OPERATION.

40328;8÷32.25, Ans.

Or, 40—32 = 8; 8 ÷ 32 — 31⁄2 = 1; 4 × 100 = 25 %.

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ANALYSIS. Since the gain on 32 cents is 40328 cents, the whole gain is 2 of the purchase money; and reduced to a decimal is 25 hundredths, equal to 25 per cent. Or, if the gain were equal to the purchase money, it would be 100 per cent. ; but since the gain is of the purchase money, it will be of 100 per cent., equal to 25 per cent. Hence the following

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RULE. Muke the difference between the purchase and selling prices the numerator, and the purchase price the denominator; reduce to a decimal, and the result will be the per cent. Or, Take such a part of 100 as the gain or loss is part of the purchase price.

EXAMPLES FOR PRACTICE.

2. A man bought a pair of horses for $275, and sold them for $330; what per cent. did he gain? Ans. 20%.

3. If a merchant buy cloth at $.60 a yard, and sell it for $.75 a yard, what does he gain per cent.?

4. A speculator bought 108 barrels of flour at $4.624 a barrel, and sold it so as to gain $114.884; what per cent. profit did he make? Ans. 23 per cent.

5. Bought sugar at 8 cents a pound, and sold it for 9 cents a pound; what per cent. was gained?

6. A drover bought 150 head of cattle for $42 per head, and sold them for $5400; what was his loss per cent.?

Ans. 14%.

7. If I sell for $15 what cost me $25, what do I lose per cent.?

8. Bought paper at $2 per ream,

a quire; what was the gain %?

Ans. 40 per cent. and sold it at 25 cents Ans. 150%.

9. If I sell of an article for of its cost, what is gained

per cent.?

Ans. 50 per cent.

10. If of an article be sold for what of it cost, what is the loss%2

Ans. 37 per cent.

11. If I 11. If I sell 3 pecks of clover-seed for what one bushel cost me, what per cent. do I gain? Ans. 33%.

12. A, having a debt against B, agreed to take $.873 on the dollar; what per cent. did A lose?

13. A grocer bought 7 cwt. 20 lb. of sugar, at 7 cents a pound, and sold 3 cwt. 42 lb. at 8 cents, and the remainder at 83 cents; what was his gain per cent.? Ans. 18 per cent.

14. Bought 2 hogsheads of wine, at $1.25 a gallon, and sold the same at $1.60; what was the whole gain, and what the gain per cent. ? Ans. Gain 28 %.

15. A grain dealer bought corn at $.55 a bushel and sold it at $.66, and wheat for $1.10, and sold it for $1.37; upon which did he make the greater per cent.?

Ans. 5 per cent., upon the wheat.

CASE III.

275. To find the selling price, when the cost and the gain or loss per cent. are given.

1. Bought a horse for $136; for how much must he be sold to gain 25 per cent.?

of $136 $170. If the horse had been sold at a loss of 25 per cent., then $1 of cost would have sold for $1 minus .25, or $.75, &c. Hence,

RULE. Multiply $1 increased by the gain or diminished by the loss per cent. by the number denoting the cost. Or,

Take such a part of the cost as is equal to 188 increased or diminished by the gain or loss

per

cent.

Case III is what? Give explanation. Rule.

EXAMPLES FOR PRACTICE.

2. If 12 hundred weight of sugar cost $140, how must it be sold per pound to gain 25 %? Ans. 14 cents.

3. Bought a hogshead of molasses for 30 cents a gallon, and paid 163 per cent. on the prime cost, for freight and cartage; how much must it sell for, per gallon, to gain 33 per cent. on the whole cost? Ans. $.46.

4. For what price must I sell coffee that cost 10 cents a pound, to gain 174 %?

5. If I am compelled to sell damaged goods at a loss of 15 per cent., how should I mark goods that cost me $.621? $1.20? $3.8712 Ans. $.534; $1.02; $3.293.

