What number 8. Diminished by 16% of itself = 700 ? 9. Diminished by 75 % of itself = 125? 10. Diminished by 131% of itself 11. Diminished by 621% of itself Ans. 840. Ans. 500. 260? Ans. 300. Ans. 350. Ans. 225. 12. Diminished by 874% of itself 281? = 13. Diminished by 933% of itself = 12? Ans. 200. 14. A drover bought 360 head of cattle, which was 25% more than he already had. How many had he before the purchase? Ans. 288 head. 15. The average school term in Pa., in 1869, was 6.04 mo., which was 11.2% more than in 1863. What was the average term in 1863 ? 16. The average Pa. school term in which was 10.05% less than in 1869. in 1869 ? Ans. 5.43 mo. 1863, was 5.43 mo., What was the length Ans. 6.04 mo. from Pittsburgh to 17. The distance by the P. R. R. Harrisburg is 246 miles, which is 125% more than the distance by the same road from Harrisburg to Philadelphia. What is the latter distance? Ans. 109.2 mi. 18. W. R. Ford bought a farm for a certain sum, expended for stock 11% of the price of the farm, and found that the whole cost was $7215. What was the cost of the farm alone? Ans. $6500. 19. H. J. Gourley raised 800 bu. wheat, which was 25% more than of what Logan raised. How many bushels did Logan raise? Ans. 1280 bu. 20. A man dying bequeathed 10% of his property to his son, 20% of the remainder to his daughter, 334% of this remainder to his wife, and the remainder, or $48000, to charitable purposes. Required the value of the estate. Ans. $100000. 305. Formulas. The entire subject of Percentage may be summed up in A thorough knowledge of the use of these formulas is about all the pupil needs to carry him through the Applications of Percentage; for by a simple substitution of the proper terms for B, P, R, &c., they can be made applicable to all cases except Interest, in which the element time (t.) is introduced. 306. Applications of Percentage. Percentage is, because of its convenience, extensively used in business calculations. Its principal commercial applications are in Profit and Loss, Insurance, Commission, Interest, Discount, Stocks, Exchange, Taxes, Partnership and Bankruptcy. 30%. Profit and Loss are terms used to express the gains or losses in business transactions. Gains and losses are computed at a certain rate per cent of the cost or the sum invested, and the operations involve the principles already explained in Percentage. 308. The Base is the cost or the sum invested. 309. The Rate % is the rate per cent of profit or loss. 310. The Percentage is the profit or loss. 311 (a). The Amount is the sum of cost and profit, or the selling price. 311 (6). The Difference is the cost less the loss, or the selling price. CASE I. 312. To find the sum gained, or lost, when the cost and rate % are given. Oral Exercises EXAMPLE 1.-A wagon that cost $150 was sold at a gain of 20%. What was the gain? SOLUTION.-Since the gain was 20%, it was, or of $150, or $30. EXAMPLE 2.-A horse that cost $300 was sold at a loss of 27%. What was the loss? SOLUTION. Since the loss was 27%, it was 2% of $300, or $81. EXAMPLE.What is the gain, when goods are bought for $250 and sold at a gain of 15% ? the cost by the rate (r), .15. In either case we obtain the same result, $37.50. 313. RULES.—Take such part of the cost as the rate % Multiply the cost by the rate. (B × r = P.) PROBLEMS. 1. Sold goods which cost me $1250, at a gain of 121%. How much did I gain? Ans. $156.25. PERCENTAGE. 2. How much do I lose by selling a horse, which cost me $542, at a loss of 18% ? Ans. $97.56. wish to sell my goods at a profit of 20%; how shall I mark calicoes that cost 10 ? Delaines that cost 40 ? Toweling that cost 121? Silks that cost $3? Broadcloths that cost $4.50? Satins that cost $5? Ans. to last, $6. 4. I am closing out my stock, and willing to lose 121% on cost of my goods. How should I mark hose that cost 32 ? Collars that cost 89 ? Cloaks that cost $32? CASE II. Ans. to last, $28. 314. To find the rate % of gain or loss, when the cost and gain, or loss, are given. Oral Exercises + EXAMPLE.-Bought a shawl for $16, and sold it at an advance of $4. What % did I gain? SOLUTION.-My gain is $4 on $16, or 1 of cost. Since cost is 100%, my gain is of 100%, or 25%. PROBLEMS. 1. Bought calico for 8 per yard, and sold it so as to gain 2 on each yard. What % did I gain? 2. Bought shoes at $5, and sold them at $6. What was the gain %? 3. Bought oranges at 3 apiece, and sold them at 5. What is the rate % gain? 4. Bought apples at 3 for 5, and sold them at 4 for 5%. What % was the loss? 5. Bought a book for $2, and sold it for $1.50. What was the loss %? |