To mark goods for different rates of profit, Add to the cost price such part of itself as the rate per cent. is part of 100.

6. To make 10 % profit, what must calico be marked, that cost 10 cts. per yard? 15 cts.? 20 cts.? 30 cts.? 40 cts.? 50 cts.? 60 cts.? Ans. to last, 66 cts. 7. To make 12% profit, how mark muslin that cost 8 cts. per yard.? 12 cts.? 16 cts.? 20 cts.?

Ans. to last, 22 cts. 8. To make 20 % profit, how mark ribbons that cost 10 cts. per yd.? 15 cts.? 25 cts.? Ans. to last, 30 cts. 9. To make 25 % profit, how mark cloth that cost $1 per yard? $1.20? $1.50? $2? $3? $4? $6?

Ans. to last, $7.50

10. To make 33 % profit, how mark ginghams that cost 25 cts. per yd.? 50 cts.?

11. To make 50 % profit, how $2? $3? $4? $5? $7?

Ans. to last, 66 cts. mark shawls that cost Ans. to last, $10.50

ART. 246. CASE III.

To find the RATE PER CENT. of profit or loss, when the cost and selling price are given.

1. I sold cloth at $5 a yard, that cost $4 a yard: what was the gain %?

SOLUTION. Take the difference between the cost and selling price, the gain is $1 on what cost $4; then find what per cent. $1 is of $4; this, (Art. 211), is 1.25=25 per cent. Ans.

Rule for Case III.—Take the difference between the cost price and selling price, and find what per cent. this is of the cost price.

2. A man paid $75 for a horse, and sold him for $105: what % did he gain? Ans. 40%.

3. I bought a piece of cloth for $30, and sold it for $40 what was the % profit?

:

Ans. 331 %.

REVIEW. 245. How mark goods to sell at different rates of profit? 246. What is Case 3? What the Rule?

4. Cloth cost 25 cts. a yard, and sold for 30 cts. a yd.: what the gain %?

5. Muslin that cost 20 cts. a yard, is yard: what the % profit?

6. Bought cloth at $8 a yard, and sold what % profit did I make?

7. Muslin that cost 30 cts. a yard, is yard: what % is lost?

8. A bought 40 bales of cotton, at $40 it at a profit of $704: what did he make?

ART. 247. CASE IV.

Ans. 20%. sold at 21 cts. a Ans. 5%.

it at $9 a yard: Ans. 121%. sold at 24 cts. a Ans. 20 %. each, and sold Ans. 44 %.

To find the COST PRICE, when the selling price and rate per cent. of profit and loss are given.

1. Cloth sold at $5 a yard, pays 25 % profit: required the cost price per yard.

SOLUTION. When the cost is $1, and 25 per cent. is gained, the selling price is $1.25 (Art. 244); hence, as many times as $1.25 is contained in the selling price, so many times is $1 contained in the cost: the cost price is as many dollars as $1.25 is contained times in $5. $5÷$1.25 4. Ans. $4.

PROOF.-25 % of $4 is $1; and $4+$1=$5.

2. If, by selling cloth at $9 a yard, 10 % is lost, what was the cost price?

SOLUTION. When the cost is $1, and 10 per cent. is lost, the selling price is $.90 (Art. 244); hence, as often as $.90 is contained in the selling price, so many times is $1 contained in the purchase price: the cost is as many dollars as $.90 is contained times in $9. $9÷$.90=10. Ans. $10.

PROOF.-10% of $10 is $1; and $10-$1=$9, the selling

price.

*3. Cloth sold at $6 a yard, pays 20% profit: what was the cost price per yd.? Ans. $5.

REVIEW.-217. What is Case 47 Rule? Rule by proportion?

*4. By selling cloth at $3 a yard, 25% was lost: what was the cost price per yd.? Ans. $4.

Rule for Case IV.—Add to, or subtract from, $1, as may be required, the per cent. of gain or loss on $1; divide the selling price by the result; the quotient will be the cost.

Or, by PROPORTION. As 100 increased by the per cent. of gain, or diminished by the per cent. of loss, is to 100, so is the selling price to the cost.

Observe, that the per cent. of profit or loss is always calculated on the cost, and not on the selling price.

5. A jockey sold a horse for $75, and gained 25 % : what did the horse cost him? Ans. $60. 6. A jockey sold a horse for $75, and lost 25 %: what did the horse cost him? Ans. $100. 7. A grocer, by selling coffee at 22 cts. a lb., gains 10% find the purchase price per lb. Ans. 20 cts. 8. By selling cloth at $8.10 per yard, I gain 12 %: what the purchase price per yd.?

