562. To find the Rate of Profit or Loss, the Cost and the Profit or Loss being given. EXAMPLE. -An agent gained $17.10 by selling a reaper which cost him $95. What was his per cent. of gain ? OPERATION. Cost. Gain. $95 ) 17.10 (.18 = 18% EXPLANATION.-If 95 dollars of cost gain $17,10, 1 dollar of 95 cost would gain as much as 95 is contained times in 17.10, or .18, 760 equal to 18 per cent, 760 Rule.- Divide the profit or loss by the cost. Formula.—Per Cent. of Profit or Loss = Profit or Loss ; Cost. EXAMPLES FOR MENTAL PRACTICE. 563. 1. I gained $12.50 on what cost me $125. Find my cent. of gain. 2. I bought a bicycle for $150, and sold it for $7.50 below cost. What per cent. did I lose? 3. What per cent. is lost by selling a $5 book at 6214 below its cost? 4. A safe costing $380 was sold at a loss of $76. Find the loss per cent. 5. A gold pen cost $2, and after being tested and found imperfect, was sold as old gold for $1. Find the per cent. of loss. 6. What per cent. of gain is realized by buying a horse for $300, and selling it at an advance of $100? 7. Find the per cent. of gain on a section of Dakota prairie, bought at $4 per acre, and sold at $10 per acre. 8. An Ohio river steamer costing $100000 was sold for $9500 profit. Find the per cent. of profit. 9. A Vermont manufacturer, having invested $40000, gained $8250 each year. What was his per cent. of gain per annum? EXAMPLES FOR WRITTEN PRACTICE. 564. 1. What per cent. is gained by selling an article for 24 times its cost? 2. I bought a quantity of cloth at $1.60 per yard, and sold it at $2 per yard. What was my per cent. of gain? 3. A speculator bought wheat at 804 per bushel, and oats at 32¢ per bushel. If he sold the wheat at 90€ per bushel, and the oats at 404 per bushel, on which would he make the greater per cent., and how much? 4. If a boy sells three apples for what four cost him, what per cent. does he gain? 5. Four-fifths of a stock was sold at 45% loss, and the remainder at 225% profit. What was the per cent. of net loss or net gain on the stock? 6. Paper bought at $2.70 per ream, and retailed at 1¢ per sheet, will yield what per cent. of profit? 7. Potatoes costing $1.35 per barrel, and sold at $1.62 per barrel, will net what per cent. of gain? 8. A wood dealer, after buying 8 car loads of mixed wood, of 16 cords each, at $5 per cord, sorted it and sold 35% of it at 12% gain, 35% of it at 10% gain, and the remainder at 20% gain? What was his average per cent. of gain? lf 331% of a barrel of salt be sold at 33% profit, and the remainder be sold at cost, what per cent. of profit is realized on the whole? 10. An agent sold a sewing machine for $45.70, and thereby gained $18.28. What per cent. did he gain? If of an article is sold for what of it cost, what is the loss per cent. ? 12. If I sell \ of an article for what 1 of it cost, what is my rate of gain? 13. A drover, buying 125 beeves at the rate o. $55 per head, and 78 at $62.50 per head, sold the lot at a profit of $2115. What was his per cent. of gain? 14. A cargo of lumber cost $3600. If į of it is sold for $2000, { of the remainder for $1250, and what is left for $420, what is the per cent. of gain or loss by the transaction? 15. Oil bought at 814¢ per barrel is sold at 8614. If & per barrel is allowed for expenses, what must have been the investment, the gain having been $1350? 565. To find the Cost, the Selling Price and the Rate per cent. of Profit or Loss being given. Rules.-1. Divide the selling price by 1 plus the rate of gain. Or, 2. Divide the selling price by 1 minus the rate of loss. a. + Formulas. — {6. Cost = Selling Price + 1 = Per Cent. of Loss. EXAMPLES FOR MENTAL PRACTICE. 566. 1. A buggy was sold for $105, at a gain of 5%. What the the cost? 2. What must have been the cost of a harness sold at 40% loss, if $24 were received for it? 3. Find the cost of making a suit of clothes, if 20% is gained by selling it at $18. 4. Find the cost of a watch that sold at a profit of 163% and brought $87.50. 5. I sold a house for 125% profit, receiving therefor $2250. What was the price paid? 6. If $15360 is realized on a stock of goods after it has been damaged 40% · what was its value before being damaged? EXAMPLES FOR WRITTEN PRACTICE. 567. 