2. Sold 160 cords of wood, which was 20 per cent. less than the whole number owned. How many cords were owned?

1

OPERATION.

Ans. 200 cords.

Since the

..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., expressed 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. 328 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. $34.271

7. A man expends in a week $24, which exceeds by 33} 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 12 per cent. nearer than is J. Mitchel's residence. At what distance does Mitchel live from the village?

Ans. 3m. 1fur. 334rd.

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 6yd. 16qr., which was 75 per cent. less than the quantity cut off. How many yards were there in the piece at first? Ans. 31yd. 1qr. 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 per cent. of his money for land, and B lost of it by gambling as much as would equal 27 per cent. of what both received. They then together had left just $36.854. 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?
2. What is 5 per cent. of $ 3266 ?

3. Find 312 per cent. of of 21.

Ans. 117.

Ans. 1744.

4. Find 13 per cent. of 180.
5. 9 is what per cent. of 3?

6. is what per cent. of?

7. Find what per cent. 3.50 is of 50. 8. 13 is 16 per cent. of what number? 9. $66 is 100 per cent. of what number? 10. is 6 per cent. of what number?

Ans. 20

Ans. 316.

Ans. 40.

Ans. 81.

Ans. $66.

11. $21.28 is 34 per cent. less than what sum?

Ans. 533.

Ans. $22.00.

12. 191b. 12oz. is 16 per cent. of how many pounds? Ans. 1178 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? Ans. 324 eggs.

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.

16. 25 per cent. of of a ship is how many per cent. of of it? Ans. 16 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. 14 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 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 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, 387 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 ago? 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 $27533; horse, $17213; and harness, $513

INTEREST.

351. INTEREST is an allowance made for the use of money, or for value received; and it is generally reckoned as a certain rate per cent. for any given time, but usually for one year.

The principal is the sum lent, on which interest is computed. The amount is the interest and principal added together. Simple interest is that reckoned on the principal only; and is that meant when the term interest is used alone.

Legal interest is the rate per cent. established by law. Usury is a higher rate per cent. than is allowed by law. The legal rate per cent. varies in the different States and in different countries.

In Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut, New Jersey, Pennsylvania, Delaware, Maryland, Virginia, North Carolina, Tennessee, Kentucky, Ohio, Indiana, Illinois, Iowa, Nebraska, Missouri, Kansas, Arkansas, Mississippi, Florida, District of Columbia, and on debts or judgments in favor of the United States, it is 6 per cent.

In New York, Michigan, Wisconsin, Minnesota, Georgia, and South Carolina, it is 7 per cent.

In Alabama and Texas, it is 8 per cent.

In California, it is 10 per cent.

In Louisiana, it is 5 per cent.

In Canada, Nova Scotia, and Ireland, it is 6 per cent.
In England and France, it is 5 per cent.

NOTE. The legal rate, as above, in some of the States, is only that which the law allows, when no particular rate is mentioned. By special agreement between parties, in Ohio, Indiana, Michigan, Illinois, Iowa, Nebraska, Missouri, Kansas, Arkansas, Louisiana, and Mississippi, interest can be taken as high as 10 per cent.; in Florida, as high as 8 per cent.; in Texas and Wisconsin, as high as 12 per cent.; and in California and Minnesota, any per cent. In New Jersey, by a special law, 7 per cent. may be taken in the city of Paterson, and in the counties of Essex and Hudson. In Vermont 7 per cent. may be taken on railroad bonds. Banks in Illinois cannot take above 7 per cent., and in Ohio, not above 6 per cent. In Mississippi, above 6 per cent. can be taken only for money lent.

352. When the rate of interest is 6 per cent. per annum, the interest for 1 year or 12 months will be 6 cents on every

100 cents on which it is reckoned, or of the principal. Hence, for 2 months or of a year, it will be 1 cent on every 100 cents, or Too of the principal; and for 1 month or of 2 months it will be 5 mills, or go of the principal. Now, since

the interest on 100 cents for 1 month, or 30 days, is 5 mills, for 6 days, or of 30 days, it will be 1 mill, or Toʊʊ of the principal; and since the interest on 100 cents for 2 months is 1 cent, or T of the principal, for 100 times 2 months, or 200 months, or 16 years 8 months, it will be 100 cents, or equal the whole principal; and in the same ratio for any other length of time.

The interest of $ 1, at 6 per cent., and the ratio of the interest to the principal, for 200 months, and other convenient parts of time, is shown in the following