1. Tea costs 60 cents per lb.: at what rate must it be sold to gain 25 %?

SOLUTION.-25% of 60 cts. is 60 X.25=15 cts., and 60 cts. +15 cts.75 cts. per lb.

Ans.

100

=

Or, thus: 25 per cent.25 2561, and 1 of 60 cts. 15 cts., which, added to 60 cts., gives 75 cts. for the selling price per lb. If it were required to lose so much per cent., the percentage of the cost price must be subtracted from it.

Rule for Case II.-Find the percentage of the cost price, Art. 210, and add it to, or subtract it from, the cost, as may be required; the result will be the selling price.

2. Silk costs 90 cts. per yard: at what must it be sold, to gain 25 %?

At what price, to lose 10%?

price per yd. Ans. $1.12 Ans. $0.81

3. If cloth cost $4.37 per yard, at what price per yd. must it be sold, to gain 33 %?

At what price, to lose 20 %?

Ans. $5.83+

Ans. $3.50

4. Cheese cost $8.50 per cwt.: at how much per cwt. must it be sold, to gain 20 %?

At how much, to lose 20%?

5. Bought 40 yards of cloth for $300:

a yard must it be sold, to gain 20 %?

At how much a yd., to lose 20 %?

Ans. $10.20

ART. 245. OF MARKING GOODS.

Ans. $6.80

at how much Ans. $9. Ans. $6.

The rate per cent. of profit at which merchants mark the selling price of goods, is generally some aliquot part of 100. The following are those most used:

REVIEW.-244. What is the Rule for Case 2? 245. What part of any thing is 5 per cent.? 8 and 1 third? 10? 12 and a half? 16 and 2 thirds? 20? 25? 88 and 1 third? 50 per cent?

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.

60 cts.?

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.? Ans. to last, 66 cts. % profit, how mark muslin that cost 12 cts. ? 16 cts.? 20 cts.?

7. To make 12

8 cts. per yard.?

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, 663 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. 33%.

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 %? Ans. 20 %.

5. Muslin that cost 20 cts. a yard, is sold at 21 cts. a yard: what the % profit?

Ans. 5%.

6. Bought cloth at $8 a yard, and sold it at $9 a yard: what % profit did I make?

Ans. 12

%.

7. Muslin that cost 30 cts. a yard, is sold at 24 cts. a 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 %. 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.-247. What is Case 4? Rule? Rule by proportion?

*4. By selling cloth at $3 a yard, 25% was lost: what was the cost price per yd.? Ans. $1.

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.

Ans. $60.

5. A jockey sold a horse for $75, and gained 25 %: what did the horse cost him? 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 121 %: 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?

4. The population of New York, in in 1840 it was 2428921: find the 10 years.

Ans. 45 cts.

at what price Ans. $7.50 and sold it for Ans. 34% %. 1830, was 1918604; gain per cent. in Ans. 26.5% + was 937903; in gain per cent. Ans. 62 % +

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

6. If calico is sold at 42 cts. a yd., at a gain of 10 %, what was the cost price? what the gain %, if sold at 51 cts. a yard? Ans. Cost, 38cts. a yd. 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 pieces of cloth at $9.60 each; sold 5 pieces at $14.40 each, and 4 pieces at $12 each: at how much a piece must he 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 $1.682 a yd., and gained 16 % what % will I lose, by selling at $1.247 a yd.?

13. How much cloth, at $5 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.