mar. 7. 36 bushels is what per cent. of 48 bushels ? Ans. 75 per cent. 8. What per cent. of 4 years is 1 year 6 months ? 9. 31 gallons 2 quarts is what per cent. of 1 hogshead ? Ans. 50 per cent. 10. Of 160 yards of cloth there have been sold 128 yards; what per cent. of the whole remains unsold ? Ans. 20 per cent. 11. What per cent. of } of of is f? Ans. 20 per cent. 12. In a certain school the number of pupils studying geography is 40 per cent. more than the number studying gram What per cent. less is the number studying grammar than the number studying geography ? Ans. 284 per cent. 13. If a miller takes out 4 quarts toll from every bushel he grinds, what per cent. does he take for toll ? 14. If a certain coin is made of 22 parts copper and 3 parts nickel, what per cent. of it is copper, and what percent. nickel? Ans. 88 per cent. copper ; 12 per cent. nickel. 15. In a certain orchard there are 250 trees, of which 40 per cent. are apple-trees, 12 per cent. cherry-trees, 8 per cent. plum-trees, and the remainder, with the exception of 25 peartrees, consist of peach-trees. What per cent. of the whole are the peach-trees ? Ans. 30 per cent. 349. To find a number when a given number is known to be a certain per cent. of it. Ex. 1. I have bought two house-lots ; for the one I paid $ 300, which was 60 per cent. of what I paid for the other. What did I pay Ans. $ 500. Since $ 300 $ 300 ; 60 $ 5 ; $ 5 x 100 = $ 500, Ans. is 60 per cent. of the unknown 5 sum, 1 per $3$ø x 100 cent. it Or, must equal to 69 of $ 300, or and 100 per cent., or the whole of it, must equal 100 times $ 5, or $ 500, Ans. And since the question is evidently the same as to find the value of 1600 of $ 300, we multiply the $ 300 by 100, and divide by 60, and obtain the same result as before. RULE. Annex two ciphers to the number denoting the percentage, and divide by that denoting the rate per cent. Or, OPERATION. = $ 500. of $ 5; As the given rate per cent. is to 100 per cent., so is the given percentage to the basis of percentage required. EXAMPLES. Ans. 26 2. 25 is 10 per cent. of what number? Ans. 250. 3. 164 is 8 per cent. of what number? Ans. 2035 4. 72 is 12 per cent. of what number? 5. } is 40 per cent. of what number? 6. $1.621 is 127 per cent. of how many dollars ? Ans. $13. 7. $ 140 is š per cent. of what sum ? Ans. $ 140. 8. A flock of sheep has lost 15} per cent. of its number, 17 sheep having been killed by the dogs, and 6 more having been drowned. What was the original number? Ans. 150. 9. If a man owning 45 per cent. of a mill should sell 33} per cent. of his share for $ 450, what would be the value of the whole mill? 10. 123 per cent. of the length of a certain railroad is equal to 3m. lfur. 1rd. What is its entire length ? Ans. 25m. Ofur. 8rd. 11. Gave to a benevolent society 19 bushels of corn, which was 174 per cent. of all I raised. How many bushels had I left ? Ans. 916 bushels. 12. Dalton says to Turner, $ 36.89 is 137 per cent of the sum you borrowed of me; and Turner replies, It is just 16% per cent. of the amount I have repaid you. How much of the money that was borrowed remains unpaid ? Ans. $ 57.66. 350. To find the number on which the percentage is reckoned, when the amount, or the remainder, and the rate per cent. are given. Ex. 1. Sold a horse for $ 200, which was 25 per cent. more than he cost. What did he cost ? Ans. $ 160. OPERATION. Since the 1+.25 = 1.25 ; $ 200 = 1.25 $ 160, Ans. $ 200 is ev idently the cost and 25 per cent. of the cost, it must equal the cost taken 1 25 times. Therefore, the given amount, $ 200, divided by 1 increased by .25, or the given per cent. expressed decimally, equals $ 160, the basis of percentage required. OPERATION. 2. Sold 160 cords of wood, which was 20 per cent. less than the whole number owned. How many cords were owned ? Ans. 200 cords. Since the 1 .20 = .80; 160 = .80 = 200 cords, Ans. 160 cords are 20 per cent. less than the whole number owned, it must equal the whole number of cords taken .80 times. Therefore the given remainder, 160 cords, divided by 1 decreased by .20, or the given per cent. expressed decimally, equals 200 cords, the basis of percentage required. Rule. Divide the given amount by 1 increased by the given per cent., or the given remainder by 1 decreased by the given per cent., ed pressed decimally. Or, As 1 increased by the given per cent., or 1 decreased by the given per cent., expressed decimally, is to 1, so is the given amount or the given remainder to the basis of percentage required. EXAMPLES. 3. 126 is 5 per cent, more than what number? Ans. 120. 4. 3281 is 10 per cent. less than what number? Ans. 365. 