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How much is

4.5% of $40?

6%?

9%?

1

%?

8.61% of $3? 121%? 5. 7% of 50 bu.? 9.8% of lb.? 331%? %? 6. 9% of 30 yd.? 11%? 10. 163% of bu.? 50%? %? 7. 12% of 75 mi.? 20%? 11. 66% of.75 yr.? 37%? 3% 12. A farmer raised 150 bushels of corn, and kept 20% of it to feed his horses. How many bushels did he keep? 13. A merchant sold 50% of a piece of muslin containing 33 yards. How many yards did he sell?

14. Henry had $75, and expended 663 % of it for a watch. How much did he pay for the watch?

15. From a hogshead of molasses 163% was drawn off. How many gallons were drawn off?

16. What is the amount of 50 ft. increased by 6% of itself? 321. Analysis. — Since 6% is 18, 6% of 50 ft. is 18, or of 50 ft., or 3 ft.; and 50 ft. plus 3 ft. are 53 ft. Hence, etc.

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17. How many men are 200 men increased by 5% of that number? By 6%? By 10%? 50%? 100%?

18. How many feet are 400 itself? By 25%? By 50%?

ft. diminished by 20% of 75%? 100%?

Find the difference of

Find the amount of

19. 15 A. at 10%; 25%.
20. 25 bu. at 8%; 121%.
21. 50 mi. at 7%; 183%.
22. 48 doz. at 5%; 37%. 26.

23.

24.

25.

hhd. at 5%; 83%. bu. at 25%; 873%; 1%. .5 cwt. at 10%; 1%; 1%.

12

2 doz. at 1%; 61%; %. 27. A drover had 48 head of cattle, and sold 25% of them. How many cattle had he left?

28. If the rent of a house, for which a mechanic pays $12 per month, be raised 20%, what must he then pay?

29. If I borrow $150, and pay 6% for the use of it a year, how much do I owe at the end of the year?

30. A horse dealer bought a horse for $225, and sold him at a loss of 20%. Find the selling price.

31. If calico is bought at 8 cents a yard, and is sold at a profit of 121%, for how much is it sold?

32. From a farm of 80 acres were sold 121% to one man, and 20% of the remainder to another. How many acres were then in the farm?

2. To Find the Rate when the Base and the Percentage are given.

1. What per cent. of $75 are $25?

322. Analysis.—Since $75 are 100%, $25, which are of $75, are 4, or of 100%, or 33% of $75. Hence, etc.

What per cent. of 48 is 8?

2. What part of 48 is 8?
3. What part of $50 are $121?
What per cent. of

What % of $50 are $121?

4. 30 lb. are 15 lb.? Are 20 lb. ? 8. $13 are $? Are $3? 5. 40 oz. are 13 oz.? Are 25 oz.? 9. bu. is bu.? Are ğ bu.? 142 6. 50 A. are 61 A.? Are 37 A.? 10. .5 lb. is .1 lb.? Is lb.? 7. $.75 are $.183? Are $.62? 11. 163 yr. are 41 yr.? & yr.? 12. What per cent. of a number is of it? .05 of it? .12 of it? .66% of it?

of it? of it?

of it?

3

13. If I pay $6 for the use of $100 for a year, what per cent. do I pay? If I pay $7? If $8? $71⁄2?

14. If a man pays $5 an acre for the use of land worth $75 an acre, what per cent. of the value does he pay?

15. A farmer had 120 sheep, and sold all but 25% of them. How many did he sell, and what % did he keep?

16. A flour dealer sold some damaged wheat so as to lose of what it cost him. What % of the cost did he receive? 17. If I buy land at $50 per acre, and sell it at $621, what % above cost do I receive for it?

18. A boy having $.75, spent $.123 for a ball. What % of his money had he remaining?

19. If a milkman adds a gill of water to every quart of milk that he serves, what % does he add?

20. An agent asked $5 for a book, but sold it for $4.59. What % of his asking price did he receive?

3. To Find the Base when the Rate and the Percentage are given.

1. 8 feet are 25% of how many feet?

