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245. The rate and percentage given, to find the

base.

ORAL

EXERCISES.

1. 84 is 7% of what number?

ANALYSIS. Since 7% or 1 of some number is 84, 1% or 1 of the number is of 84, or 12; and 100% is 100 times 12, or 1200.

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8. 121% of 96 is 333% of what number?

9. 25% of 800 bu. is 21% of how many bushels?

10. Sold 105 bbl. of potatoes, which was 35% of all I raised. How many did I raise?

11. A farmer sold 7.5 A. of land, which was 15% of all he owned. How many acres did he own?

PRINCIPLE.-The base is the quotient of the percentage divided by the rate.

WRITTEN

EXERCISES.

246. 144 is 75% of what number? EXPLANATION. -Since the percentage, 144, is the product of the base by the rate, the base is the quotient of the percentage divided by the rate, or 144÷.75 192, the required base.

=

FORMULA: Percentage

2. 6.5 gal. are 5% of what?
3. $18.75 are 61% of what?
4. 420 bbl are 121% of what?
5. $300 are 48% of what?

rate = base.

Rate. Percentage.

.75) 144.00

192 Base.

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8. 78.5 is 25% of what?

9. 19.8 lb. are 71% of what?

10. 2% of $125.50 is 8% of what sum?
11. 121% of 400 ft. is 21% of how many feet?

12. A man spends $825.60, which is 33% of his salary. How much is his salary?

13. A man drew out 9% of his bank deposit to pay a debt of $243.72. How much had he in bank?

14. If a man, owning 40 per cent. of an iron foundry, sells 25 per cent. of his share for $1246.50, what is the value of the whole foundry?

15. A farmer sold 3150 bushels of grain and had 30% of his entire crop left. What was his entire crop?

16. If a man owning 45% of a steamboat sells 16% of his share for $5860, what is the value of the whole boat?

247. The amount, or difference, and rate given, to find the base.

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1. What number increased by 25% of itself amounts to 60? ANALYSIS. Since 60 is 25% more than the number, 60 is 125% or 185, equal to of the number, and the number is 4 times or 48.

100

of 60,

2. What number diminished by 20% of itself is 36 ? ANALYSIS. Since 36 is 20% less than the number, 36 is 80%, or 100 equal to of the number, and the number is 5 times of 36, or 45.

3. What number increased by 10% of itself is 55?

4. What sum increased by 121% of itself is $18.90? 5. $45 is 25% more than what sum?

80

6. A tailor sold a coat for $26, which was 30% more than it cost him. What did it cost him?

7. What number diminished by 5% of itself is 57?

8. What sum diminished by 50% of itself is $12.50?

9. 60 cwt. are 40% less than what number?

10. 35 yd. are 12% less than what number?

11. A boy spent 25% of his money, and had 75 cents left ? How much had he at first ?

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248. 1. What number increased by 37% of itself amounts to 2055?

EXPLANATION.-Since 2055 is the num

ber increased by 37% of itself, 2055 is 137%,

or 1.37 times the number; and 2055 ÷ 1.37

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1 + rate. Amount.

1.37) 2055.00 1500 Base.

2. What number increased by 18% of itself equals 2950 ? 3. What sum increased by 15% of itself is $6900?

1-rate. Difference.

4. What number diminished by 12% of itself is 2640? EXPLANATION.-Since the number is diminished by 12% of itself, 2640 is 88%, or .88 of the number. Hence, 2540÷.88 == 3000, the required number.

.88) 2640.00

3000 Base.

5. What number diminished by 30% of itself is 350?
6. What number diminished by 41% of itself is 1640 ?
(1. Amount ÷ (1+rate)}
2. Difference ÷ (1- rate) S

FORMULAS:

What number increased
7. By 15% of itself is 345?
8. By 36% is 238 A.?
9. By 100% is 84.6 cwt.?
10. By 6% is 1272 bu.?
11. By 22% is $549?

= base.

What number diminished 12. By 65% of itself is $2590? 13. By 50% is 28.5 ft.? 14. By 16% is 1035 mi.? 15. By 4% is $465.60? 16. By 371% is $203.375?

17. Sold a horse for $340, which was 15% less than his value. What was his value?

18. A man having increased his bank deposit 40%, it amounted to $840. How much had he at first?

19. My income this year is $2232, which is 7% less than it was last year. How much was it last year?

20. A man sold 160 A. from his farm, which was 121% less than the number of acres he retained. How many acres in his farm?

249. The applications of percentage are twofold:

1st. Those in which time is not an element; as, Profit and Loss, Commission and Brokerage, Insurance, Taxes, and Duties. 2d. Those in which time is an element; as Interest, Discount, Stocks, Equation of Payments, and Exchange.

Since the principles, and some one of the four formulas of percentage already considered will apply to some extent to all these topics, the pupil should carefully observe what elements or parts are given in the example, and what required, and then apply the corresponding rule or formula.

TRADE DISCOUNT.

250. Trade discount is a percentage deducted from the face of bills, the list price of goods, or from the amount of debt, without regard to time, and is expressed by the term "per cent. off."

Thus, 20% off, or 20 off, means a deduction of 20% from the nominal or asking price. 20 and 5% off means a discount, first of 20%, and then 5% from the remainder. 2 tens and 5% off means two successive discounts of 10%, and 5% from the remainder, etc.

251. The net price is the price received for goods, etc.

The invoice price, or the debt, corresponds to the base in percentage; the per cent. off to the rate; and the sum of the discounts to the percentage.

WRITTEN EXERCISES.

252. 1. What is the net cost of a bill of goods amounting to $975, bought on 4 mo., at 10% discount, and 5% off for cash?

This means that the goods bought are at the regular rates, on the usual time, at 10% off, but for cash a further discount of 5% is made.

Find the discount and net cost of the following bills of goods: 2. Bought for $750, on 3 mo., at 20% discount, and 4% off for cash.

3. Bought for $1584.50, on 60 da., at 124% discount, and 21% off for cash?

4. Bought for $365.75, on 4 mo., at 20, 10, and 5% off for cash.

5. Bought for $260, on 90 da., at 2 tens and 3% off for cash. 6. What is the difference on a bill of $650, between a discount of 30%, and a discount of 25 and 5% off?

7. School slates, marked to sell at $12.75 a case, were sold at 50, 10, and 5% off. What was the net price?

8. What is the difference between 15, 2 tens, and 5% off, and 40% off?

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253. Profit and loss are commercial terms used to express gain or loss in business transactions.

254. The terms corresponding to those of percentage are as follows:

1. The cost, or capital invested, is the base.

2. The rate of profit or loss is the rate.

3. The profit or loss is the percentage.

4. The selling price is the amount or difference.

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255. To find the profit or loss, and the selling price. 1. A watch that cost $80 sold for 20% more than cost. What was the gain, and the selling price?

ANALYSIS. Since the gain was 20%, it was, or of $80, equal to $16, and the selling price was $80+$16 = $96. (241.)

Find the profit or loss, and selling price of

2. Cloth bought at $4 a yard, and sold at 25% advance; 10%. 3. A cow bought for $48, and sold at a loss of 121%; 15%. 4. A carriage that cost $120, and sold at 10% loss; 16%.

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