1. One of a pair of horses was sold for $180, at a loss of 12}%; the other was sold for $200, at a gain of 25%. What did the pair cost? 2. A fruit dealer, after losing163%of his apples by frost, has 1471 barrels left. If he bought his stock at $2.50 per barrel, what was his outlay? 3. What was the original value of Calumet copper mining stock, which, when sold at a gain of 175%, brought $20625? 178 REVIEW OF THE PRINCIPLES OF PROFIT AND LOSS. 4. A paid 6% tax on his income. What was his income, if, after paying the tax, the remainder equalled $7050.94. 5. A dairy produced 20% more cheese in March than in February. What was the product for March, if that for the two months was 1980 pounds? 6. I sold a house to A at a profit of 10%; he sold it to B, gaining 15%; and B, by selling it to C for $6072, gained 20% on his purchase. How much did the house cost me? REVIEW OF THE PRINCIPLES OF PROFIT AND LOSS. 568. 1. To find the gair, the cost and per cent. of gain being given. RULE.- Multiply the cost by the per cent. of gain. 2. To find the loss, the cost and per cent. of loss being given. RULE.— Multiply the cost by the per cent. of loss. 3. To find the selling price, the cost and gain being given. RULE.—Add the gain to the cost. 4. To find the selling price, the cost and loss being given. RULE.—Subtract the loss from the cost. 5. To find the cost, the gain and per cent. of gain being given. RULE.— Divide the gain by the per cent. of gain. 6. To find the cost, the loss and per cent. of loss being given. RULE. —Divide the loss by the per cent. of loss. . To find the selling price, the gain and per cent. of gain being given. RULE.—Divide the gain by the per cent. of gain, and to the quotient add the gain. 8. To find the selling price, the loss and per cent. of loss being given. RULE.—Divide the loss by the per cent. of loss, and from the quotient subtract the loss. 9. To find the per cent. of gain, the gain and cost being given. RULE. — Divide the gain by the cost. To find the per cent. of loss, the loss and cost being given. RULE.—Divide the loss by the cost. 11. To find the per cent. of gain, the selling price and gain being given. RULE.—Subtract the gain from the selling price and divide the gain by the difference. 12. To find the per cent. of loss, the selling price and loss being given. RULE. — Add the loss to the selling price, and divide the loss by the sum obtained. MISCELLANEOUS EXALIPLES. 569. 1. What is that sum of money of which 50% is $19.20 more than 374%? 2. What amount of money must an attorney collect, in order that he may pay over to his principal $475, and retain 5% for his services? 3. A woman is 72 years old, and 103% of her age is 25% of the age of her daughter. Find the daughter's age. 4. Gunpowder is made of nitre, and the remainder of equal parts of sulphur and charcoal. Find the per cent. of each. MISCELLANEOUS EXAMPLES IN PROFIT AND LOSS. 179 5. A milkman increased his herd of cows by a purchase of 36, which was 45% of the whole number he then owned. How many had he before buying the last lot? 6. If I make a profit of 16}% by selling a horse at $7.50 above cost, how much must I have advanced on the cost to have realized a profit of 25%? 7. Two persons contributed $2100 towards a business venture, from which their part of the gain was $350. If of this gain the share of one was $70 more than that of the other, what part of the original contribution must have been made by each ? 8. How much money must be invested in notes, at 45% below their face value, in order that, when sold at 3% above their face, a profit of $225 may be realized ? 9. I bought a warehouse of Brown for 12% less than it cost him, and sold it for 16%% more than it cost him, gaining thereby $963.60. How much did I pay for the warehouse ? 10. What per cent. is gained by buying pork at $17.50 per barrel, and retailing it at 12¢ per pound ? 11. A lady wishing to sell her piano, asked 15% more than it cost, but finally sold it at 12% less than her asking price. What did the piano cost, if by its sale she gained $5 ? 12. Having bought 75 barrels of apples for $187.50, I sold them at a loss of 20%. How much did I receive per barrel ? 13. A sells a steam tug to B, gaining 12%, and B sells it to C for $4130, and makes a profit of 18%. How much did the tug cost A ? 