ORAL PROBLEMS

1. In a school containing 540 pupils 45% are boys. How many boys are there?

2. If potatoes shrink 10% in weight from November until March, how many bushels in October will amount to 270 bushels in March? 3. In a town of 1200 inhabitants 51% are females. How many males are there?

4. In 250 bushels of berries 4% are poor. How many bushels are poor?

5. In a distance of 96 miles 25% of the road is paved. How many miles are unpaved?

6. A man sold 10% of his cows and had 9 left. How many had he at first?

7. A man added 20% to his farm and had then 120 acres. How many acres had he at first?

8. I bought 560 fruit trees and lost 80. What per cent did I lose? 9. I sold 40 bushels of apples, which was 25% of my crop. How many bushels did I raise?

10. A paper had 5000 subscribers, and lost 100. How many per cent were lost?

11. A grocer had 72 barrels of flour and sold 18. How many per cent remained?

12. A man owned 250 acres of land, which was 250% of the amount his neighbor owned. How many acres did his neighbor have?

13. In a class of 250 students 20% failed. How many passed? 14. In a class of 360 students 18 failed. How many per cent failed? 15. At the end of a year I had added 25% to my bank accounts and then had $6250. How much had I at the beginning of the year? 16. On a certain day 3800 children attended school. This was 95% of the enrollment. What was the enrollment?

17. A man sold 25 head of young cattle for $1200, which was 20% more than they cost. What did they cost per head?

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 XIX

GROSS PROFIT AND LOSS; DISCOUNTS

248. 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.

249. 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.

250. 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.

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

252. 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

=

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:

253. 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%?