for the article, and not on the selling price, or sum received, as it is often supposed. 17. A merchant bought a piece of cloth for $2.75 per yard, and sold it for $3.25. What per cent. did he gain? Solution. Since he gained 50 cents on a yard, his gain was of the cost. And 5.18 Ans. 18 per cent. 50 275 18. A boy purchased a book for 20 cents, and sold it for 30 cents: what per cent. did he make? 19. A merchant bought a box of sugar at 6 cents a pound, and sold it for 74 cents a pound: what per cent. was his profit? 20. A grocer bought eggs at 9 cents, and sold them for 12 cents per dozen: what per cent. was his profit ? 21. A man bought a hat for $4.50, and sold it for $6: what per cent did he gain? 22. A jockey bought a horse for $73, and sold him for $68 what per cent. did he lose? 23. A merchant bought a quantity of goods for $155.63, and sold them for $148.28: what per cent. did he lose? 24. A gentleman bought a house for $3500, and sold it for $150 more than he gave: what per cent. was his profit ? 25. A speculator laid out $7500 in land, and afterwards sold it for $10000: what per cent. did he make? 26. A drover bought a herd of cattle for $1175, and sold them for $1365: what per cent. did he gain? and how much did he make by the operation? 27. A merchant bought $10000 worth of wool, and sold it for $12362: what per cent. and how much was his profit? CASE IV. 28. A jockey sold a horse for $250, which was 25 per cent. more than it cost him: how much did he pay for the horse? Analysis. It will be observed that the selling price ($250) is equal to the cost and the amount gained added 25 1 100: together. Now considering the cost a unit or 1, the gain, which is a certain per cent. of the cost, (Art. 266,) is 100, consequently 1+25=125. (Art. 127,) will denote the sum of the cost and the gain. The question therefore resolves itself into this: 250 is 125 of what number? If 250 is 125 1 is 2; and 100 is 100 times 2, or 200. Or, we may simply divide 250 by the fraction 125. (Art. 141.) The quotient $200 is the cost required. 100, 100 100 100 PROOF.--$200 x .25 $50; and $200+$50-$250, the selling price. 29. A merchant sold a quantity of goods for $180, which was 10 per cent. less than cost: how much did the goods cost him? 100 100 Analysis. It will be observed that the selling price ($180) is equal to the cost diminished by the sum lost. Now reasoning as in the last example, 1-10 90 will denote the cost diminished by the loss. The question now is this: 180 is of what number? If 180 is 100, 100 is 2, and 100 is 200. Or thus: $180$200. Ans. 90 100 90 100 PROOF.-$200 ×.10-$20, and $200-$20-$180, the selling price. Hence, 270. To find the cost when the selling price and the per cent. gained or lost are given. Make the given per cent. added to or subtracted from 100 (as the case may be) the numerator, and 100 the denominator of a common fraction; then divide the selling price by this fraction; (Art. 141 ;) and the quotient will be the cost required. OBS. 1. It is not unfrequently supposed that if we find the percentage on the selling price at the given rate, and add the percentage thus found to, or subtract it from the selling price, (as the case may be,) the sum or remainder will be the cost. This is a mistake, and leads QUEST.-270. How is the cost found, when the selling price and the rate per cent. gained or lost, are given? Obs. What mistake is sometimes made in finding the cost? How may it be avoided? to serious errors in the result. It will be easily avoided by remembering, that the basis on which profit and loss are calculated, is always the purchase price, or sum paid for the articles under consideration. (Art. 269. Obs. 2.) 30. A grocer sold a hogshead of molasses for $24, and gained 20 per cent. on the cost: what was the cost of the molasses? 31. A merchant sold a piece of broadcloth for $85, which was 10 per cent. less than cost: what was the cost of it? 32. A butcher sold a yoke of oxen for $125, and thereby made 15 per cent.: how much did they cost him? 33. A bookseller sold a lot of books for $200, which was 12 per cent. more than cost: what was the cost? 34. A wholesale druggist sold a quantity of medicines for $560, and made 50 per cent. profit on them: what was the cost of them? 35. A merchant bought a cargo of rice for $1500, which was 12 per cent. less than cost: what was the cost? EXAMPLES FOR PRACTICE. 