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9. What number added to 20% of itself gives 564? 10. $4.80 is 33% more than what sum?

11. A man receives $1650 a year, and his expenses are 872% of his income: how much has he left?

12. The number of children of school age in a certain city is 5220, which is 36% of the number of inhabitants: what is the population of the city?

13. A farm was sold for $6390, which was 121% more than it cost. What was the cost of the farm?

14. A man sold a stock of goods for $10811, and gained 131%. What was the cost of the goods?

15. A owns 421% of a farm worth $35000, B owns 37% of it, and C owns the remainder. What is the value of each of their shares? Verify your work.

16. A farmer's crop of corn this year is 8% greater than his crop last year, and the two crops amounted to 5200 bushels. What was his last year's crop?

17. In the erection of a house, I paid twice as much for material as for labor. Had I paid 6% more for material, and 9% more for labor, my house would have cost $1284. What was its cost?

18. A clerk whose wages had been reduced 10% was receiving $63 per month. What were his wages before the reduction? Verify your work.

19. A man sold two horses for $360 each. On one he gained 25%, and on the other he lost 25%. Did he gain or lose, and how much?

20. Our stock decreased 331%, and again 20%; then rose 20%, and again 33%; we have thus lost $66: what was the stock worth at first?

APPLICATIONS OF PERCENTAGE

WITHOUT TIME

298. The applications of percentage may be divided into two classes: those in which time is not considered, and those in which time is an element.

In this chapter there will be considered only those applications of percentage in which the time element does not enter.

I. PROFIT AND LOSS

299. Fundamental Principle. The gain or loss is reckoned at a certain per cent of the cost or sum invested.

EXAMPLES 1. A merchant sold a hat which cost $2.40, at a gain of 15% What did he receive for it?

SOLUTION :
1. 100% of cost = $2.40, cost.
2. 1% of cost ibo of $2.40 $0.024.
3. 15% of cost = 15 x $0.024 $0.36, gain.
4. .. $2.40, cost, + $0.36, gain, $2.76, amount received.

SHORT PROCESS :
$2.40 x .15 = $0.36, gain.
$2.40 + $0.36 = $2.76, amount received.

2. A hat that cost $4.50 was sold for $4.95. What was the gain per cent?

SOLUTION :
1. $4.95 - $4.50 = $0.45 = the gain.
2. $4.50 $100% of the cost.
3. $0.01 ato of 100% of the cost %% of the cost.
4. $0.45 45 x 3% of the cost = 10% of the cost.

SHORT PROCESS.
$4.95 — $4.50 = $0.45 = the gain.
$0.45 – $4.50 .1 10%, ans.

Exercise XXXIV

1. A man sold cotton costing him $1500 at a gain of 163%. Find the gain.

2. Mr. Smith bought goods and sold them at a loss of 121%, losing $137. Find the selling price.

3. By selling a horse for $70, 163% of its cost was gained. What did the horse cost?

4. A grain dealer sold { of his wheat for what the whole amount cost him. How many per cent did he gain?

5. A's home cost him $800; he sold it for $900; he bought it back for $1000. What % did he gain or lose?

6. A man bought cotton at 163% less than the market price, and sold it at 20% more than the market price. What per cent did he gain?

7. A merchant sells hats for $5 apiece, making a profit of 331%. What did the hats cost apiece?

8. John bought a pony for $25, and set a price so that after deducting $18 he gained 20%. What % of the asking price did he deduct?

9. If the selling price of an article is á of its cost, what per cent is lost?

10. A merchant bought a barrel of maple syrup, containing 46 gallons, at $2.50 per gallon. If 6 gallons leaked out, at how much per gallon must he sell the rest so as to gain 25%?

II. COMMERCIAL OR TRADE DISCOUNT

300. Commercial or trade discount is a deduction of a certain rate from bills, or from the list price of goods.

Manufacturers, publishers, and wholesale dealers usually issue catalogues in which the prices of their goods are listed. Trade discounts are made to avoid the necessity of changing the prices printed in the catalogues. As the cost of production varies, the market price changes accordingly, and the discounts are changed to meet the rise or fall in prices while the list price remains the same.

301. The discounts are reckoned at so many per cent. Frequently more than one discount is allowed.

Thus, “20 and 10 off” means 20% less than 100% of the list price, or 80% of the list price, and then 10% less than 80% of the list price, which is 72% of the list price.

The cost of an article at a discount of 20% and 10% off is 72% of the list price.

EXAMPLES

1. What is the cost of an article listed at $760, if the discounts are 20% and 15%? SOLUTION : 1. $760 – 20% of $760 $608.

2. $608 15% of $608 $516.80, ans. 2. Find the cost of an article listed at $520, the discounts being 15% and 10%.

$520 x 85 x 90 SOLUTION: Cost

$397.80, ans.

100 x 100 NOTE.-Show that this solution is virtually the same as the preceding one.

Exercise XXXV

1. The list price of a bill of goods is $450; if the discounts are 30%, 10%, and 5%, what is the cost?

2. If an article sells at 30 and 10 off for $6.30, find the

list price.

3. Show that 30% and 20% off is equal to 44% off.

4. If an article is bought at a discount of 30% and 10%; and sold at list price, find the rate per cent profit.

5. A man bought goods listed at $250 at a discount of 10% and a certain per cent off for cash. If the cost was $213.75, what was the per cent off for cash?

6. A merchant buys goods listed at $2359 at discounts of 331%, 10%, and 5%. Find the cost.

7. A man settled a bill of $20 with $13.50, the discounts being (-) and 10% off. Fill the blank.

8. A merchant sold an article at 20% and 10% off. If the discounts amounted to $5.60, for how much did the article sell?

9. What was the list price of the article in problem 8? 10. Show that 30%, 20%, and 5% off amounts to the same as 5%, 20%, and 30% off.

11. What is the difference on a bill of $650, between a discount of 30%, and a discount of 25% and 5% off?

12. How must I mark goods that cost me $450 so that I may sell at 10% off from marked price at a gain of 20%?

13. Find the difference between a direct discount of 30% and discounts of 15% and 15%.

14. A merchant paid $1323 for goods, and the discounts were 25%, 121%, and 10%. Find the list price.

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