3. What number increased by 32% of itself equals 198?

Ans. 150.

4. What number increased by 15% of itself equals 1748? Ans. 1520.

5. What number diminished by 70% of itself equals 432? Ans. 1440.

6. What fraction increased by 20% of itself equals ? Ans. .

7. What fraction diminished by 40% of itself equals ? Ans.

8. A has $306, which is 66% less than B has: how much has B? Ans. $900. 9. A merchant cut 34 yd. from a piece of calico, and 15% remained how much was there in the piece? Ans. 40 yd. 10. A man failing in business had $3350 cash, which paid 67% of his debts: how much were his debts?

Ans. $5000. 11. A merchant failing paid 27% of his debts with $4546.80: what was his indebtedness? Ans. $16840.

12. The number of pupils enrolled in the schools of a certain town is 1161, which is 35% more than the number in attendance: what is the number in attendance? Ans. 860. 13. The population of a town increased in 10 yr. 72%; in 1870 its population was 11180: what was it in 1860?

Ans. 6500. 14. The profits on a business in two years were $3105; the profits the second year were 7% more than the first year: what were the profits each year? Ans. 1st, $1500; 2d, $1605.

15. A man sold two farms for $7000 each; for the first he received 121% less than its value, and for the second 163% more than its value: what was the value of each?

Ans. 1st, $8000; 2d, $6000. 16. When gold is at a premium of 124%, what is the value

in gold of $1 currency?

Ans. 888 cents.

17. When gold was at a premium of 115, what was the value in gold of $1 currency? Ans. 462 cents.

18. Bought a house for $3200 when property was depreciated 40% in value: what was the value of the house? Ans. $53331.

19. $2460 is 59% less than A's and B's money; A's is 60% of B's: how much has each? Ans. A, $2250; B, $3750. 20. Sold gold at a premium of 15%, and received $1386 currency: how much gold did I sell? Ans. $1200.

APPLICATIONS OF PERCENTAGE.

161. The principal applications of percentage are Profit and Loss, Commission and Brokerage, Capital and Stocks, Taxes, Customs, Insurance and Bankruptcy, in all of which time is not an element.

Also, Interest, Discount, Exchange, Equation of Payments and Equation of Accounts, in which time enters as an element or factor.

All the problems in these applications are solved by the application of one or more of the four cases of Percentage.

SECTION III.

PROFIT AND LOSS.

162. Profit and Loss are the terms used to indicate gain or loss in business transactions. The difference gained between the cost and the selling price is called Profit, and the difference between the cost and the selling price when an article is sold at less than cost is called Loss.

The cost may be regarded as the base, and the profit or the loss as a percentage of the cost.

CASE I.

When the Cost and Rate are given, to find the Gain or Loss.

ORAL EXERCISE.

1. If a man have a horse worth $100, for how much must he sell him to gain 25% ?

SOLUTION.-If he gains 25%, he gains 2%, or 1; the gain, equals of the cost, or the selling price;

4, the cost, plus, of $100 equal $125.

2. Bought muslin at 10 cents a yard, and sold it at a gain of 20% what did I sell it at?

3. A house cost me $1200, and I sold it at a gain of 40% : what did I receive for it?

:

4. A merchant bought 40 bbl. of flour for $240, and sold them at a gain of 16% what was the selling price per barrel? 5. If eggs cost me 20 cents a dozen, for how much must I sell them to make 20% ?

6. Paid $12 for 20 hats for how much must they be sold to gain 25% ?

7. Bought a house for $2500, but property depreciating in value I sold it at a loss of 30%: how much did I get for it?

8. A bought a horse for $120; he sold it to B at a gain of 25%; B sold it to C at a gain of 10% how much did C pay for the horse?

9. A miller bought $1200 worth of wheat, and lost on it 10%; he bought a second lot for $1500, and made on this 12% how much did he gain or lose?

10. A drover bought 12 cows at an average of $60 each, and sold them at a gain of 35%: what did he receive for the lot?

WRITTEN PROBLEMS.

