18. By having 5 pupils absent from school my attendance is 93%; if my attendance had been 95%, how many pupils must have been absent? Ans. 4 pupils,

19. What will be the %of gain on the ccst of 174 shares of Roxbury Gas Co.'s stock, nominal value of shares being $87.50, if it be bought at 15% below par, and sold at 19% above par? 20. If I buy coal at $4.12 per ton on 6 months' credit, for what must I sell it immediately to gain 10% ? Ans. $4.40.

21. If I pay $3.90 cash, for what must I sell it on 4 months to gain 20% ?

22. If, by selling wood at 75 cts. per cd. ft., 61% be lost, for what should it have been sold per cord to gain 33%? Ans. $6.624, 23. I sell of a lot of goods for $9, and thereby lose 25%, for what must I sell the remainder to make 83% on the whole? Ans. $30.

24. A grocer bought 100 gallons of oil, at $1 per gallon; he mixed with it 50 gallons that cost $1.60 per gallon, then sold the whole at the rate of $1.44 per gallon; did he gain or lose, and what %?

25. Suppose the above was sold on a credit of 6 months, what was the % of gain?

26. Suppose the oil to have been bought on 4 months, and sold for cash; what % was gained?

27. For what should he sell the above per gallon to make 25 %, if he bought for cash and waited 10 months for his pay ?

28. How much water must be mixed with a barrel of ink (31 galls.), which cost $34.10, that it may be sold at $1.10 a gallon, and a profit of 25% be realized by it? Ans. 7 gail,

29. What water would be required in the above, if the cost had been $25, the profit 20%, and the selling price $.75 per gallon?

30. If 20% of what I receive for an article is gain, what is the gain %?

NOTE.

-If 20% is gain, 80% is cost; the gain then is of the cost, which equals 25%, Ans.

31. If 25% of what I receive is gain, what is the gain %?

32. When two sovereigns are sold for $24.20, what is the premium on gold, estimating the sovereign at its legal value?

33. What amount of current money must a broker give me for $20 in gold, when the premium on gold is 178%?

34. A man hands a broker $40 in currency, saying, "Give me the value of this in gold;" gold is "quoted" at $2.64; how many dollars did the broker return, and how much change in currency

?

35. Suppose the broker paid 20% premium for this gold, what did he gain upon the $15, no allowance for interest?

36. What % did he gain on the money he expended to pur chase the gold?

37. A man about to travel in Canada bought $50 in gold, when gold was at a premium of 150%; what amount of current money did he pay for it?

38. When gold is at a premium of 50%, what is the depreciation in the currency?

39. A merchant imports from Hamburg a bale of cloth, containing 12 pieces, 40 yards each; the cloth, with charges there, cost him $480; he pays a duty here of 35 cts. per yd., freight $28.50, and other charges $7.11; at what must he sell the cloth per yd. to gain 10% above all charges?

40* Vinton & Morris imported a lot of W. I. sugar, for which they paid $15272 in Havana; their expenses amounted to 5% of the first cost; 10 months after, they sold it so as to gain $5512.46 above all expenses, including interest at 6%; what % did they gain?

41. An importer received from Holland 75 gross quart bottles of beer, invoiced at 10 cts. per bottle; a duty of 30 cts. per gal was paid at the custom house after 10% had been deducted for breakage; if all the bottles be found sound, what % will be gained by selling the beer at 25 cents per bottle?

356. GENERAL REVIEW, No. 7.

1. What is per cent. of $56.49?

2. What is the amount of $84.20 for 3 yrs. 5 mo. 12 ds., at 5 per cent.?

3. What is the interest of 24 £. 7 s. 6 d. for 2 yrs.

4. Oct. 12, 1861, gave my note on demand, with interest, for $480. Feb. 6, 1862, paid $120. What remained due Aug. 24, 1862 ?

5. I held a note for $500, which bore interest from May 10, 1859. Sept. 16, 1860, received $140; July 28, 1862, received $50. What remained due Sept. 4, 1862?

6. If I pay $45 interest for the use of $500 for 3 years, what is the rate per cent?

7. How long must $204 be on interest at 7 per cent. to amount to $217.09?

8. What principal will gain $9.20 in 4 mo. 18 ds., at 4 per cent.?

9. What sum, at 7 per cent., will amount to $221.075 in 3 yrs. 4 m.?

10. What is the compound interest of $600 for 1 yr. 4 mo interest payable semi-annually?

11. What is the present worth of a note for $488.50, due in 2 yrs. 5 mo. 15 ds., at 9 per cent.?

12. What is the discount of $105.71, due 4 yrs. hence?

13. What commission must be paid for collecting $17380, at 34 per cent.?

14. What amount of stock can be bought for $9682, and allow per cent. brokerage?

15. What is the value of 20 shares bank stock, at 84 per cent. discount, the par value of each share being $150?

16. What sum will be received from a bank for a note of $260, payable in 4 months?

17. What is the bank discount on $320 for 90 days?

18. What is the face of a note which yields $112.803, when discounted at a bank for 60 days?

19. A house, valued at $4750, is insured at 2 of 1 per cent. what is the premium?

20. What is the duty, at 15 per cent. ad valorem, on 20 bags of coffee, each containing 115 lbs., valued at 42 cts. per lb.?

RATIO.

357. Ratio is the relation which one number bears to A Lother number of the same kind.

Ratios are of two kinds, Arithmetical and Geometrical. 358. Arithmetical Ratio is ratio of numbers with respect to their difference; as 6 42.

GEOMETRICAL RATIO.

359. Geometrical Ratio is ratio of numbers with respect to their quotient; as 2:4= , read 2 is to 4, or the ratio of 2 to 4 = ; 6:3= 2, read 6 is to 3, or the ratio of 6 to 3 = 2.

360. The first term of a ratio is called the Antecedent, the second, the Consequent; both together are called a Couplet.

What is the antecedent in the first illustration in Article 359? the consequent in the second? the ratio in the first? the consequent in the first? the ratio in the second ?

361. When the terms of a ratio are equal, the ratio is one of equality; when the antecedent is greater than the conse quent, it is a ratio of greater inequality; when the antecedent is less than the consequent, it is a ratio of less inequality.

362. It will be readily seen that ratios, being expressions for division, are similar to fractions. They can at any time be written in a fractional form, the antecedent taking the place of the numerator, and the consequent that of the denominator. The principles applicable to fractions apply also to ratio. Hence,

363. Ratios, like fractions, may be simple, complex, or compound. A ratio is simple when each term is a simple number; it is complex when either term contains a fraction; it is compound when it is the indicated product of two or more ratios.

1. Write the ratio of 2 to 3; of 7 to 10; of to §; of 2 × 7

to 5 X 4.

2. Multiply the ratio 3: 4 by 2.

3. Divide the same by 2.

4. Reduce the ratio 6: 8 to lower terms.

5. Write any ratio of equality; of greater inequality; of less inequality.

5

365. ILL. Ex. Reduce : to a simple ratio.

21

OPERATION.

5

15. Multiplying each term of the ratio : 15 by 3 × 7, we

21

have

14:45, Ans. Hence,

2 X 3X7 15 × 3 × 7

3

7

To reduce a complex ratio to a simple one: Reduce each term to its simplest form, then multiply each by the least common multiple of the denominators, and cancel.