76. CHAPTER VIII. PERCENTAGE. THE terms, percentage and per cent.,signify by the hundred, or hundredths, that is, a certain number of parts of each one hundred parts, of whatever denomination. Thus, by 5 per cent. is meant 5 cents of every 100 cents, $5 of every $100, 5 bushels of every 100 bushels, &c. Therefore, 5 per cent. equals 5 hundredths, (180) or b. 8 per cent., 8 hundredths, (180) or of the given number or quantity. 1. A man, having $40, lost 3 per cent. of it; how many dollars did he lose? ANALYSIS. Since he lost 3 per cent., or 1åd, on $1, on $40 he lost 40 times 180, or 138 of $1, equal to $1. Therefore, &c. 2. What is 5 per cent. of $25? of $30? of $45? 3. What is 7 per cent. of $15? of $40? of $200 ? 4. What is 6 per cent. of $18? of $37? of $54 5. What is 3 per cent. of 50 bushels of corn? 6. What is 10 per cent. of 160 tons of plaster? 7. What is 25 per cent. of 96 gallons of wine? 8. What is 12 per cent. of 331 pounds of sugar? 9. What is 15 per cent. of 110 barrels of flour? 10. What is 8 per cent. of 28 yards of cloth? 11. What is per cent. of $45? ANALYSIS. Since 1 per cent of $45 is 45, & of 1 per cent. is of 456, or 3, equal to $. Therefore, &c. 12. What is 13. What is 14. What is per cent. of $28? of $44? of $56 ? 17. A man bought 75 barrels of apples, and on opening them, found 8 per cent. of them spoiled; how many barrels did he lose? 18. If I have $200 deposited in the bank, and draw out 15 per cent. of it, how much remains? 19. A farmer, having 176 sheep, sold 75 per cent. of them, and kept the remainder; how many did he Keep? 20. A young man, having $104, lost 121 per cent. of it in gambling; how many dollars did he lose, and what per cent. of the whole had he left? 99. of it? 1. What fraction of a number is 8 per cent. ANALYSIS. Since 1 per cent. is bo, 8 per cent. is 8 times do, or 180,25 Therefore 8 per cent. equals 25 of any number or thing. = 2. What fraction of a number is 6 per cent.? 7 per cent.? 10 per cent.? 12 per cent.? 3. What fraction of a number is 6 per cent.? 163 per cent.? 20 per cent.? 371 per cent.? 40 per cent.? 4. If you have $120, and lose 331 per cent. of it, what part of it will you lose? 5. James, having 250 marbles, lost 40 per cent. of them at play; what part of the whole had he left, and how many did he lose? 6. What per cent. of a barrel of flour is of it? ANALYSIS. Since the whole of any number or thing is equal to 100 per cent., & of one barrel of flour is equal to of 100 per cent., or 40 per cent. Therefore, &c. 7. If a man save of his income, what per cent. does he spend? of his money in dry 8. If a merchant invest goods, what per cent. does he invest? 78. 1. A farmer, having 20 sheep, lost 5 of them by disease; what per cent. did he lose? ANALYSIS. Since 20 sheep are 100 per cent., or all that he had, 5 sheep are, or, of all he had; and of 100 per cent. is 25 per cent. Therefore, &c. 2. What per cent. of 21 is 7? 3. What per cent. of 50 is 5? 10? 20? 25% 4. What per cent. of $40 is $5? $8? $25? $30 ? 5. What per cent. of 18 pounds is 3 pounds? 12 pounds? 6. What per cent. of 42 miles is 6 miles? 7 miles? 7. What per cent. of 121 is 21? 61? 8. What per cent. of 30 is 12? 15? 20? 9. What per cent. of 18 is 9? 12? 15? 10. 1 is what per cent. of 9? of 15? of 21? 11. 2 is what per cent. of 71? of 121? of 10 12. is what per cent. of 31? of 163? of 20? 13. 12 is what per cent. of 8? of 12? of 20? 14. If from a hogshead of molasses a grocer draw 42 gallons, what per cent. of the whole will remain ? 15. From a box of tea containing 60 pounds, 15 pounds were sold at one time, and 25 pounds at another; what per cent. of the whole remained unsold? 16. In a heap of potatoes containing 150 bushels, 3 bushels of every 5 are bad; what per cent. are bad, and how many bushels are good? 17. A gambler, having $250, lost $80 at play ; what per cent. of his money did he lose, and what per cent. had he left? 18. James, having 623 cents, gave 37 for a book; what per cent. of his money had he left? 19. A grocer, having a barrel of sugar containing 200 pounds, sold of it at one time, and of the remainder at another time; what per cent. remained unsold? 79. 1. A person collects $240, and receives & per cent. commission on what he collects; what com pensation does he receive ? ANALYSIS. Since the commission is 5 per cent., or τόσ equal to 2, of the sum collected, he receives 20 of $240, which is $12. Therefore, &c. 2. What will be the expense of collecting a note of $800, at 10 per cent. commission ? 3. What must be paid for collecting a tax of $300, allowing 12 per cent. commission? 4. An agent sells $1200 worth of merchandise, at 25 per cent. commission; how much will he receive for his services? 5. An auctioneer sold goods to the amount of $500; what will his commission amount to, at 2 per cent.? 6. Paid an attorney 3 per cent. to collect a debt of $640; how much did he receive for his services? 7. If a man fail in business, and can pay but 40 per cent. of his debts, how much will a creditor receive on a debt of $175? 8. Bought $1000 worth of books, receiving a commission of 33 per cent.; how much did I receive for my services ? 9. If a broker sell $600 worth of New York Central Railroad stock, and charge & per cent. for selling, how much will he receive? 10. At of 1 per cent., what will be the expense of negotiating a bill of exchange of $625? 11. A broker in Chicago exchanged $1200 on the Chemical Bank of New York, at per cent.; what amount of brokerage did he receive? 12. A real estate agent sells a house and lot for $2000, and charges 14 per cent. commission for selling; how much does he receive ? 80. 1. A merchant sends his agent $780 to expend for merchandise, after, deducting his commission of 4 per cent.; what sum will he expend? ANALYSIS. The money to be expended is 188 of itself, and the commission 130, or 5, of this sum; hence the whole amount sent to the agent is 183, or 38. Since $780 is 38, is 6 of $780, or $30, his commission; and is 25 times 30, or $750, the sum to be expended. 26 25 2. I gave a broker $810 to invest in bank stock, after deducting his commission of 11 per cent. ; what was his commission, and how much did he invest? 3. A distiller sent Mr. B. $1550, with which to buy corn, after deducting his commission of 3 per cent.; how much did he expend, and how much did his commission amount to? 4. How many bushels of wheat, at $1 a bushel, can an agent buy for $1230, and retain 21 per cent. commission for his trouble? 5. A farmer employed a man to thresh his wheat, agreeing to give him 12 per cent. of all he threshed; how many bushels must he thresh that the farmer may retain 66 bushels? ANALYSIS. Since the thresher received, or of all he threshed, the farmer received the difference between 188, or and, which is 3. Then 66 bushels is of the whole number of bushels threshed; since 66 bushels is 32, is of 66, or 3 bushels, and 25 is 25 times 3 bushels, or 75 bushels. Therefore, &c. 6. What amount must be collected on a rate bill, that the collector may retain his fee of 5 per cent., and pay over $228 ? 7. What amount of accounts must an individual collect in order to pay over $1100, and retain 8 per cent. for collecting? |