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EXERCISE 133

PROBLEMS WITHOUT NUMBERS

1. How do you find some required per cent of a number? 2. How do you express per cent as a decimal fraction? 3. How do you express a decimal fraction as per cent? 4. How do you express per cent as a common fraction? 5. How do you express a common fraction as per cent? 6. Name eight of the most important per cents, and the corresponding common fractions.

7. If you know the base and rate, how do you find the percentage?

8. How do you find what per cent one number is of another?

9. How do you find the number of which a given number is a certain per cent?

10. If you know your weight a year ago and also to-day, how do you find the gain? the per cent of gain?

11. If you know how many pounds you have gained, and the per cent, how do you find your weight a year ago?

12. Knowing how much a man paid for his farm, and the amount for which he is selling it, how can you find the per cent of gain or loss?

13. Knowing that a farmer paid a certain amount for a team of horses, and sold them at a certain per cent of profit, how do you find the selling price?

14. If a boy had a kite string of a certain length, and lost a certain per cent of it, hov you find the amount left?

15. If a boy had a fishing line of a certain length, and you know how many feet of it he lost, how do you find the per cent of loss?

CHAPTER XII

PROFIT AND LOSS

229. Profit and Loss. In business transactions profit and loss are often computed as certain per cents of the cost of the property. The following may be taken as typical problems in profit and loss, including the marking of goods:

(1) At what price must a merchant mark goods that cost $275, so as to gain 20% ?

If he gains 20% of $275 he gains of $275, or $55. Therefore he must mark the goods $275 + $55, or $330.

(2) If goods marked $75 are sold at a bargain sale for 15% off the marked price, at what price are they sold?

If the goods are sold at 15% off the marked price, they are sold for $75 less 15% of $75, or $75 – $11.25, or $63.75.

(3) If some goods are damaged so that they are marked down to $120, or 25% below cost, how much did they cost?

100% of the cost = the cost.
25% of the cost = the loss.
75% of the cost

1% of the cost = 100% of the cost =

the selling price
5 of $120.

100 (or) of $120, or $160.

(4) A dealer sold a hat that cost $2.40 so as to gain 25%. The selling price was 20% less than the marked price. What was the marked price?

80% of the marked price 1% of the marked price 100% of the marked price

He gained 25% (or 4) of $2.40, or $0.60. Therefore the selling price was $2.40 + $0.60, or $3. Now show that

=

=

$120.

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EXERCISE 134

For how much must a merchant sell goods that he bought at the price here given, so as to gain the per cent specified?

17. $480, 163%. 18. $540, 333%. 19. $720, 121%. 20. $172.80, 121%. 21. $373.20, 16%. 22. $45,550, 17%. 23. $27,475, 22%.

24. $75,250, 25%.

1. $30, 10%. 2. $45, 12%.

3. $75, 15%.

4. $25, 12%.

5. $36, 14%.

6. $65, 15%.

7. $72, 18%.

8. $85, 25%.

9. $240, 121%. 10. $375, 15%. 11. $675, 16%.

12. $175, 81%.

13. $190, 91%.
14. $250, 12%.

15. $375, 15%.
16. $735, 18%.

If goods marked as here shown are sold at a bargain sale for the given per cent off, find the selling price :

25. $60, 15%.
26. $85, 18%.
27. $72, 22%.
28. $75, 10%.

31. $176, 61%.
32. $712, 12%.
33. $972, 16%.
34. $720, 61%.
35. $840, 12%.
36. $636, 16%.

37. $975, 20%.
38. $960, 25%.
39. $981, 33%•
40. $225.40, 25%.
41. $27,250, 20%.
42. $22,400, 17%.

29. $65, 12%.
30. $96, 15%.

If goods are sold for the sum specified, which is the given

per cent below cost, find the cost:

43. $71.25, 5%. 50.
44. $72.16, 12%. 51.
45. $58.48, 14%. 52.
46. $66.75, 11%. 53.
47. $72.98, 11%.
48. $140, 20%.
49. $726, 12%.

$735, 121%. 57. $358.80, 22%. $506, 12%. 58. $568.80, 21%. $382.50, 15%. 59. $226.20, 13%. $848.40, 12%. 60. $11,780, 20%. 54. $736.89, 121%. 61. $12,300, 18%. 55. $207.20, 30%. 62. $14,025, 15%. 56. $265.60, 17%. 63. $14,700, 12%.

Given the cost and rate of gain as follows, find the amount

of gain:

64. $275, 15%. 69. $275.40, 15%. 65. $365, 121%. 70. $346.50, 16%. 66. $4723, 14%. 71. $492.75, 18%. 67. $3965, 16%. 72. $575.50, 24%. 68. $7287, 22%. 73. $812.50, 16%.

79. $275, 6%. 82. $362.50, 4%. 80. $345, 4%. 83. $427.50, 8%. 81. $463, 8%. 84. $732.25, 12%.

74. $4275.50, 8%. 75. $2936.40, 12% 76. $3275.75, 16%. 77. $4206.03, 331%. 78. $3742.20, 16% %.

Given the cost and rate of loss as follows, find the amount of loss:

85. $4725.25, 8%.

86. $2632.50, 12%.

87. $4170.20, 15%.

88. Some goods were sold for $1015.30 at a loss of 311%. Find the loss.

89. Beans bought @ $1.60 a bushel are sold @ 7 a quart. Find the per cent of gain or of loss.

90. A dealer sold some goods that cost $875 so as to gain 15%. What was the selling price?

91. A man bought a farm for $4800 and sold it at a gain of 25%. What was the selling price?

92. A merchant's stock of goods cost him $8450. It was damaged 45% by fire. What was it then worth?

93. Papers bought at the rate of 60 for 50 are sold for 10 each. Find the per cent of gain and the cost of 90 papers.

94. A box of 180 oranges is bought for $5.40. The oranges are sold at 50 per dozen. Find the gain per cent.

95. A dealer buys 320 yd. of cloth at 87 a yard. At what price per yard must he sell the cloth to make a profit of $40?

96. A merchant marked his goods by private signs so as to conceal the exact cost. He used this scheme:

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BKE

An article worth between $1 and $2 was marked
9 indi-
cating the cost and the selling price. What was the cost?
the selling price? the gain? the per cent of gain?

97. Using the key words of Ex. 96, what is the per cent of gain on a hat that cost LEE and sells for LKE?

98. Using EDUCATIONX for 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, what is the per cent of profit on an arithmetic that costs AA and sells for OX?

99. Using the key of Ex. 98, how must a dealer mark a pair of shoes that cost UUX so as to sell them at a profit of 33% ?

100. Using ARITHMEtiC as the key, and X and Y as duplicate symbols for 0, how may a dealer mark goods that cost tTX and IIY so as to make a profit of 25% on the former and 33% on the latter?

The class may be encouraged to devise similar key words and make examples to correspond.

101. A merchant sold some goods that cost $175 so as to gain 20%. The selling price was 20% less than the marked price. What was the marked price?

102. A dealer sold some furniture for which he had paid $240 so as to gain 12%. The selling price was 25% less than the marked price. What was the marked price? What per cent was the marked price above cost?

103. A grocer buys 50 bu. of potatoes at 60g a bushel and retails them at 20 a peck. Find his whole gain and his gain per cent.

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