49. How much bank currency could be bought for $ 4500, in coin, in 1864, when gold was at 285%?

50. A man having $8550 bequeathed 33% to his wife and the remainder to his children. How much did he give his children?

51. A bought goods to the value of $345.75, and sold them to B at 15% advance on his outlay, and B sold them to C at 15% less than his outlay. How much did C give for them?

Base and Percentage given, to find the Rate per cent
ORAL EXERCISES.

52. What per cent of 12 is 3?

Solution.

3 is of 12; and, or 0.25, or 25%.

53. What per cent of $35 is $7 ? Is $14? Is $28?

54. What per cent of 24 is 6? Is 12?

What per cent

55. Of 42 miles is 21 miles?

56. Of 75 tons is 45 tons?

57. Of 48 pounds is 30 pounds?

Is.18?

L

61. If 4 quarts of grain are given for grinding a bushel, what per cent is the cost of grinding?

62. John earns each week $7.50. He spends for board $2.50, and as much more for other things. What per cent of his earnings are his spendings?

64. What per cent of 600 bushels is 57 bushels ?

243. Rule for finding the Rate per cent.

Divide the percentage by the base, extending the division to hundredths.

73. Of a farm containing 1640 acres there are 246 acres in meadow. What per cent is in meadow ?

74. If the income on $1346 is $168.25, what is the rate?

Rate and Percentage given, to find the Base.

ORAL EXERCISES.

75. $25 is 5% of my money.

How much have I ?

Solution. As $25 is 5% of my money, 1 % of my money is of $ 25, or $5; 100 % of my money must be 100 times $5, or $500. Or, As $25 is 5%, or of my money, 20 of my money must be 20 times $25, or $500.

76. $6 is 20% of what number? 40 rods is 12% of what number?

77. 1 pound 4 ounces is 25 % of how many pounds?

78. A number increased by 25 % of itself is 60. What is the number?

Solution. As a number increased by 25 % of itself must be 125 %, or of itself, 60 must be of the number, and 4, or the number,

must be 48.

79. Sold a watch for $55, which was 10 % above its cost. What was its cost?

80. 42 is 33% less than what number? 33% more than what number?

Or, as $3550 is 25%, or of the number, the number must be four times $3550, or $14200.

82. $16.22 is 5% of what number?

83. Having sold 40 % of my sheep, I have 177 left. What number had I at first?

244.

Rule for finding the Base.

Divide the percentage by the rate per cent.

FORMULAS. b=p÷r. b = a ÷ (1+r). b = d÷ (1 − r).

89.

$14 is %.

90. I burned 1750 lb. of coal, or 25% of my supply, in a

single week. How much had I?

91. The expenses of a charity concert were 40% of the receipts. The poor received $250. What were the expenses? 92. An agent's salary having been decreased 33% is now $1600. What was it at first?

93. A man owes $ 6750, which is 75% as much as he is worth. How much is he worth?

94. The voters of a certain city number 16386, which is 20% more than the number 3 years ago. What was the number then?

PROFIT AND LOSS.

95. At a gain of 20 % of the cost of an article, what part of the cost equals the gain?

96. How much is gained by selling goods at 10 % profit when the cost is $25 ?

97. How much is lost on goods which cost $40 by selling them at a loss of 12% ?

98. A grocer buys tea at 45 cents a pound, and sells it at 60 cents a pound. What is the gain per cent?

99. Sold a cow

the gain per cent?

which cost me $40 for $45. What was

100. Sold a horse for $120, and gained 163 %. What did it cost?

101. Sold goods for $108, and lost 10 %. What was their cost?

245. Profit and Loss, as commercial terms, express the gain or loss in business transactions.

246. The base of computation is the cost, the gain or loss is the percentage; and the cases which occur correspond to, and are solved like the preceding cases of percentage.

WRITTEN EXERCISES.

102. How much is made by selling flour at 20% profit which cost $7.75 a barrel?

103. A dealer sold a stock of goods, damaged by fire, at an average of 66% less than cost. The cost being $ 18240, what was the loss?

104. Of a carload of fruit 25% is spoiled. I sell the remainder for 16% advance on its cost. What is my profit or loss on the load if it cost $400 ?

105. A merchant sold a cask of molasses which cost him $69.60 at a profit of 15%. What did he gain?

106. If I pay for goods $ 350.50, and sell them at 61% loss, how much shall I lose?

107. Sold a house which cost me $3500 at a gain of 8%. What did I receive for it?

108. Sold a carriage for $ 210 at a loss of 16%. What was the cost?

109. What per cent was gained by selling property that cost $2400 for $2550 ?

110. Bought hams for 8 cents a pound.

What per cent will be gained by selling them at 12 cents a pound?

111. Sold goods for $ 3312.70, and made 51⁄2 %. What was the cost?

112. If I am compelled to lose 121% on damaged goods, how should I sell those that cost me $560 ?

113. When the cost of flour is $7.50 a barrel, and the ex pense of selling 6%, at what price must it be sold to gain 5%?

114. Of goods worth $ 1600, one fourth is sold at a profit of 15%. For how much must the remainder be sold to gain 20% on the whole ?

115. Sold a watch for $28, and gained 12%. What per cent would I have gained or lost if I had sold it at $ 24 ?

116. Bought a cask of molasses containing 120 gallons for $ 50. But, a fifth of the molasses having leaked out, for what must the remainder be sold a gallon to gain 10% on the purchase?

117. By selling hay at $15 a ton I lose 10%. At what price must I sell it to gain 15% ?

118. A merchant sold goods for $150 and lost 10%, whereas he should have gained 30 per cent. How much were they sold under their proper value?

119. Bought goods for $14500. Half of them I am obliged to sell at a loss of 20%. If I sell the other half at a gain of 20%, what shall I gain or lose on the whole?