1. Paid $1620 for a house and lot, and I sell it at a gain of 22% what is the gain?

SOLUTION. $1620

.22

3240 3240

Let the pupil explain; also derive the rule from the solution.

$356.40

2. A merchant invests $6575 in spring goods, and sells them at a gain of 18%: what is his gain? Ans. $1183.50. 3. Bought some hay for $560: for how much must I sell it to gain 15% ? Ans. $644. 4. Bought 500 tons of coal at $4.20 a ton, and sold it at 27% advance: what was the total gain, and the gain per ton? Ans. $567; per ton, $1.13.

5. A miller bought 700 bu. of wheat at $1.20 per bushel, and sold it at a gain of 151%, after paying $28 for hauling: what was his gain? Ans. $102.20. 6. The cost of coal is $2.60, and the freight $1.30 per ton: at what must I sell it to gain 30% ? Ans. $5.07 per ton.

7. Bought 60 bbl. of flour at $6 a bbl., paid for freight $36: at what must I sell it per bbl. to gain 30% ? Ans. $8.58. 8. If 16 cows cost $464.80, how much will be the profit on each cow at 18% gain? Ans. $5.23-. 9. A man has $6740 invested at 6%, but his taxes are 14%: how much does he make? Ans. $283.08.

10. Bought a farm for $16500; sold it to B at a gain of 12%; he sold it to C at a loss of 3% : what did B and C each pay for the farm? Ans. B, $18480; C, $17925.60.

CASE II.

The Base and the Gain or Loss given, to find the Rate.

ORAL EXERCISE.

1. If a boy buy a knife at 12 cts., and sell it at 15 cts., what per cent. does he gain?

SOLUTION.-If he pay 12 cts. for the knife, and sell it at 15 cts., he gains the difference between 15 cts. and 12 cts., which is 3 cts.; 3 cts. is of 12 cts., or of 100% of 12 cts., which is 25%.

2. Bought a hat at $4, and sold it at $6: what is the gain per cent.?

3. If I buy $300 worth of grain, and sell it for $360, what is the gain per cent.?

4. What per cent. is lost on delaine worth 60 cts. a yard when it is sold at 55 cts. a yard?

5. A farmer refused to sell his potatoes at 50 cts. a bushel, but afterward was compelled to sell them at 35 cts. a bushel : what was the loss per cent.?

6. A huckster bought chickens at 7 cts. a pound; he paid 1 ct. a pound freight on them, and sold them in the city at 11 cts. a pound: what per cent. did he gain?

7. A fruit-dealer bought lemons at 15 cts. a dozen, and sold them at 2 for 5 cts.: what was his gain per cent.?

8. If $140 is of the cost of a horse, what per cent. will be gained by selling him at $273?

9. If of a farm is sold for the value of of it, what is the gain per cent.?

10. Bought chestnuts at $4 a bushel, and retailed them at 10 cts. a pint: what was the gain per cent.?

WRITTEN PROBLEMS.

1. If I buy an acre of land for $80, and sell it for $90, what is the gain per cent.?

SOLUTION.

90-80=10

10+80=-121%.

Let the pupil give the explanation and derive the rule.

2. A knife cost $1.20, and is sold for $1.40: what is the gain per cent.? Ans. 16.

Ans. 12.

3. If tea costs 75 cents, and I sell it for 95 cents, what is the gain? Ans. 26%. 4. Bought a house for $1250, and sold it for $1400: what was the gain per cent.? 5. Bought a buggy for $220, and sold it for $240: what was the gain per cent.? 6. A merchant having $5000 worth of goods, lost 25% by fire, and sold the remainder at a gain of 40% gain or loss per cent.?

7. Sold a bookcase for $125, and cleared

Ans. 9.

what was the Ans. 5% gain.

of this money:

what would I have gained per cent. by selling at $120?

Ans. 6.

8. $147 is of the cost of a piano: what per cent. is gained by selling it at $300? Ans. 19 9. A carload of grain worth $620 is found to be damaged, and is sold at $500: what is the loss per cent.?

Ans. 191.

10. 7 of a farm is sold for the value of of it: what is the

loss per cent.?

Ans. 2317.