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Find the number of which

11. 50 is 621%. 12. 36 is 444%. 13. 24 is 37%.

PROCESS.

$56, Ans.

20. $17.36 is 31% of what sum?

.31)$17.36

155

186

186

14. 42 is 87%.
15. 63 is 90%.
16. 56 is 70%.

WRITTEN EXERCISES.

If $17.36 is 31% of some number, then .31 times that number equals $17.36, hence the number is $17.36.31, which is $56.

21. 120 is 888% of what number?

PROCESS.-888%

If of the number is 120, that number is of 120, or 135, Ans.

ole

=

888 800

100

RULE.

Divide the percentage by the rate.

FORMULA.-P ÷ R = B.

17. 90 is 30%. 18. 12 is 81%. 19. 5 is 61%.

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8.

22. A farm was sold for $425 less than cost, which was at a loss of 20%; what was the cost of the farm?

23. B owns 420 acres of land, which is 25% of what C owns; how much land has C?

24. A merchant lost $340, which was 17% of all his money; how much money had he?

25. Mr. Noble gained $175 by selling his horse and carriage at a gain of 314%; required the selling price.

26. A miller lost 12% by selling a quantity of flour for $616; required the cost of the flour.

SUGGESTION.--The difference ÷ (1 − rate)

base.

27. An army lost 20% of its men in battle, and 25% of the remainder were discharged; how many men were there in the army at first, if there were 33,240 men remaining?

28. A gained 15% of his capital, and then had $4830; what was his capital?

SUGGESTION.-The amount ÷ (1 + rate)

base.

29. By selling my horse for $207 I gained 15%; how much would I have received for him if I had sold him at a loss of 15%?

30. A speculator lost $660 by selling goods at 411% below cost; required the selling price.

31. A merchant clears $1240 by selling goods for 51% more than cost; required the selling price.

32. What must I ask for a farm worth $6000, so that I may fall 4% on my asking price and still gain 20% ?

33. 40% of the inhabitants of an Asiatic city perished from cholera, leaving 7560 alive; what was the original population? 34. I paid $300, which was 163% of my indebtedness; how much did I then owe?

CASE III.

157. Given the base and percentage, to find the rate.

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22. C bought a horse for $210 and sold him at a gain of $42; what was the gain per cent.?

23. A merchant bought goods for $540 and sold them for $500; what was the loss per cent.?

24. A regiment entered battle with 960 men and came out with 912 men; what per cent. were missing?

25. If A's salary is $1500 and his expenses are $1250, what per cent. of his salary does he save?

26. What per cent. do I gain by buying apples at $4.25 a barrel and selling them at $6 a barrel?

27. A merchant buys lead-pencils at a cent apiece and sells them at 3 cents apiece; what per cent. does he gain?

28. B sold his farm for $10,200, which was at a gain of 33 per cent.; what would have been his gain per cent. if he had sold it for $8109?

29. If I gain 15% by selling a carriage for $184, what would I have lost per cent. by selling it for $150?

30. If of the cost of an article is loss, what is the loss per cent.?

31. If a merchant buys goods for of his selling price, what per cent. does he gain?

32. A speculator bought 80 horses at $150 apiece and sold 30 of them at a gain of 163%; at what price per head must he sell the remainder so as to lose but 16% on the transaction?

MISCELLANEOUS PROBLEMS IN PERCENTAGE.

1. What is 40% of £214 5 s.?

2. 10 A. 120 P. is 33% of how much land?

3. 4 lb. 6 oz. is what per cent. of 15 lb.?

4. What is 16% of 1163?

5. 82 is 421% of what number?

6. 212 is what per cent. of 916 ?

7. If I buy goods at 20% below cost, and sell them at 20% above cost, what per cent. do I gain?

8. A miller bought 1200 barrels of flour for $4500, and sold 1000 barrels for what they all cost; what was the gain %?

9. A merchant sold goods worth $6544 at a gain of 371%; required the gain.

10. A firm makes a reduction of 8% for cash; how much is A's bill, who pays $368?

11. How must cloth which cost $2.25 a yard be marked to gain 20%?

12. B invests 45% of his capital in railroad stock, and has $11,000 remaining; what is his capital?

13. B sold cattle at an average price of $35 a head, and thus lost 16%; would he gain or lose, and how much per cent., by selling them at an average price of $44 a head?

14. What must I ask for a house which cost $6400, so that after falling 20% from my asking price I may still gain

15. From a tank containing 120 gallons of oil 14 gallons leaked out; what per cent. of the contents remained ?

16. Mr. Smith bought a horse for $210, and set such a price on him that after falling $18 he still gained 20%; what per cent. did he abate from the asking price?

17. A merchant who sells goods at a gain of 16% clears $368; what is the cost?

18. The number of boys in a certain school is 75% of the number of girls; what per cent. of the number of boys is the number of girls?

19. A fruit-dealer bought 300 barrels of apples for $660, and lost 20 barrels; at what price per barrel must he sell the remainder to gain 10% on the transaction?

20. What per cent. is gained when chestnuts are bought at $1.60 a bushel and sold at 7 cents a quart?

21. Mr. Sumner sold his horse for $240, and thereby cleared of this money; what would he have gained per cent. if he had sold him for $300?

22. A house was sold for $3160, which was at a loss of 21%; for what should it have been sold to gain 21% ?

23. If I buy at 40% below cost and sell at 40% above cost, what per cent. do I gain?

24. Mr. Reed drew 45% of his bank deposit to pay for a house which he bought for $9000; what amount of money remained on deposit?

25. A bought 120 barrels of flour at $4 a barrel, and paid $30 freight for shipment; at what price per barrel must he sell it to gain 20% on the transaction?

26. A book-case was sold for $60, which was at a gain of 12%; what would have been the loss per cent. had it been sold for $40?

27. A farmer sold two cows for $40 apiece: on the one he gained 20%, and on the other he lost 20%; did he gain or lose, and how much?

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