1. A merchant bought 25 boxes of raisins for $45: at what price per box must he retail them to gain 10 per cent. by his bargain? more than the cost. Suggestion. He must sell the whole for 10 per cent. Hence, if we add 10 per cent. to the cost, and divide the sum by the number of boxes, it will give the retail price per box. (Art. 217.) 2. A shopkeeper bought a piece of cotton containing 40 yards, at 6 cents a yard, and sold it for 7 cents a yard what per cent. profit did he gain, and how much did he make by the bargain? 3. A merchant bought 60 yards of domestic flannel at 25 cents per yard, and sold it at 30 cents per yard: what per cent. was his profit, and how much did he clear by the operation? 4. A bookseller bought 100 Arithmetics at 31 cents apiece, and retailed them at 37 cents apiece: what per cent. and how much did he make by the operation. 5. A drover bought 175 sheep for $350, and sold them so as to gain 15 per cent.: how much did he sell them for per head? 6. A baker paid $2500 for 480 barrels of flour, and finding it damaged sold it at a loss of 8 per cent.: how much did he sell if for per barrel? 7. A merchant bought 10 pieces of broadcloth, each piece containing 30 yards, for $1400, and retailed the whole at a profit of 20 per cent. : at what price did he sell it per yard? 8. A grocer bought 500 lbs. of butter for $75, and sold it at a loss of 7 per cent.: how much did he get per pound? 9. A merchant bought 12 hogsheads of molasses at 25 cents per gallon: how must he sell it by the gallon in order to gain 20 per cent.; and how much was his profit? 10. A farmer raises 750 bushels of wheat at an expense of $675: how must he sell it per bushel, in order to make 18 per cent.? 11. A provision merchant bought 1500 barrels of pork at $10.25 per barrel, and sold it at a loss of 9 per cent. : how much did he lose, and what did he get per barrel? 12. An inn-keeper bought 150 bushels of oats at 25 cents a bushel, and retailed them at the rate of 12 cents a peck: what per cent., and how much did he make on the oats? 13. A miller bought 500 bushels of wheat at 75 cents per bushel how much must he sell the whole for in order to gain 20 per cent.? 14. A grocer bought 1630 pounds of tea at 62 cents per pound, and sold it at 10 per cent. loss: how much did he sell it at per pound? 15. A merchant bought a bale of calico prints containing 750 yards, and paid $75: how must he retail it per yard, in order to gain 20 per cent., and how much did he make on a yard? 16. A book-seller purchased 1000 geographies, at 84 cents apiece how must he retail them to gain 20 per cent. ? 17. A milliner bought 1200 yards of ribbon at 30 cents per yard: how must she sell it per yard to gain 50 per cent.? 18. A grocer bought 5000 lbs. of sugar for $350, and retailed it at 6 cents per pound: what per cent. loss did he sustain ? 19. A man purchased goods amounting to $1635: what percent. profit must he gain, in order to make $350 ? 20. A speculator bought 10000 acres of land for $12500, and afterwards sold it at 25 per cent. loss: for how much per acre did he sell it; and how much did he lose by the operation? DUTIES. 271. The term Duty in commerce signifies a sum of money required by Government to be paid on imported goods. Duties are of two kinds, specific and ad valorem. A specific duty is a certain sum imposed on a ton, hundred weight, hogshead, gallon, square yard, foot, &c. without regard to the value of the article. Ad valorem duties are those which are imposed on goods at a certain per cent. on their value or purchase price. OBS. The term ad valorem is a Latin phrase, signifying according to, or upon the value. 272. Before specific duties are imposed, it is customary to make certain deductions called tare, draft, or tret, leakage, &c. Tare, in commerce, is an allowance of a certain QUEST.-271. What are duties in commerce? How many kinds are they? What are specific duties? Ad valorem duties? Obs. What is the meaning of the term ad valorem? 272. What deductions are made before specific duties are imposed? What is tare? Draft or tret? Leak age? |