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15. The yearly production of quinine throughout the world is 4,500,000 avoirdupois ounces, of which America consumes 40% : how many tons are consumed in America ?
16. A bookkeeper receives an annual salary of $3,500. He expends 10% for board, 6% for clothing, 4% for charity, and 35% for other expenses : how much does he save each year ?
17. A merchant bought of a vessel for $15,000, and sold of his share at a gain of 8%: how much did he receive ?
18. Illustrate by an original problem the method of finding the percentage when the base and rate per cent. are given.
ART. 261.—To find the rate, when the base and
percentage are given.
1. What per cent. of 20 is 5 ?
Solution.—20 is 100% of 20 ; and since 5 is of 20, it is ¢ of 100%, or 25% of 20.
What per cent. of 2. 25 is 10? 15 ?
5. 75 is 60 ? 371 ? 3, 40 is 20 ? 25 ?
6. 80 is 20 ? 25 ? 4. 50 is 30 ? 40 ?
7. 90 is 30 ? 50 ? 8. A house rents for $600, which is 5% of its value: what is its value ?
9. John is 12 years old, and his brother's age is 16 years : what per cent. of his brother's age is John's
10. Mr. Hall had $550 in bank, and drew out $50 : what per cent. did he draw out ?
WRITTEN EXERCISES. 1. What per cent. of 60 is 36 ? Process.
Analysis.--1% of 60 = .06. 36 con36.00 = 60 = .60.
tains .06 sixty times, so it is 60% of
60. REMARK.—To obtain hundredths in the quotient, the dividend must contain two more decimal places than the divisor.
ART. 262.-Rule for finding the rate when the base and percentage are given.—Divide the percentage by the base, and the quotient is the rate per cent. required. Formula.—Rate per cent. =
percentage = base. What per cent. of 2. 125 bu. is 100 bu.? 4. 624 yds. is 121 yds.? 3. 81 qts. is 27 qts.? 5. 3} in. is 7 in. ? 6. 4 of 25 is what % of of 60 ?
7. A drover had 1,254 cattle, and sold 418 of them : what % of his drove did he sell ?
8. Horace, while fishing, brought 12 fishes to the surface, but 3 got away : what per cent. did he land ?
9. Newbold, having 24 apples, gave of them to his sister and 25% of the remainder to his brother : what % of them had he left ?
10. From a hogshead of molasses containing 63 gallons, 10 gallons 2 quarts leaked away : what % of the whole remained ?
11. Timothy set out to walk 68 miles. He walked 22 miles the first day, 24 the second, and the remainder on the third day: what % of the distance did he walk on the third day?
12. A pound Troy is what % of a pound avoirdupois ?
13. If a miller keeps 3 quarts of every bushel he grinds, what % does he keep as pay for grinding ?
14. A grocer having 1 ton 24 cwt. of sugar, sold 5 cwt. 25 lb. : what % of the whole remained ?
15. A company numbering 98 men went into battle; 17 were killed and 23 wounded : what % were unhurt?
16. Certain mining stock bought for $53.25 a share was sold for $129.75 a share: what % was the increase in the value ?
17. Illustrate by an original problem the method of finding the rate when the base and percentage are given.
ART. 263.-To find the base, when the percentage
and rate per cent. are given.
ORAL EXERCISES. 1. 90 is 15% of what number? Solution.—15% of any number is to, or of it; and since 90 is og of a certain number, j of 90, or 30, is zo of the number. 20 x 30 = 600, the number.
2. 15 pounds is 20% of how many pounds ?
WRITTEN EXERCISES. 1. What number increased by 25% of itself equals 555 : Process.
Analysis.—A number increased by 25% 100% + 25%=125% or or of itself is 125% or of itself; and 555; 5 X 4=444.
since of a certain number = 555, that
number 4 times } of 555 = 444. REMARK.—Percentage is a certain number of hundredths of any number, and hence includes the sum or difference of 100% and any given rate per cent.
ART. 264.-Rule for finding the base, when the percentage and rate are given.—Divide the percentage by the rate per cent. expressed decimally, and the quotient is the required number.
rate per cent.
2. 360 is 45% of what number? 3. 25.50 is 37% of what number? 4. 62! is 14% of what number? 5. 35.4 is 14% of what number? 6. 2503 is 60% of what number? 7. 600.75 is 70% of what number? 8. What fraction increased by 20% of itself equals 113?
9. I sold 148 bushels of wheat which was 37% of what I raised : how much did I raise ?
10. A man owning 35% of a ship, sold 40 per cent. of his share for $907.55 : what was the value of the ship?
11. A sold 25% of his apples to B and 50% of the remainder to C. If C bought 189 bushels, how many bushels had A at first ?
12. B loaned 33% of his money to his brother, who paid a debt of $550 with 163% of what he borrowed : how much money had B at first ?
13. Sold two horses for $360 each. On one I gained 25%, and on the other I lost 25% : did I gain or lose, and how much ?
14. A merchant failed owing $18,500, with $7,200 assets: what per cent. of his debts could he pay ?
15. 124 cords of wood was sold for $589.79, which was 11 per cent. more than it cost: what did it cost a cord ?
16. Illustrate Art. 259 by an original problem. 17. Illustrate Art. 261 by an original problem. 18. Illustrate Art. 263 by an original problem.
Applications of Percentage.
Profit and Loss.
1. At a gain of 50% what part of the value equals the gain ?
Solution.—50% gain on anything is to or ļ of the value.
2. What part of the value equals the gain, when the gain is 4% ? 5% ? 8% ? 15% ?
3. What part of the value equals the loss, when the loss is 10% ? 20% ? 25% ? 35% ? 60% ?
4. What part of the cost equals a gain of 83% ? 163% ? 621% ?
5. A farmer bought a horse for $120 and sold it at a gain of 10% : for what sum did he sell the horse ?
6. A merchant paid $60 for a piece of cloth and sold it at a gain of 20% : what sum did he receive ?
7. Coats worth $40 apiece were sold at a loss of 25% : how much money was lost on each coat ?
8. Harvey paid $150 for a carriage and sold it at a gain of 20% to his neighbor, who sold it at a loss of 25% : how much did the neighbor receive ?
9. 10% of $50 is of what Horace paid for a dictionary: how much did the dictionary cost?
10. Susan bought 8 yards of muslin for 64 cents and sold it at a gain of 25%: how much did she receive per yard ?