NOTE. Since per cent. can be expressed both by decimal and common fractions, the rules given in decimal and common fractions for changing from one to the other are equally applicable in percentage.

93. To find the percentage, the base and rate being given.

RULE.-Multiply the BASE by the RATE expressed decimally.

NOTE.

If the rate is an aliquot part of 100 it is often quicker and easier to take the parts denoted by the corresponding fraction. Thus for 25% take of the Base; 33 take; 50% take.

9. A merchant bought goods for $475.25 and sold them so as to gain 22% on the cost. How much did he gain?

0458

ސ

10. A collecting agent collected for his client $2340, charging 5% fee for his services. How much should he receive? How much should he pay to his client?

11. A merchant who failed in business owed me $1465. He was able to pay only 46% of his debts. On that basis, how much should I receive?

12. A merchant bought a bill of goods amounting to $367.40 on 60 days' time, less 5% if paid within 10 days. On the tenth day he paid the bill. How much did he save

by doing so?

13. A. B. had an estate valued at $15000. He gave 10% of it to a church, 12% to a college, and 5% to charitable purposes. How much had he remaining?

14. A man had an annual income of $1200. He paid 20% of it for board, 2% for incidentals, and 5% for clothing. What was the cost of each item of expense, and how much had he left at the close of the year?

15. A manufacturer's price-list of cardboard is $25 per 1000 sheets. He sold a dealer 10000 sheets at a discount of 28% from list price. How much did he receive?

16. A and B invested $2950 each in business. A lost 143%, and B gained 9%. How much did B then have more than A?

17. Bought 29 bales of cloth, 12 pieces to the bale and 45 yds. to the piece, at $1.123 per yd. For what must I sell the. lot to gain 83% ?

18. For what sum must I give my note for 30 days, at 6%, to secure the money to pay for the following insurance: On my store, $7000, at 3% premium; stock, $15000, at 1%; on my house, $4000, at §%; furniture, $1800; plate, $450; pictures, $800, and clothing, $250, all at %; cost of policy, $1.50, and survey of premises, $2?

19. I mixed 45 bu. corn at 90c. with 40 bu. at 95c., and 27 bu. at 85c. At what price per bu. must I sell the mixture to gain 15% ?

20. An insolvent firm owes me $4800. If I settle at 65c. on the $1, and discount 3% for prompt payment, what is my loss?

21. What will it cost to insure a store worth $9000 at 3% on of its valuation, and $15000 worth of stock at % on of its valuation?

22. I purchased 19750 lbs. of hay at $16.24 per ton and 9600 lbs. oats at 45c. per. bu. Sold the hay at a gain of 12%, and the oats at 4% loss. What were the proceeds of the sale? How much did I gain or lose?

23. A savings-bank, having failed, declared a dividend of 85% in favor of depositors. A's balance of deposit was $5347.60, B's, $8665.95, and C's, $7680. How much did each lose?

24. The freight of 24685 lbs. of iron was at the rate of $4.50 per ton. The amount of the bill was divided among three railroads, one taking 25%, one 35%, and the other the rest. How much did each get?

25. 12% of a merchant's sales is profit. The sales amount to $28400. What is the cost of the merchandise

sold?

94. To find the rate, the base and percentage being given.

RULE. - - Divide the number denoting the PERCENTAGE by the BASE.

NOTE 1. Percentage is found by multiplying the Base by the Rate. It is therefore the product of two factors. To find the Rate we have given the Product and one of the factors which produced it. Dividing the product by one factor must of course give as a result the other factor.

1. A merchant purchased goods for $465 and sold them for $560. How many dollars did he gain? What per cent. on the cost did he gain ?

2. A collector charged $23.35 for collecting a bill of $467. What rate per cent. did he charge?

3. A bank having a capital of $300000 declared a semiannual dividend of $1350. What per cent. of the capital was the dividend?

4. A merchant invested a capital of $36498 in business, and found at the expiration of a year that he had made a net gain of $8212.05. What per cent. did he gain?

5.

The cost of insuring a cargo worth $6540 was $81.75. What rate did the insurance company charge?

6. A merchant failing in business owes $4560. His assets amount to only $3078. What per cent. of his indebtedness can he pay?

7. A person whose annual income is $1250 pays $275 for board, $125 for clothing, $25 for books, and $37.50 for sundries, and deposits the remainder in a savings bank. What per cent. of his income is each item, and what per cent. does he deposit?

8. Goods that were bought at $4.50 per yard were marked to sell at $6.00. What was the per cent. of gain charged?

9. A farmer owning 100 acres of land sold 50 acres for what the whole lot originally cost him. What per cent. did he gain?

10. Sold 25 tons of coal at $4.75 per ton, and gained $31.25. What is the per cent. of profit?

11. A's money is $1800, and B's is 25% more than A's. What % less than B's is A's?

12. Two men had each $500; one expended 25% and the other 20%. How much % did one then have more than the

other?

13. A contractor builds a railroad at $30000 per mile, and when it is completed he finds it has cost him $92.50 per rod. What % does he gain? What is his total gain on a section of 5 miles? 320rds = im

14. An insolvent debtor owes $33500, and has property worth $23500. What % of his debts can he pay, and what will a man receive who has a claim of $1450?

15. Bought furniture at auction for $75 less than manufacturer's cost, and sold it for $960. What % did I gain if the manufacturer's cost was $975?

16. A merchant's capital is $12000. At the close of the last year his purchases amounted to $28375, and sales $34750. The expenses were $2375. What was his % of gain?

17. I bought a horse for $250 and sold him for $262.50. I afterwards bought him back for $240 and sold him for $255. What was my gain and gain %?

18. A merchant who has a capital of $15000 gains $3875 the first year and loses $2525 the second year. What is his % of gain for the two yrs.?

19. The freight on 4750 lbs. of Mdse. is at the rate of 85c. per 100 lbs. The distance is 320 miles, and the freight is divided between two railroads in proportion to the mileage of each. The distance of the first was 180 miles and of the second 140 miles. What % of the freight-bill will each receive? How much?

20. A merchant lost $3000 of his capital, and had $24000 remaining. What % of his capital did he lose?

95. To find the base, the rate and percentage being given. RULE.

Divide the PERCENTAGE by the RATE.

The percentage which is given being the product of the base multiplied by the rate per cent., it follows that the percentage [product] being divided

by the rate [multiplier] must produce the base [multiplicand].

9.

60 gallons are 40% of how many gallons?

10. 10 grains are 50% of how many scruples?

PROBLEMS.

1. A merchant sold 15% of his stock of goods for $36250

What was his entire stock before the sale?