7. What number diminished by 20% of itself is 36? ANALYSIS. Since 36 is the number diminished by of itself, 36 is, or of the number; and if of the number is 36, the number itself is 5 times of 36, which is 45. 8. What number diminished by 5% of itself is 57 ? 11. 35 yd. are 121% less than what number? 12. A boy spent 25% of his money, and had 75 cents left. How much had he at first? 13. A grocer sells coffee for 36 cents a pound, which is 12% above cost. What did it cost? 14. A farmer sold 334% of his flock of sheep, and kept 100. How many had he at first? 15. In a grammar class there are 18 girls, which is 20% more than the number of boys. How many pupils in the class? WRITTEN EXERCISES. 1. What number increased by 20% of itself amounts to 360 ? 용 188 = $ 360300 Since a number increased by 20% or of itself is of the same number, 360 is of the required number, etc. 2. What number increased by 15% of itself is 644 ? 3. What sum increased by 8% of itself is 1475? 4. What number diminished by 121% of itself is 175? OPERATION. 1 .125.875 175.875= = 200 Or, 871 100 8 175200 ANALYSIS.-Since the number is diminished by 12%, or .125 of itself, 175 is 87%, or .875 of the number. Hence dividing 175 by .875 equals 200, the required number. Or, Since a number diminished by 12%, or of itself, is of the same number, 175 is of the required number, etc. 5. What number diminished by 30% of itself is 350? 6. What number diminished by 41% of itself is 1640? RULE.-Divide the amount by 1 plus, or 1 minus the rate, as the case may require. The nature of the question will sufficiently indicate whether 1 is to be increased or diminished by the rate, to form the divisor. What number increased 7. By 15% of itself is 345 ? 8. By 36% is 238 A.? 9. By 100% is 84.6? 10. By 6% is 1272 bu.? 11. By 22% is $549 ? What number diminished 12. By 65% of itself is $2590? 13. By 50% is 28.5 ft.? 14. By 163% is 1035 mi.? 15. By 4% is $465.60? 16. By 371% is $203.375? 17. Sold a horse for $340, which was 15% less than his value. What was his value? 18. A man having increased his bank deposit 40%, it amounted to $840. How much had he at first? 19. My income this year is $2232, which is 7% less than it was last year. How much was it last year ? 20. A man sold 160 A. from his farm, which was 12% less than the number of acres he retained. How many acres in his farm? PROFIT AND LOSS. 381. Profit and Loss are commercial terms used to express the gain or loss in business transactions. 382. Profits and losses are usually estimated at some rate per cent on the cost, or on the money or capital invested. 383. Four cases occur which involve the same principles and operations as those of Percentage already considered. The corresponding terms are the following : The Amount is the cost plus the gain, or the Selling Price. The Difference is the cost minus the loss, or the Selling Price. ORAL EXERCISES. 384. 1. A watch that cost $80 sold for 20% more than cost. What was the gain, and the selling price? 1009 ANALYSIS. Since the gain was 20%, = 20, or of $80, or $16, the selling price was $80 + $16 $96. Hence, etc. (374). 2. Paid $48 for a cow, and sold her for 121% less than cost. What was the loss, and the selling price? 3. A merchant bought cloth at $4 a yard, and sold it at 25% advance. How much was his profit? 4. A carriage that cost $120 sold at a loss of 10%. How much did it bring? 5. A grocer bought sugar at 12 cents a pound. For how much must he sell it to gain 25% ? 6. Bought gloves at $12 a dozen. For how much a pair must they be sold to gain 50%? 7. Butter, bought at 32 cents a pound was sold at a loss of 121%. At what price did it sell? 8. Flour was bought for $8, and sold for $10 a barrel. What was the gain per cent? ANALYSIS.-The whole gain is the difference between $8 and $10, which is $2. Since $8 gains $2, or of itself, the gain per Hence, etc. (376). cent is of 100%. 9. What is gained per cent, by selling tea at $.90 that cost $.80 ? 10. Sold oranges for 2 cents each that cost 36 cents a dozen. What was the loss per cent? 11. A man sold a boat for $20, which was of what it cost him. What was his loss per cent? 12. Sold damaged goods at a loss of of what they cost. What was the loss per cent? 13. If an article be sold at double the cost, what % is gained? 14. What % is lost on articles sold at one-half the cost? 15. What per cent does a merchant lose, who sells goods at their cost? 16. What % profit does a grocer make who buys coffee at 30 cents and sells it at 35 cents? 17. A fruit dealer sold pears at a profit of $3 a barrel, which was a gain of 20%. What did they cost? ANALYSIS. Since the gain was 20%, the cost; $3 is of 5 times $3, or $15. = 20 100 or, $3 is 20%, or Hence, etc. (378). 18. Sold a horse for $30 more than cost, and gained 16%. What did he cost? 19. A dealer gained 30% by selling boots at $1.50 a pair above cost. What did they cost, and what was the selling price? 20. A drover sells sheep at a profit of $14 a head, which is a gain of 25%. What did they cost, and what is the selling price? 21. Sold muslin at 45 cents a yard, and gained 12%. What did it cost? ANALYSIS.—Since the gain was 12%, or the cost, 45 cents, the selling price, is the cost. of 45 cents, or 5 cents, is the cost, and is 8 times 5 cents, or 40 cents. Hence, etc. (380). 22. A music-box sold for $72, which was 10% less than cost. How much did it cost? 23. Sold turkeys at 30 cents a pound, and gained 20%. How much did they cost a pound? 24. If I lose 20% by selling flour at $8 a barrel, how much would I receive if I sold it at 20% above cost? WRITTEN EXERCISES. 385. The difference between the cost and selling price is the gain or loss. Gain, when the selling price is the greater. Loss, when the cost is the greater. 386. To find the selling price, Add the gain to the cost. Or, Subtract the loss from the cost. Find the profit, or loss, 1. On tea that cost $135, and sold at 20% gain (374). |