6. A man, wishing to raise some money, offers his house and lot, which cost him $3240, for 18 per cent. less than cost what is the price?

7. C bought a farm of 120 acres, at $28 an acre, paid $480 for fencing, and then sold it for 12 per cent. advance on the whole cost; what was his whole gain, and what did he receive an acre? Ans. $480 gain; $36 an acre.

8. Bought a cask of brandy, containing 52 gallons, at $2.60 per gallon; if 7 gallons leak out, how must the remainder be sold per gallon, to gain 37 per cent. on the cost of the whole? Ans. $4.13.

9. A merchant bought 15 pieces of broadcloth, each piece containing 23 yards, for $840, and sold it so as to gain 18₫ per cent.;` how much did he receive a yard ?/

CASE IV.

276. `To find the cost, when the selling price and the gain or loss per cent. are given.

1. A merchant sold cloth for $4.80 a yard, and by so doing made 333 per cent.; how much did it cost?

ANALYSIS. Since the gain is 33 per cent. of the cost, $1 of the cost, increased by 33 per cent., will be what $1 of cost sold for: therefore there will be as many dollars of cost, as 1.33 is contained times in $4.80, or $3.60. Or, since he gained 33 per cent. of the cost, $4.80 is of the cost; $4.80=$3.60.

NOTE. If the rate per cent. be loss, we subtract it from 1, instead of adding it. Hence the following

RULE. Divide the selling price by 1 increased by the gain or diminished by the loss per cent., expressed decimally, or in the form of a common fraction, and the quotient will be the

cost.

EXAMPLES FOR PRACTICE.

2. By selling sugar at 8 cents a pound, a merchant lost 20 per cent.; what did the sugar cost him? Ans. 10 cents.

3. Sold flour for $6.124 per barrel, and lost 121 per cent. ; what was the cost? Ans. $7.00. 4. A grocer, by selling tea at $.96 a pound, gains 28 per cent.; how much did it cost him? Ans. $.75.

5. Sold a quantity of flour for $1881, which was 18 per cent. more than it cost; how much did it cost?

6. Sold 25 barrels of apples for $69.75, and made 24 per cent.; how much did they cost per barrel?

7. Sold 94 cwt. of sugar at $81 per cwt., and thereby lost 12 per cent.; how much was the whole cost?

8. Having used a carriage six months, I sold it for $96, which was 20 per cent. below cost; what would I have received had I sold it for 15 per cent. above cost? Ans. $138.

9. B sells a pair of horses to C, and gains 121 per cent. ; C sells them to D for $570, and by so doing gains 18 per cent.; how much did the horses cost B? Ans. $426.663.

10. A grocer sold 4 barrels of sugar for $24 each; on 2 barrels he gained 20 per cent., and on the other 2 he lost 20 per cent.; did he gain or lose on the whole? Ans. Lost $4.

11. A person sold out his interest in business for $4900, which was 40 per cent. more than 3 times as much as he began with; how much did he begin with? Ans. $1166.663.

Give explanation. Rule.

INSURANCE.

277. Insurance on property is security guaranteed by one party to another, for a stipulated sum, against the loss of that property by fire, navigation, or any other casualty.

278. The Insurer or Underwriter is the party taking the risk.

279. The Insured is the party protected.

280. The Policy is the written contract between the parties.

281. The Premium is the sum paid by the insured to the insurer, and is estimated at a certain rate per cent. of the amount insured, which rate varies according to the degree of hazard, or class of risk.

NOTE. As a security against fraud, most insurance companies take risks at not more than two thirds the full value of the property insured.

282. To find the premium when the rate of insurance and the amount insured are given.

1. What must I pay annually for insuring my house to the amount of $3250, at 14 per cent. premium?

RULE. Multiply the amount insured by the rate per cent., and the product will be the premium. Or,

Take such a part of the amount insured as the rate is part of 100.

Define insurance. Insurer, or underwriter. Policy. Premium. To what amount can property usually be insured? Give analysis of example 1. Rule.