00

323. Analysis. — Since 25%, or 25%, of some number is 8 ft., 1%, or, of the number is 2 of 8 ft., or 2 ft.; and 100%, or 188, of the number is 100 times, which are 800 ft., or 32 ft. Hence, etc.

25

2. 50 is of what number? 50 is 25% of what?

100

6

3. $4 are of what number? $4 are 6% of what?

Of what are

8. 21 bu. 121%? 1%? %? 9. 4 pk. 100%? 1%? %? 10. 5 qt. 125%? %? 1.25%?

4. 12 mi. 6%? 121%? 25%? 5. 25 yd. 8%? 61%? 163%? 6. 371⁄2 ft. 10%? 81%? 12.5%? 7. 6 in. 2%? %? %? %? 11. 1.5 pt. 200%? 1%? §%? 12. Find the base, if the rate is 61% and the percentage $3. 13. If $10 are % of my bank deposit, what is the amount of my deposit? If $20 are 1% of it?

14. If A pays $12 a year for the use of a sum of money, at the rate of 6%, how much money does he use? 15. A man loaned another a sum of money. the sum loaned, if $75 were 163% of the amount?

What was

16. If a man owns 25% of a mill, and sells 33% of his share for $1000, what is the value of the mill?

17. A drover bought 25 cattle, and this number was 621% of what he had at first? How many had he after buying?

18. From of my money I spent 121% of my money, and then had $27 left. How much had I at first?

19. Harry is 16 years old, and 37% of his age is 66% of Frank's age. How old is Frank?

20. A farmer sold 20% of his wheat to one miller, and 37% of the remainder to another, and had 70 bu. left. How many bushels had he raised?

4. To Find the Base when the Amount or the Difference and the Rate are given.

1. What number increased by 25% of itself amounts to 75? 324. Analysis. Since the number is 100% of itself, 75 is 100% plus 25%, or 125%, of the number. If 75 is 125%, or 125, of some number, 1%, or of the number is, etc. (323).

00

2. 150 is 128 of what number? 150 is 120% of what? 3. $75 are 125% of what number? 20% more than what? 4. What number increased by 61% is 85 ft.? Is $34? 5. What number diminished by 20% of itself equals 60? 325. Analysis. —Since the number is 100% of itself, 60 is 100% less 20%, or 80%, of the number. If 60 is 80%, or 18%, of some number, 1%, or of the number is, etc.

80

100

6. 150 is 75% of what number? 150 is 75% of what?

100

7. $75 is 60% of what number? 20% less than what ? What number increased by

8. 10% of itself is 55? 9. 121% is $72? Is $1%? 10. 81% is 39 ft.? Is 2 yd.? 11.1% is $50? Is 301 ft.?

What number diminished by 12. 20% of itself is 64? 13. 37% is 5 bu.? & bu.? 1.5? 14. 61% is 45 qt.? 3 pt.? 4.5 pt.? 15.1% is $79? $997? 1.594?

16. 42 miles are 121% less than how many miles? 163%? 17. If the amount is $200, and the rate is 25%, what is the base? If the difference is $200, and the rate 25%?

18. If a horse cost $120, and this sum is 20% less than the cost of a carriage, what was the cost of the carriage?

19. A grocer sells tea at $.98 a pound, and this sum is 163% more than cost. Find the cost.

20. After selling 75% of a piece of cloth, a tailor had remaining 7 yd. How much was in the piece at first?

21. A clerk expended 75% of his salary for his support, and saved $20 a month. What was his salary?

22. If a grocer sells coffee at 314 cents, at an advance of 25% over the cost, what was the cost?

23. A man on a journey traveled 371% of the whole distance by stage, and the remaining 120 miles by railroad. How far did he travel?

Section II.

APPLICATIONS OF PERCENTAGE.

1. Profit and Loss.

326. Profit and Loss are terms used to denote the gain and the loss in business transactions.

327. The corresponding terms of Profit and Loss and Percentage are—

1. The Cost or Sum Invested is the Base.

2. The Rate of Profit or Loss is the Rate. 3. The Profit or Loss is the Percentage.

4. The Selling Price, or cost plus the profit, is the Amount.

The Selling Price, or cost minus the loss, is the Difference.

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