APPLICATIONS OF PERCENTAGE.

218. The principal applications of percentage are Profit and Loss, Commission and Brokerage, Capital and Stocks, Insurance, Taxes, Customs, Bankruptcy, Interest, Discount, Exchange, Equation of Payments, and Equation of Accounts. All the problems are solved by the application of one or more of the four cases of percentage.

PROFIT AND LOSS.

219. The Cost of an article is the price paid for it, or the total expense incurred in producing it.

220. The Selling Price of an article is the amount asked or received for it by the seller.

The selling price of the seller is the cost to the buyer, and vice versa.

221. When an article is sold for more than its cost, it is said to be sold at a profit or gain; when it is sold for less than its cost, it is said to be sold at a loss or discount. Hence,

222. Profit or Gain is the amount which the selling price of an article exceeds its cost.

223. Loss or Discount is the amount which the selling price of an article is less than its cost.

NOTE. The terms gain and loss are not limited to business transactions. When any quantity undergoes an increase or decrease, from any cause, there is a gain or loss, and when such gain or loss can be expressed in hundredths, it may be computed by the principles of percentage.

MENTAL PROBLEMS.

1. A merchant bought a piece of cloth for $80, and sold it at 25% profit: for how much did he sell it? (Case I.)

2. A dealer bought hats at $5 apiece, and sold them at 20% profit: what was the selling price?

3. Hats, costing $5 apiece, were sold at a loss of 20%: what was the selling price?

4. At what price must flour, costing $6 a barrel, be sold to gain 163%?

5. A grocer bought sugar at 12 cts., 16 cts., and 18 cts. a pound for how much must each kind be sold to gain 20%? To gain 25%?

6. A merchant sells broadcloth, costing $4, for $5 a yard: what per cent. does he gain? (Case II.)

7. When broadcloth, costing $5 a yard, is sold for $4 a yard, what is the loss per cent.?

8. Teas costing $1.20 and $1.50 a pound, are sold respectively at $1.50 and $1.80 a pound: what is the gain. per cent.?

9. A merchant sold velvet at a profit of $2 a yard, and gained 20% how much did it cost? (Case III.)

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10. A dealer sold boots at $1.50 a pair less than cost, and thereby lost 33% what did they cost?

11. A grocer sold tea at 30 cents above cost, and gained 16% what was the cost of the tea? What was the sell

ing price?

12. A man sold a horse for $90, and gained 20%: what was the cost of the horse? (Case IV.)

13. A man sold a horse for $80, and lost 20 %: what was the cost of the horse?

14. Sold butter at 40 cts. a pound, and gained 25 %: how much did it cost?

15. A watch, costing $80, was sold at a loss of 10% for how much was it sold?

16. How must shoes, costing $2, $2.50, and $3 a pair, be sold respectively to gain 25%? How must each kind be sold to gain 30%?

17. How must muslin that cost 10 cts., 15 cts., and 18 cts. a yard, be sold to gain 20% ?

18. Sold tea at 90 cts. a pound, and gained 20%: what would have been my gain per cent. had I sold it at $1 a pound?

WRITTEN PROBLEMS.

19. A house and lot, which cost $6750, were sold at a gain of 12% for how much were they sold?

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20. Carriages, costing $165, are sold at 18% profit: what is the gain on each carriage?

21. A man paid $4500 for a farm, and sold it for $5400: what was the gain per cent.?

22. A drover bought cattle at $65 a head, and sold them at $84.50 a head: what was the gain per cent.?

23. Carpeting, costing $1.75 a yard, is sold for $2: what is the gain per cent.?

24. A drover bought horses at $130 a head, expended $6 each in taking them to market, and then sold them at $153.50 a head: what was the gain per cent.?

25. A cargo of wheat costing $16500, being damaged, is sold for $13750: what was the loss per cent.?

26. A merchant sold a lot of goods at 12% profit, and gained $8160: what was the cost?

27. A grocer sold 82 barrels of apples at 22 % profit, and gained $45.10: what was the cost per barrel?

28. A man sold a watch for $180, and lost 163 %: what was the cost of the watch?

29. A house and lot were sold for $7762.50, at a gain of 15% what was the cost?

30. A dry goods firm sold $45000 worth of goods in a year; of the receipts were sales at 20 % profit, at 25% profit, and the rest at 33% profit: what was the cost of all the goods?

31. Sold a piece of carpeting for $240, and lost 20 % : what selling price would have given a gain of 20% ?

32. A merchant sells goods at retail at 30% above cost, and at wholesale at 12% less than the retail price: what is his gain per cent. on goods sold at wholesale?

33. How must cloth, costing $3.50 a yard, be marked that a merchant may deduct 15% from the marked price and still make 15% profit?

34. A merchant marked a piece of silk at 25% above cost, and then sold it at 20% less than the marked price: did he gain or lose, and how much?

225. RULES.-1. To find the gain or loss when the cost and rate per cent. are given, Multiply the cost by the rate per cent. expressed decimally. (Form. 1.)

2. To find the rate per cent. when the cost and the gain or loss are given, Divide the gain or loss by the cost, and the quotient expressed in hundredths will be the rate per cent. (Form. 2.)

3. To find the cost when the gain or loss and the rate per cent. are given, Divide the gain or loss by the rate per cent. expressed decimally. (Form. 3.)

4. To find the cost when the selling price and the rate per cent. of gain or loss are given, Divide the selling price by 1 plus or minus the rate per cent. (Form. 4.)

NOTE.-Let the pupil review the above problems, solving those in which the rate is an aliquot part of 100, by using the fraction. (Art. 210, Note.)

COMMISSION AND BROKERAGE.

226. An Agent is a person who transacts business for

another.

227. A Factor is an agent who buys and sells goods intrusted to his possession and control. A mercantile factor is also called a Commission Merchant.

When a factor lives in a different country or part of the country from his employer, he is called a Correspondent or Consignee. The

goods shipped or consigned to a Consignee are called a Consignment; and the sender of the goods is called a Consignor.

228. A Broker is a person who buys and sells gold, bills of exchange, stocks, bonds, etc.; or an agent who buys and sells property in possession of others.

229. A Collector is an agent who collects debts, taxes, duties, etc. (Arts. 263, 267.)

230. Commission is an allowance made to a factor or other agent, for the transaction of business. The commission allowed a broker is called Brokerage.

231. Commission is computed at a certain per cent. of the amount of property bought or sold, or of the amount of business transacted. The rate per cent. is called the Rate of Commission, and the amount of business transacted is the Base.

The rate of commission varies with the amount and nature of the business. A broker's commission is usually less than a factor's.

232. The Net Proceeds of a sale or collection are the proceeds less the commission and other charges.

MENTAL PROBLEMS.

1. An auctioneer sold $300 worth of furniture, and charged a commission of 5% how much did he receive?

2. A peddler bought $500 worth of rags, at a commission of 10% what was his commission?

3. An agent sold $1200 worth of school furniture, at a commission of 163% how much did he receive?

4. An attorney collected bad debts to the amount of $800, and charged 20% commission: what was his commission?

5. A society paid a lad $6 for collecting membership dues, to the amount of $100: what rate of commission did he receive?

6. A bookseller received $30 for selling $150 worth of maps: what was his rate of commission?