushels of clover seed @ 75, through an agent to whom I pay 14%; how much do I clear, my commission being 24% ? Ans. $14.06. 7. Frantz, Herr & Co. bought 600 tons of railroad iron at $30 a ton, through their agent in Pittsburgh, and shipped it to Omaha, where it was sold by an agent at $38 a ton; how much did they clear, transportation costing $250, and commission being 21% ? Ans. $3632. 8. An agent bought 580 yards of woolen goods at an average price of 75g a yard; paid $50 storage and $25 transportation, and sold it for $1 a yard; how much should he remit to his principal, commission 21% ? Ans. $47.16. CASE II. 538. Given, the rate and the commission or the net proceeds or the entire cost, to find the base. 1. An agent's commission in one year for collecting money at 31% is $2600; how much did he collect? SOLUTION. At a commission of 31%, .031 times the cost of the goods equals the commission, which is $2600; hence the cost equals $2600 divided by .031, which we find is $80,000. OPERATION. $2600 = $80,000 Rule I. Divide the commission by the rate, to find the base. Rule II.-Divide the net proceeds by 1 minus the rate, or the entire cost by 1 plus the rate, to find the base. 2. An agent bought 2400 bu. of wheat, his commission at 2% was $68.75, and charges for storage, freight, etc., $191.25; what was the actual cost a bushel? Ans. $1.15. 3. A lawyer collects a debt for a client, takes 31% for his fee, and remits the balance, $19,350; what was the debt and fee? Ans. Debt, $20,000; fee, $650. 4. An agent buys goods on commission at 11%, and pays $35 for freight; the whole amount was $4080; what was the amount expended? Ans. $4000. 5. Sold 200 barrels of pork, commission 21%, guaranty 15%, net proceeds due consignor, $2876.25; ceive per barrel for the pork? what did I re Ans. $15. 6. My agent bought 40 horses, and paid $105 for their transportation, which, with his commission, 31%, amounted to $6315; what did the horses cost apiece? Ans. $150. 7. I sent orders to my agent to buy a certain quantity of woolen goods, allowing him 21% commission and paying 14% for delaying payment a month; his bill was $2898; how many yards did he buy at $1.12 a yard? Ans. 2500 yd. 8. I sold a consignment of cotton, commission 4%; invested the net proceeds in flour, commission 2%; my whole commission was $180; required the value of the cotton and flour. Ans. Cotton, $3060; flour, $2880. 9. I sold a consignment of grain and invested the proceeds in sugar, deducting my commissions, 41% for selling and 21% for buying; the sugar cost $7640; what did the grain sell for, and what were my commissions? Ans. Grain, $8200; 1st com. $369; 2d com. $191. 10. I sold a consignment of goods through a factor who charged me 11%; I was allowed 21% commission and 34% for insuring payment, and I cleared $68; what was my commission and the sum remitted to the consignors? Ans. Sum remitted, $1512; com., $88. |