Ans. $7.20

9. By selling tea at $1.19 per pound, I lost 15 %: what the cost price per lb.?

Ans. $1.40

ART. 248. PROMISCUOUS EXAMPLES.

1. A buys 30 yd. muslin, at 6 cts. a yd., and sells it at 25% profit: what does he gain?

2. B bought 40 yd. of cloth for $250 per yd. must he sell to gain 20 %?

3. A bought 1 hhd. of wine for $75, 40 cts. a qt.: what the % profit?

Ans. 45 cts.

at what price Ans. $7.50 and sold it for Ans. 34% %.

4. The population of New York, in 1830, was 1918604; in 1840 it was 2428921: find the

10 years.

gain per cent. in Ans. 26.5% +

5. The population of Ohio, in 1830, 1840 it was 1519467; what was the in 10 years?

was 937903; in gain per cent. Ans. 62 % +

6. If calico is sold at 42 cts. a yd., at what was the cost price? what the gain cts. a yard? Ans. Cost, 33cts. a yd.

a gain of 10 %, %, if sold at 51 Gain, 334 %.

7. Sold a bushel of rye for $1, and gained 25%; purchased a bu. of wheat with the $1, and sold it at a loss of 25% what did I lose? Ans. 5 cts.

8. A merchant bought 14 picces of cloth at $9.60 cach; sold 5 pieces at $14.40 cach, and 4 picces at $12 cach: at how much a picce must be sell the remainder, to gain 20% on the whole? Ans. $8.256 9. Sold wine at $1.29 a gal., and lost 14% at what price per gal. must it sell, to gain 14%? Ans. $1.71

10. Sold cloth at $1.36 a yd., and lost 15 %: what % would I gain by selling at $1.856 a yd.?

Ans. 16 %.

11. Sold silk at $1.96 a yd., and gained 12 % at what price per yd. should I sell, to lose 16% ? Ans. $1.47 12. Sold satin at $1.632 a yd., and gained 16% what % will I lose, by selling at $1.247 a yd.?

13. How much cloth, at $3 a yd., must $100 by selling it at 25 % profit?

14. A grocer buys 200 casks of raisins cask; by selling at 5 cts. per pound, he what was the weight of each cask?

I

Ans. 14 %.

buy, to clear Ans. 80 yd.

at $2.50 per gains 20%: Ans. 60 lb.

15. Sold a quantity of corn, at $1 per bu., and gained 25%; sold of the same to the amount of $59.40, and gained 35%: at what rate did I sell: how many bu. in the last lot?

Ans. $1.08 per bu., and 55 bu.

For additional problems, see Ray's Test Examples.

ASSESSMENT OF TAXES.

ART. 249. A TAX, is a sum assessed on the citizens of a town, county, state, or district, for public purposes. Taxes are of two kinds-a property tax and a poll-tax.

A PROPERTY TAX is a certain per cent. assessed on the taxable property held by each person.

A POLL-TAX is a specific sum assessed on male citizens over 21 years of age. Each person so taxed is called a poll.

REM. In some States the whole tax is raised on property; in other States, partly on property and partly on polls.

ART. 250. When a tax is to be assessed, first obtain a list or inventory of the amount of taxable property, from which the tax is to be collected.

If there be a poll-tax, make a list of the polls.

TO ASSESS A TAX, OBSERVE THIS

Rule.-1. If there be a poll-tax, find its amount, by multiplying the tax on each poll by the number of polls. Subtract this from the whole amount of tax to be raised; the remainder will be the sum to be raised on property.

2. Divide the tax to be raised on property by the whole amount of property; the quotient will be the per cent. of tax on $1.

3. Multiply the per cent. of tax on $1 by the amount of each person's property, the product will be his property tax.

4. Add the poll-tax, if any, of cach person to his property tax; the sum will be his whole tax.

1. A tax of $500 is assessed in a district, to build a school-house; the property is valued at $125000: what the % of tax? Ans. .004, or 4 m. on $1.

What the tax on $1650?

Ans. $6.00

2. A tax of $9057.00 is assessed in a county whose taxable property is valued at $534650; also, a list of 1258 polls, cach taxed $1.25: what the % of tax on property? Ans. .014, or 1c. 4m. on $1.

NOTE. In preparing tax lists, after finding the per cent. of tax, assessors make a table embracing the tax on dollars from 1 to 10; then on 10, 20, &c., to $100; then on 100, 200, &c., to $1000.

The following table, computed for the preceding example, is calculated by multiplying the tax on $1 by the number of dollars on which the tax is required.

REVIEW.-249. What is a tax? What a property tax? A poll-tax? 250. When a tax is to be assessed, what is to be first obtained? 250. How assess a tax, Rule? Nor. How calculate a tax-table?