MISCELLANEOUS PROBLEMS

What per cent

1. In 1911 the number of new pupils in a certain city was 3107, of which number 1584 were boys, and 1523 were girls. of the whole were boys? What per cent were girls? . of the number of boys was the number of girls?

What per cent

2. In 1913 the total enrollment in a certain city was 60,367, of which 278 were in the normal school; 3788 in the high schools; 54,291 in the elementary schools; 2010 in the kindergartens. What per cent of the whole were registered in each kind of school?

3. In 1914-15 the cost of instruction in the academic high schools in a city was $236,015.60; and in 1915-16, $276,443.20. What was the per cent increase of 1916 over 1915?

4. In 1917-18 the cost of instruction in the same schools was $320,666.18, which was an increase of 5.31% over the preceding year. What was the cost for 1916-17?

5. In 1917 the enrollment of the academic high schools at the close of the year was 4614, of which 1504 were classical students, and 3110 were scientific. How many per cent of the whole was each of these? The number left or withdrawn during the year was 679. Find the total registration, and the per cent of the total registration which left or withdrew during the year.

6. I owe A $142.80, which is 12% of all my debts. How much do I owe?

7. A man bought 20 cows for $85 per head. He sold 85% of them for $105 per head, and the remainder for $50 a head. Did he gain or lose, and how much?

8. A invests 25% of the capital of a firm; B, 40%; and C, the remainder which is $7000. What is the capital of the firm?

9. A man's salary is $4000. He spends 22% for fuel and rent; 12% for clothing; 3% for books; and $1018 for other expenses. What has he left?

10. I have in the bank $2750, which is 25% of what I have invested. What is the total amount of my investment?

CHAPTER XXII

GROSS PROFIT AND LOSS; DISCOUNTS

334. Applications of Percentage. - Percentage is of very general application in business. The treatment of profit and loss, discounts, interest, bank discount, brokerage, taxes, customs, stocks and bonds, and many other subjects, is based on percentage.

The element of time enters into such subjects as interest and bank discount, and makes them more difficult than subjects such as profit and loss, and trade discount in which time is not an essential element.

335. Profit and Loss. Practically the only reason why people engage in business is that they wish to make money. The money made in business is derived from what is called profits. Thus, a manufacturer who makes an article at a total cost of $10, and sells it for $12, makes a profit of $2. A merchant who buys a suit of clothes for $20, and sells it for $27.50, makes a gross profit of $7.50. 336. What is Meant by Cost. It is not absolutely clear what should be included under the term cost. A retail merchant buys a piece of furniture for $40 and pays $2.50 for freight and cartage. Should the $2.50 be counted as part of the cost? There are other incidental expenses such as interest on money invested, rental for store space, salaries of employees, etc.

Shall all of these elements be computed and entered as a part of the cost, thus leaving the amount by which the selling price exceeds this cost as a sort of net profit to the merchant, or shall the amount by which the selling price exceeds the buying price be regarded as profit, and then all these other items be paid out of profit?

While usage is not uniform on this point, it is pretty generally agreed that for the purpose of figuring gross profit "cost" shall be regarded as including the purchase price plus the freight and cartage and import duties if any, leaving out the other more incidental expenditures.

337. The Base on which Profit and Loss are Computed. The rate gain or loss is computed as so many per cent of the cost.

338. Finding the Selling Price. gain or the cost less loss.

The selling price equals cost plus

Thus: A dealer buys a baby cart for $2 and sells it at a gain of 50%. The gain is computed on the cost as a base. Hence the gain is 50% of $2 = $1 and the selling price is $2 + $1 = $3.

Again, if a dealer pays $50 for a farm wagon and sells it at a gain of 20%, the gain is 20% of $50 = $10, and the selling price is $50 + $10

=

$60.

Rule: To find the selling price, add the gain to the cost, or subtract the loss from the cost.

ORAL EXERCISES

Find the selling price of each of the following:

339. Finding the Rate Gain or Loss. Rule: To find the rate of gain or loss, find the gain or loss, and then find how many per cent of the cost this is.

Example. A dealer bought a plow for $16, and sold it for $20. What was the rate of gain?

Solution. The gain was $4, which equals 25% of $16, the cost.

ORAL EXERCISES

Find the rate of the gain or loss, in each of the following:

To find the selling price when the cost and the rate of gain or loss are given it is often most convenient to add the rate of gain to 1 or subtract the rate of loss from 1, and then multiply.

Example 1. Find the selling price of an article costing $45 and sold at a gain of 35%.

Solution. Multiply $45 by 1.35.

Example 2. Find the selling price of an article costing $125 and sold at a loss of 15%.

Solution. Multiply $125 by .85.

WRITTEN EXERCISES

Find the selling price in each of the following:

Find the rate of gain or loss on each of the following:

25. An agent bought two lots, paying $600 for each. He sold one at a loss of 15%, and the other at a gain of 15%. Did he gain or lose on the whole transaction, and how much?

26. Shirts were bought at $17.50 per dozen. At what price per shirt should they be marked to gain 33%?

340. Example 1.

FINDING THE COST

A manufacturer finds that he must make a profit of 25% in order to pay cost of selling his goods (advertising, traveling men, etc.), and make a reasonable net profit. He finds that the retail dealers are not willing to pay more than $10 for a certain article. At what cost must he aim to make the article?

Solution. The selling price equals 125% of the cost. Hence cost

= 10 ÷

Example 2. Find the cost of an article sold for $8.50, which was a loss of 15%.

Solution. 10

.85)8.50

850

Analysis: The selling price equals 85% of the cost. Hence $8.50 .85 $10 is the cost.

=

Rule: To find the cost when the selling price and the rate of gain or loss are given, divide the selling price by 1 + rate of gain or by 1 - rate of loss, expressed as a decimal.

15. An automobile is advertised to sell at $1575. At what price must the company sell it to the dealer to enable him to make a profit of 20%?