5. $ 19.50 is 7 per cent. less than how many dollars? 6. $ 34.40 is & per cent more than how many dollars ? Ans. $34.2707 7. A man expends in a week $ 24, which exceeds by 334 per cent. his earnings in the same time. What were the earnings? Ans. $ 18. 8. D. Chandler lives distant from the village 2m. 6fur. 24rd., which is 124 per cent. nearer than is J. Mitchel's residence. At what distance does Mitchel live from the village ? Ans. 3m. lfur. 33/rd. 9. Bought a carriage for $ 123.16, which was 16 per cent. less than I paid for a horse. How much was paid for the horse ? 10. A carpet having been cut from a piece of carpeting, there were left hyd. 11oqr., which was 75 per cent. less than the quantity cut off. How many yards were there in the piece at first ? Ans. 31yd. lqr. 2na. 11. A steamer with a cargo of flour, having been lightened, during a storm, of 10 per cent. of her freight, at the end of the voyage had but 279 barrels to deliver. How many barrels were taken aboard, and how many were lost? Ans. Taken 310 barrels; lost 31 barrels. 12. A and B each received the same sum. A spent 86.4 per cent. of his money for land, and B lost of it by gambling as much as would equal 274 per cent. of what both received. They then together had left just $ 36.851. What was the sum received by each, and how much had each left ? Ans. Each received $ 63 ; A had left $ 8.50; and B had left $ 28.35. MISCELLANEOUS EXAMPLES. 1. What is 7 per cent. of 1672 ? Ans. 1172's: 2. What is 5} per cent. of $ 3266 ? Ans. 17475 Ans. 270 Ans. 3165 6. } is what per cent. of 16 ? Ans. 40. 7. Find what per cent. 3.50 is of 50. 8. 13 is 16 per cent. of what number? Ans. 814 9. $ 66 is 100 per cent. of what number? Ans. $ 66. 10. } is 6} per cent. of what number? Ans. 53. 11. $ 21.284 is 31 per cent. less than what sum? Ans. $ 22.00. 12. 191b. 12oz. is 164 per cent. of how many pounds? Ans. 11784 pounds. 13. A grocer bought 6 boxes of eggs, each containing 30 dozen, and found that 15 per cent. of the whole were bad ; how many eggs did he lose ? 14. There is paid for sawing a cord of wood $ 0.69, which is 12 per cent. of the cost of the wood. What did the wood cost ? 15. Three men agreed to excavate 40500 cubic feet of earth; by the first week's labor they excavate 200 cubic yards; by the second, 6000 cubic feet; and by the third, 25 per cent. of what remained at the end of the second week. They then called the work half done; but how many cubic feet did the job lack of being half completed ? Ans. 1575 cubic feet. Ans. 324 eggs. 16, 25 per cent. of 1 of a ship is how many per cent of 1 of it? Ans. 167 per cent. 17. If molasses cost 20 per cent. less than $ 0.50 per gallon, and it be sold at 25 per cent. more per gallon than it cost, at what price is it sold ? Ans. $0 50 per gal. 18. I have 20 yards of yard-wide cloth, which will shrink on sponging 4 per cent. in the length, and 5 per cent. in the width; how much less than 20 square yards will there be of it after sponging ? Ans. 135 yards. 19. A gentleman having a large farm gave 15 per cent. of it to his oldest daughter, 10 per cent. of what remained and is of an acre he gave to his oldest son, and 25 per cent. of the remainder he gave to his wife. The residue he divided equally among his other 5 children, who received each 39 acres. How many acres did his farm contain ? Ans. 340 acres. 20. If the population of the United States in 1858 be 30,500,000, what will it be in 1868, allowing the increase should be at the rate of 34.1 per cent. ? 21. In a certain battle in which the English, French, and Turks were allied against the Russians, there were 33} per cent. more French than English, and the Turks were 8} per cent. more than the French and 1600 more than the English. Required the whole number of the allies, and the per cent. the English, the French and the Turks each were of that number. Ans. Whole number 13600; English, 26 & per cent.; French, 35 per cent. ; and Turks, 384 per cent. 22. Bought a cargo of flour, consisting of 560 barrels, at $ 7.25 per barrel, less 10 per cent., and sold the same at 10 per cent. more than $ 7.25 per barrel. At what per cent. above the cost was the flour sold? How much was made by the operation ? 23. The population of a certain city, whose gain of inhabitants in 5 years has been 25 per cent., is 87500; what was it 5 years ag)? Ans. 70000. 24. Bought a horse, buggy, and harness for $500. The horse cost 37 } per cent. less than the buggy, and the harness cost 70 per cent. less than the horse. What was the price of each ? Ans. Buggy $ 2753%; horse, $1724%; and harness, $ 513 |