14. What per cent. is lost on an article that is sold for two-thirds of its cost ? A farmer, after selling 1760 barrels of apples, had 20% of his crop left. . How many barrels had he at first? 16. I lost 25% of a consignment of berries. At what per cent. of profit must the remainder be sold, in order that I may gain 10% on the whole ? 17. A Texas farm of 160 acres was bought at $15 per acre; $354 were paid for fencing, $480 for breaking, $626 for a house, and $220 for a barn. At what price per acre must it be sold, to realize a net profit of 25% on the investment ? 18. King sold his wheel at 33% gain, and with the money bought another, which he sold at a loss of 25%, receiving therefor $120. Did he gain or lose, and how much ? 19. What per cent. more is } than ? 20. Cloth, bought at $4 per yard, must be marked at what price in order that the seller may make a reduction of 10% from the asking price and still gain 12% on the cost ? 21. If 25% of the selling price is gain, what is the per cent. of gain ? 22. I sell of a stock of goods for $27, thereby losing 20%. For what must I sell the remainder, to make a profit of 20% on the whole ? 23. If 30% of a farm sold at 33% gain, and 30% of the remainder at 15% gain, how much was the total gain, if the remainder was sold at cost for $7350 ? 24. What per cent. of cost is realized on goods marked 25% advance and sold at 20% off from the marked price ? 15. 180 MISCELLANEOUS EXAMPLES IN PROFIT AND LOSS. 25. A banker bought a mortgage at 71% less than its face value, and sold it for 3% more than its face value, thereby gaining $981.75. What was the face value of the mortgage ? 26. At what price should damaged goods be marked to lose 25%, the first cost having been 364 per yard ? 27. A man sold a carriage and gained 25%, and with the proceeds bought another, which he sold at a profit of 10%, thus realizing a total gain of $75. What did he pay for each ? 28. If I sell of an acre of land for what 5 of it cost, what will be my gain or loss per cent. ? 29. 21% was lost by selling an engine for $2355. How much would it have brought had it been sold at a loss of 10%? 30. What price must be asked for 1000 pounds of coffee, costing 18¢ per pound, in order that the seller may deduct 10% from the asking price for bad debts, allow 10% for loss in roasting, and still gain 20% on the cost? 31. B and C each invested an equal amount of money in business; B gained 123% on his investment, and C lost $5275 ; C's money was then 42% of B’s. How many dollars did each invest? 32. A trader lost 33% on 20% of an investment, and gained 124% on the remainder, thus realizing a net gain of $1000. Had he gained 20% on }, and lost 25% on the remainder, what would have been his net profit ? 33. A manufacturing company's per cent. of gain on a self-binder was 25% less than that of the general agent; the general agent's profit was 20%, he thereby gaining $25.30. What did it cost to make the machine ? 34. Of a cargo of 8000 bushels of oats, costing 350 per bushel, 25% was destroyed by fire. What per cent. will be gained or lost, if the remainder of the oats are sold at 45° per bushel ? 35 For what must hay be sold per ton, to gain 16%, if, by selling it at $18 per ton, there is a gain of 25% ? 36. Jones sold } of a stock of goods at cost, 4 at a gain of 35%, at a loss of 25%, and go at a gain of 10%. At what per cent. of its cost must he sell the remainder to net cost on the whole ? 37. After a carriage had been used two years, it was sold for $5 less than it cost, the seller thereby sustaining a loss of 3% of the selling price. How much was the first cost of the carriage ? 38. If oranges cost $1.80 per hundred, at what price must they be marked to ensure a gain of 20%, and make allowance for 28% decay, and 25% bad debts in selling? 39. IIaving paid 40% per pound for tea, at what retail price must it be marked, that I may allow 12% for bad debts and gain 40% on the cost ? 40. Six wheel-rakes were sold for $21 each; three of them at a gain of 20%, and the others at a loss of 20%. What was the net gain or loss ? 41. A stock of goods is marked 22% advance on cost, but becoming damaged, is sold at 20% discount on the marked price, whereby a loss of $1186.40 is sustained. What was the cost of the goods ? |