WRITTEN EXERCISES.

464. To find the Rate when the Base and Percentage are given.

1. What per cent of $63 is $42 ?

ANALYSIS.-Percentage is the product of the base and the rate; therefore, the percentage $42, divided by the base $63, gives .66%, or 66 %, the rate. Hence, the

RULE.-Divide the percentage by the base.

2. What % of £18 is 15s. Ans. 41%. 3. What % of 96 meters is 28 meters? 4. What % of $18 is 12 cts. ?

5. What % of 168 is 15?

6. What % of 275 is 18?

7. What % of $5 is 5 dimes?

8. What % of ton is ton and 16 pounds?

OPERATION.

63) 42.00 Ans. .66%

9. Henry spelled 225 words out of 250, and his sister 235; what per cent of the words did each spell correctly?

10. From a cask of kerosene containing 52 gal., 6 gal. 2 qts. leaked out; what per cent of it was lost?

11. A farmer having 250 bu. of wheat, sold ğ of it; how many bushels and what per cent did he sell?

12. A man worth $12500, bequeathed $3125 to his wife and the rest to his 3 children; what per cent of it did his wife have, and how much had each child?

13. What per cent of 365 days are 30 days?

14. Of 1880 years are 4000 years?

15. Of 27 lb. Avoir. are 12 oz. ?

16. Of 125 miles are 250 rods?

17. Of 88 kilograms are 75 grams?

18. If a man owns of a ship and sells of her, what per

cent of his part does he sell?

19. What per cent of 75 bu. 3 pk. are 50 bu. 2 pk.?

20. A man gave $9863 to 3 charities; to the first $2500, to the second $4500; how much was left for the third and what per cent did each receive?

465. 1. $48 are 6% of what number?

ANALYSIS.—Since $48 are 6% of the number, 1% is of $48, which is $8, and 100% is 100 times $8, or $800, Ans.

466. To find the Base when the Rate and Percentage are given. 1. 192 is 25% of what number?

ANALYSIS.-Percentage is the product of the base by the rate. The base 192÷.25 768, the base required. Hence, the

.25) 192.00 P.

RULE.-Divide the percentage by the rate.

FORMULA.-Base = Percentage

Ans. 768 B.

Rate.

15. The number of children of age to attend school is 862, which is 20% of the population; what is the whole population?

16. A man sold a house, making $360, which was 5% more than it cost him; what did he pay for the house?

17. 4% of $230 is 5% of what? 124% of $530 is 61% of what? 18. A man paid a war tax of $73.50, which was 2% on the value of his property; what was he worth?

467.

PROBLEM IV.

ORAL EXERCISES.

1. A man sold a cow for $40, which was 25% more

than she cost him; what did he pay for her?

ANALYSIS. $40 is the cost increased by 25% of itself; and since the cost is 100 of itself, $40 must be 125, or 5 of the cost. Now, as $40 = § of 188 the cost, is of $40, which is $8, and 4 are 4 times $8, or $32, Ans.

2. What number increased by 25% of itself, is 100?

3. A furniture dealer sold a bureau for $20, which was 10% more than it cost him; how much did it cost him?

4. What number plus 121% of itself amounts to 96?

A grocer sold a barrel of apples for $5.50, and gained 20% on the sum it cost him; what did he pay for it?

6. A jeweller sold a watch for $150, which was 50% more than it cost him; what did he pay for it?

7. What number diminished by 25% of itself is 60 ?

ANALYSIS. AS 60 is the number after it is diminished, 60 must be 100%-25% 75 =, or of the number. Now if 60 is of the number, of it is 60÷3 = 20, and 4 fourths are 4 times 20, or 80, Ans.

8. What number diminished by 20% of itself is 48?

9. A pupil answered on examination 45 questions correctly, which was 10% less than the number asked him; how many were asked him, and how many did he miss?

WRITTEN EXERCISES.

468. To find the Base when the Amount or Difference, and the Rate are given.

1. What number increased by 25% of itself is 3500 ?

ANALYSIS.-Since 3500 is the number after it is

increased by 25% of itself, 3500 must be 125% of the number, or 1.25 times the number, and 3500

1.25 1.25 1.25) 3500.00

Ans. 2800

2. What number diminished by 20% of itself is 2560 ?

ANALYSIS.-Since 2560 is the number after it is diminished by 20% of itself, 2560 must be 80%, or .80 times the number, and 2560÷.80 3200, Ans.

1.20.80

.80) 2560.00

Ans. 3200

469. From the operations above, we derive the following

RULE.-Divide the amount by 1 increased by the rate. Or, Divide the difference by 1 diminished by the rate.

15. At the end of the year, a merchant's stock was $8400, which was 17% more than his capital; what was his capital? 16. A man sold his house for $2700 and lost 121%; what did the house cost him?

17. A grocer sold 950 barrels of flour for $5760, which was 20% advance on the cost; what was the entire cost, and the cost per

barrel?

18. A provision dealer sold 800 barrels of beef for $12000, which was a loss of 25%; what was the whole cost, and how much per barrel?

470. Percentage is applied to two classes of problems.

First. Those which are independent of Time; as, Profit and Loss, Commission and Brokerage, Insurance, Taxes, Duties.

Second.-Those in which Time is an element; as, Interest, Discount, Equation of Payments, Averaging Accounts, Stocks and Exchange.

NOTE.-In applying the PRINCIPLES of Percentage to these subjects, the pupil should carefully observe what elements or parts are given and what required in each example, and then apply the corresponding rule or formula.

PROFIT AND LOSS.

ORAL EXERCISES.

471. 1. A man paid $60 for a watch, and sold it at 10% above the cost; how much did he gain ?

ANALYSIS. He gained 10% of $60.
; and of $60 is $6. Therefore, etc.

Now 10% of a number is 10%, or

2. If a man pays $40 for a cow, and sells her at 20% advance, what will be his profit?

3. A jockey bought a horse for $80, and sold it at a loss of 5%; how much did he lose?

4. A man having 120 acres of land, bought 25% more; how many acres did he buy?

5. What part of a number is 12% of it?

6. What is 121% of 32?
7. What is 61% of 32?
8. What is 334% of $15?

Of 48? Of 96?

Of 64?

Of 80?

Of $50? Of $60 ?

9. A merchant sells flannel at a profit of 10 cts. on a yard, and gains 121%; what is the cost?

ANALYSIS.-121%; hence, 10 cts. = the cost; and are 8 times 10 cts., or 80 cts., Ans.

10. A farmer lost $32.40 on a reaping machine, which was 331% of the cost; what was the cost?

11. A goldsmith sold a watch at 25% profit, and made $26; what was the cost?

12. A tradesman sold out his stock of goods for $2760, which was 8% less than he paid; what did they cost him? 13. A grocer sold strawberries at 15 cts. a liter and made 20%; what did he pay for them?

14. A fruit dealer sold a barrel of apples for $1.50, which was a loss of 50%; what did he pay for them?

15. A newsboy sells papers at 5 cts. apiece, and makes 100%; what does he pay for them?

16. A man sold his house for $7500, which was 33% more than he paid for it; required the cost?