Each of the following problems may be changed so as to become a problem under one or more of the three general problems in percentage, decimals, or fractions.

Change to problems in fractions and solve:

5. A lot costing $ 1600 is sold at a profit of 12%. What is the gain? The selling price?

6. A 50-cent knife is sold for 70 cents.

per cent.

Find the gain

7. A man makes 163 % of a 72-mile journey in 2 hours. How many miles remain to be finished?

8. A jeweler sold a watch for $32, thereby gaining 33%. Find the gain and the cost.

9. By selling corn at 54 cents a bushel, I lose 10%. Find the cost and the loss.

10. What per cent do I lose when I buy at 20 cents and sell at 10 cents? What per cent is gained in buying at 10 cents and selling at 20 cents?

11. A 60-acre farm costing $4800 is sold at a gain of 121%. Find the selling price.

12. A merchant buys pianos at $250 apiece. How much must he charge for them in order to make a profit of 20%?

13. What must be the list price of a watch in order that I may give a discount of 10% and yet receive $36 for it?

WRITTEN

14. For how much must apples costing $2.40 a barrel be sold to bring a gain of 37% ?

15. I lose 30% in selling a suit for $21.70. What is the cost?

16. I lose 10% in selling an article for $15.30. What would have been the selling price had I gained 10% ?

17. A house costing $3750 is sold for $3975. the gain per cent?

What is

18. An article costing $7.50 is sold at a loss of 20%. The purchaser sells it for $10. What is his gain per cent?

19. A certain piano costs the manufacturer $150. He sells it at a profit of 20%. The retail merchant who buys the piano pays $5 freight, and sells it at a profit of 25%. Find the selling price.

20. A merchant sells carpet at 75 cents a yard, and gains 20%. What would be the gain if the carpet were sold at 85 cents a yard?

21. By selling an article for $7.20 I gain 12%. What per cent should I gain by selling it for $7.50?

22. A dealer sells two wagons for $75 each. gains 25%, and on the other he loses 25%. or lose by the transaction, and how much?

Analysis by question and answer.

On one he Does he gain

A gain or loss of 25% is what part of the cost? Ans. the cost. If a gain of the cost is made by selling a wagon for $75, $75 is what fraction of the cost? Ans. of the cost. $75 is of what sum? Ans. $60. $60 cost.

=

If a loss of the cost results from selling a wagon for $75, $75 is what fraction of the cost? Ans. of the cost. $75 is of what sum? Ans. $100, or cost. ($100 + $60), cost, ($150), selling price, $10, loss.

23. I sell two machines at $150 each.

=

On the first I gain

25%, and on the second I lose 20%. Do I gain or lose, and how much?

24. A boy buys 6 apples for a dime, and sells them at the rate of 2 for 5 cents. What is his gain per cent?

25. A boy buys apples at the rate of 5 for 5 cents, and sells them at the rate of 3 for 5 cents. What is his per cent

of gain?

26. A boy buys 120 oranges at the rate of 4 for 10 cents, and sells them at the rate of 3 for 10 cents. What is his per cent of gain or loss? What is his per cent of gain or loss if 10% of the oranges are unsalable?

27. A farmer sells 75 sheep for what 80 cost. Find his gain per cent.

28. A merchant buys bankrupt stock at 45 cents on the dollar, and sells it at 10% below the original list price. What is his gain per cent? What is meant by "buying at 45% on the dollar"?

29. I buy an article for $10 and sell it for 10 cents. What is the loss per cent? Another article costing 10 cents. is sold for $10. What per cent is gained?

30. Mr. Lewis bought 12,000 bushels of wheat at $.60, and 6500 bushels of corn at $.55 a bushel. In selling, he gained 16% on the wheat and lost 20% on the corn. Did he gain or lose on the whole transaction, and how much? What per cent?

31. At what price must goods costing $40 be listed so that a discount of 163 % may be allowed and yet a profit of 20% may be realized?

Make two problems of the foregoing. Thus, at what price must goods costing $40 be sold to realize a profit of 20%? Ans. $48. If $48 are received for goods sold at a discount of 16% from the list price, what is the list price?

32. How must I mark a suit costing $16 that I may make a profit of 25% after giving a discount of 20% ?

A dealer "marks" his goods, or puts a price upon them, which he asks the buyer. He may give a discount from this price. Goods are frequently marked at a higher price than the merchant expects to receive, so that he may give the buyer a discount, and thus make him think he is getting a "bargain."

33. A merchant sold cloth at $1.50 a yard, thereby gaining 20 %. The cloth did not sell well, and he listed it to sell at a loss of 20%. What was the second list price?

34. How many bushels of wheat, at $.60 a bushel, must I purchase, so that if I sell at a profit of 81%, a gain of $250 may be made?

35. A merchant lists his gives a discount of 10 %. He gains $8 on an article. of this article.

goods 331% above cost, and then What is his per cent of gain? Find the list price and the cost

36. Fifty pounds of soap are purchased at 5 cents a pound. In a damp cellar it absorbs water equal to 10% of its weight, and is then sold at 6 cents a pound. What is the gain? The gain per cent?

37. I sell of an article for what of it costs. Find the gain per cent.

38. A tailor purchases cloth at $3 a yard. How much must he charge per yard in order to make a profit of 20% should the cloth shrink 10% in length?

39. Gloves that cost $18 per dozen pairs were sold at $2.25 per pair. What per cent was gained?

40. Construct two problems involving profit and loss, and solve them.

TRADE DISCOUNT

Study Recitation

153. Manufacturers and merchants frequently deduct a certain per cent from the list price of goods when selling them, or offering them for sale. This deduction is called a discount. We studied it in preceding problems. Many business houses give two or more discounts off the list price on account of payment in cash, changes in market price, or for other reasons.

These deductions are called trade discounts or commercial discounts.

NOTE. — Discounts made for payments in cash are sometimes called cash discounts, and discounts made for payment within a certain time, as 10 days, 1 month, etc., are called time discounts.

The net price is the list price less the discounts; it is the price the buyer pays.

Business usage or principle.

In trade discounts, the first discount is computed on and deducted from the list price; the second is computed on and deducted from the resulting remainder, etc.

A piano was catalogued at $600 with a discount of 331% and another discount of 10% for cash. Find the net price.

A discount of 33%, or, of the cost, leaves of the cost. A further discount of 10%, or, of the remainder, leaves f of, or §, of the cost; or, net price = } of $600 = $360.