CASE I.

285. To find any given per cent. of profit or loss on a quantity.

1. If a house be bought for $8500, and sold at a gain of 12

per cent., what was the gain?

OPERATION.

$8500 .12 $1020, Ans.

=

Since the house was bough'

for $8500, and sold at a gain of 12%, the gain was 12%, or .12, of $8500, or $1020. That is,

The profit or loss is equal to the base multiplied by the rate per cent., expressed decimally.

2. Mr. Edson bought flour on speculation for $2340, but he was obliged to sell it at 15% below cost; how much was his loss? Ans. $351.

3. Sold goods for which were paid $8500, at a gain of 211 per cent.; how much was the profit?

4. A man sold a farm, for which he gave $5000, at 9 per cent. below cost; how much was his loss? Ans. $450.

5. If cloth cost $4 a yard, at what price must it be sold to gain 25% ?

SOLUTION. 25%, or 4, of $4, is $1; $4+ $1 = $5 per yard, Ans.

6. If sugar cost 12 cents a pound, at what price must it be marked to make 33 % profit? Ans. 16 cents per pound. 7. To make a profit of 12% per pound, at what selling price must tea, that cost 80 cents per pound, be marked?

8. A trader having some shop-worn articles that cost him $130, has marked them down 10% below cost; what is his reduced price? Ans. $117.

9. A merchant bought 60 casks of molasses, each containing 63 gallons, for $1512; at what price per gallon must it be sold for him to gain 15 per cent.? Ans. 46 cents per gallon.

Explain the operation. To what is the profit or loss equal?

286. To find the rate per cent. of profit or loss.

1. If a house be bought for $8500, and sold for $1020 more than the cost, what was the gain per cent.?

OPERATION.

1020 ÷ 8500.12, or 12 %, Ans.

Since the gain is $1020

on $8500, it is 1020=.12, and since .12 = 12%, the gain was 12%. That is,

The rate per cent. of profit or loss is equal to the profit or loss divided by the base, with the division extended to hundredths.

2. From a cask containing 84 gallons, 14 have leaked out; what per cent. is the loss? Ans. 16 %. 3. If a merchant sell cloth, which cost him $4.50, at a profit of $.90, what is the gain per cent.?

4. When cloth, which cost $4.50 per yard, is sold at $6, what is the gain per cent.?

Ans. 33%. 5. Bought a horse for $250, paid for keeping him $10, and sold him for $234; what was the loss per cent.?

Ans. 10 %. 6. A merchant bought 50 barrels of flour for $10.20 a barrel, and was obliged to lose $85.00 in selling it; what per cent. was his loss?

Ans. 16 %.

7. If I sell of a lot of land at of its cost, what is the profit per cent. ?

Ans. 60 %.

8. If I sell of a cord of wood at the cost of a cord, what is the gain per cent. ? Ans. 33%. 9. Sold a house for $5000, and gained $500; what would have been the loss per cent. if I had sold it at $4000?

CASE III.

287. To find the base of profit or loss.

Ans. 111 %

1. What is the cost of a house, if in selling it at a profit of $1020, the gain is at the rate of 12 per cent.?

Explain the operation. To what is the rate per cent. of profit or loss equal? Explain the operation.

Or,

OPERATION.

$1020 X 100 12

= $8500, Ans.

$1020.12= $8500, Ans.

Since 12% of the cost is $1020, 1% of it is of $1020, or $85, and 100 %, or the whole cost, is 100 times $85, or $8500.

Or, since 12%, or .12, of the = $8500

cost is $1020, the cost must be of $1020, or $1020 ÷.12 That is,

The base is equal to the profit or loss divided by its rate per cent., expressed decimally.

2. If by selling cloth at $.90 per yard above cost, the gain is 20 %, what was the cost? Ans. $4.50 per yard.

3. A house was sold at a loss of $15, which was 14% of the cost; what was the cost?

Ans. $1200. 4. Sold coal at 125 % of its cost and thereby gained $1.75 per ton; what was the cost per ton?

SOLUTION. 125 % - 100 %

Ans.

=25%; $1.75.25 $7 per ton,

=

5. Sold cloth at 95 % of its cost, and thereby lost $.30 on a yard; what was the cost per yard?

Ans. $6. 6. Sold coal at $8.75 per ton, and thereby gained 25 %; what was the cost per ton?

