PRACTICE.

96. 1. A merchant offered a bill of goods at 12% less than list price, and gave a 3% discount on the remainder for cash. What was the merchant's list price if the cash paid was $3841.20?

2. The tax rate of a city is $10.50 on the $1000. The valuation is real estate, $12978456.40, and personal property, $5816743.57, and 14% of the real estate is exempt from taxation. A discount equal to 4% of the whole tax is given for prompt payment. What is the amount of tax collected?

3. A railroad has a capital stock of $33000000. Its business at the end of the last year showed the following results: Received - From passengers, $4872656.88; freight, $8846943.40; mails, express, and other sources, $564379.65. Expended For repairs of road and for taxes, $2425574 37; repairs of rolling-stock, tools, fuel, watchmen, etc., $2148632.20; salaries of officials, agencies, and for contingent expenses, $5009194.85. The debt of the road was $7500000, on which it paid interest at 6% for the year. The rent of branch roads was $1115689.10. An accident during the year cost $159875.70. The Government tax on passenger earnings and dividends was $201458.35. The road proposes to reserve at least $450000 before declaring a dividend. Omitting fractions of 1%, what % dividend can the road declare on its capital stock, and what is the total surplus reserved?

4. A gentleman owns three farms worth, respectively, $3800, $3000, and $4200. The first increases in value 15% and the second 12%. The third decreases 144%. What is the % of increase in the value of all?

5. A is a half owner in a vessel, and sells 20% of his share for $850. What is the value of B's shares, if he owns 371% of the vessel?

6. A's stock of goods is worth $8534, or 15% more than B's, and 15% less than C's. These three men propose to purchase a store for $10500, and unite in business, each investing, besides his share of the cost of the store, his stock and $300 cash. What will be the total worth of the firm?

7. At his death A's property was valued at $42360,

$27360 being in real estate and the remainder in personal property. His heirs were the widow, three sons, and two daughters. The will provided that the widow should receive

of the real estate and 20% of the personal property; and that the remainder should be divided among the sons and daughters, each daughter receiving 25% less than a son. What was the share of each?

8. A house completely finished has cost the owner $12894; it is 4 stories high, and on the ground floor are two stores, one of which rents at $225 and the other at $200 per year. Each of the other floors rents at $12.50 per month. The annual expense of the building is $36.89. What is the % of net income?

9. A grocer has two chests of tea, each weighing 60 lbs., one costing $45 and the other $84. He makes the price so as to gain 25%, and sells 8 lbs. from the first chest and 5 lbs. from the second. What did he receive?

10. Bought 60 bbls. of flour at $9 per bbl., but a part of it having been damaged, half of it was sold at a loss of 10%. The remainder was sold at $9.50 per bbl. What was lost by

the transaction?

11. Let each of the following columns be considered a separate question and find how the term marked ? may be found if the terms are given.

TRADE DISCOUNTS.

97. In many branches of business the manufacturers and dealers catalogue, or list, their goods at a certain price, called the LIST PRICE. When sales are made the bills sold show this price and the allowance, or TRADE DISCOUNT, that is given the purchaser.

NOTE 1. To avoid the trouble of re-listing their goods each time the market price changes, this list price is made large enough to cover all ordinary market changes by simply changing the rate of discount on bills sold. NOTE 2. - Discounts are also given in proportion to the amount of the bill. Thus, a bill of goods listed at $100 is sold subject to a 5% discount, while a bill amounting to $1000 may be subject to a 10% discount.

NOTE 3. Many establishments sell their goods on a certain term of credit with the privilege of a certain discount if paid before the term expires and another discount for cash. Sometimes, when goods are sold on credit and no other discount is allowed, the seller is willing to discount at a certain rate per annum for the unexpired term, when the bill is paid before it is due. This is similar to Bank Discount. Sometimes, also, this discount is given in addition to the ordinary Trade Discount.

98. The principles used in finding Trade Discounts are like the principles of percentage. The list price is always the base, the discount is the percentage, and the net amount is the difference.

99. To find the net selling price.

RULE.

list price.

Find the discount by Art. 93, and subtract it from the

1. $450 sold at a discount of 10%.

2. $1175 sold at a discount of 10% and 5%. $375 sold at a discount of 20% and 10%.

4. $3400 sold at a discount of 10%, 10%, and 24%. $1960.50 sold at a discount of 25%, 20%, and 10%.

5.

6. What is the net cost of a case of prints containing 32443 yds. at 6c. per yd., less 5% and 2%, cooperage, 50c.?

7. What is the net value of 5 bales cotton cloth, each containing 450 yds., at 7c., less 10% and 1%,- charges, $1.50?

8. I can buy goods of one man for $1250, with a discount of 30% and 10%. At another place I can get the same goods at the same price with 40% off. At which place should I buy and how much will I save?

9. July 27 I purchased goods amounting to $1360 on the following terms: 60 days, or less 5% if paid in 30 days, or less 12% if paid in 10 days. How much will settle the bill August 9? How much August 26?

10. A bill of hardware is sold as follows: $45 at a discount of 20% and 10%; $11.50 at a discount of 9%; $18.20 at a discount of 20%, 10%, and 5%; $36.75 at a discount of 10%, 5%, and 2%; $63.75 at a discount of 40%, 10%, and 2%; $192 at a discount of 60%, 10%, and 2%; $300 at a discount of 50%, 20%, and 1%; and $90 net. What is the net amount of the whole bill?

100. Often a discount series is given instead of a single discount. In this case it may sometimes be more convenient to reduce the series to an equivalent single discount before performing operations.

101. To change a discount series to a single discount. RULE. Take 100% as the base. On this base find the first percentage of the series, and subtract this percentage from the 100%. Find the second percentage of the series on this remainder and sub'tract this percentage from this remainder, and so continue till all the discounts have been taken. The last remainder will be the cent. of net proceeds. Subtract this per cent. of net proceeds from 100%, and the remainder will be the single discount.

EXAMPLES.

What single discount is equivalent to the series

per

102. To find at what price goods should be marked, or listed, in order to give a certain discount on the marked price and net a certain selling price.

RULE. Find the % of net proceeds as in Art. 101, Rule. Divide the required selling price by the % of net proceeds.

EXAMPLES.

At what price must goods be marked to net —

1. $15, after giving a discount of 20%?

2. $5.60, after giving a discount of 163%?

3. $2.50, after giving a discount of 10% and 5% ?

4.

$9.40, after giving a discount of 20%, 10%, and 5% ? 5. $8.20, after giving a discount of 10%, 10%, and 5% ? 6. 10% profit, after giving a discount of 20% and 5%, if the cost is $20?

NOTE. Add the amount of profit to the cost to get the net selling price. Then apply the rule.

7. 12% profit, after giving a discount of 25% and 10%, if the cost is $18.60 ?

8. 61% profit, after giving a discount of 10%, 10%, and 5%, if the cost is $45?

9. 16% profit, after giving a discount of 30%, 20%, and 10%, if the cost is $75?

10. 10% loss, after giving a discount of 10%, 5%, and 2%, if the cost is $24?

NOTE. price.

Take the amount of loss from the cost to get the net selling Then apply the rule.

11. 5% loss, after giving a discount of 30% and 10%, if the cost is $150?

12. 8% loss, after giving a discount of 15% and 5%, if the cost is $240 ?

13. 114% loss, after giving a discount of 40%, 5%, and 2%, if the cost is $9.27 ?