SOLUTION. Since $8.75 is 25% more than the cost, it is equal to 125% of the cost. If 125 %, or 1.25, of the cost is equal to $8.75, the cost must be equal to of $8.75, or $8.75 1.25 = $7. That is,

The cost is equal to the selling price divided by 1 increased by the rate per cent. of profit, or by 1 diminished by the rate per cent. of loss, expressed decimally.

7. Sold a horse for $204, and lost 15 %; what did the horse cost me ? Ans. $240.

8. By selling molasses at $.55 a gallon, I suffer a loss of 83%; what was the cost price?

9. By selling wheat at $1.70 a bushel, I gain 18 %; what was the cost price? Ans. $1.44+. 10. If 700 barrels of flour are sold for $4550, and thereby at a gain of 4%, what was the cost per barrel?

Ans. $6.25.

To what is the base equal? Explain the solution of example 6. To what is the cost equal?

REVIEW EXERCISES.

1. If wood, which should be cut 4 feet in length, fall short 3 inches, what per cent. should the price be reduced to correspond? Ans. 64 %.

2. A merchant paid $25 commission on sales amounting to $1250; at what rate per cent. was the commission?

3. If I pay a premium of $550 for insurance at 5 %, what is the amount for which the property is insured?

4. Sold corn at $1.00 a bushel, and gained 25 %; what per cent. should I have gained, had it been sold at $.88 a bushel? SOLUTION. Since $1.00 is 25% more than the cost, it is equal to 125% of the cost. If 125 %, or 1.25, of the cost is equal to $1.00, the cost must be equal to 5 of $1.00, or $.80.

т

=

Since the cost is $.80, if it should be sold for $.88, the gain would be $.08 on $.80, and if the gain should be $.08 on $.80, it would be :08 .10, or 10%. Therefore, etc.

5. Sold tea at $.88 a pound, and made 10 %; what should I have made if I had sold it at $1.00 a pound?

per cent.

6. Sold a horse, at a loss of 12 %, for $132; what per cent. should I have gained, if it had been sold at $159? Ans. 6 %.

7. Goods marked at 30 per cent. above cost, having depreciated in value, were sold at 28 % off the price as marked; what per cent. did I gain or lose?

SOLUTION. Since 30% above cost is 130% of the cost, 28% off the marked price must be 28% of 130% of the cost, or 36% % of the cost. 130% · 36%% = 938 %, and if sold at 933% of the cost, they must have been sold at 100%, or cost, less 93 %, or at a loss of 6%. Therefore,

etc.

8. How much is made or lost by selling goods marked 25 % above cost, at 20% off?

9. Sold 2 farms for $6000 each; on the and on the other I lost 25 %; what did I whole?

Ans. Nothing. one I made 25 %, gain or lose on the

Ans. Lost $800.

REVIEW QUESTIONS. What is Commission? (274) Brokerage? (275) Insurance? (278) Profit and Loss? (283) What is the Base of commis sion or brokerage? (275) Of Insurance? (280) Of Profit and Loss? (284)

INTEREST.

288. Interest is percentage allowed for the use of money, or for value received.

The PRINCIPAL is the sum on interest.

The RATE of interest is the rate per cent. for one year, or any given time.

The AMOUNT is the sum of the principal and interest.

289. Legal Interest is that reckoned by the rate per cent. established by law.

USURY is illegal interest.

The rate per cent. of legal interest varies in different states and countries.

In most of the United States, Canadas, and Nova Scotia, the legal rate, especially where no other is mentioned, is 6 per cent. In some of the States it is 7 per cent., and in others, any rate which may be agreed upon between the parties.

The rate for one year, and at 6 per cent., is to be understood in this book when no other is named.

SIMPLE INTEREST.

290. Simple Interest is that which is reckoned on the given principal alone for the given time.

291. Since the interest of $1, at 6 per cent. for 1 year, or 12 months, is 6 cents, for 1 month it will be of 6 cents, which is 5 mills, and for 2 months, 2 times 5 mills, or 1 cent; also,

Since the interest for 1 month, or 30 days, is 5 mills, the interest for 6 days, or of 30 days, will be 1 mill, and for 2 days, 3 days, etc., as many sixths of a mill as there are days. Hence, the

What is Interest? The Principal? The Rate? The Amount? Legal Interest? Usury? What is the legal rate in most of the United States? In some of the others? What rate is understood in this book when no other is named? What is Simple Interest?