<PRE><B>Question 1080864</B>
1) The difference between a discount of 35% and two successive discounts of 20% and 20% on a certain bill was 22.


find the amount of the bill.


let x equal the amount of the bill.


a discount of 35% on the bill makes the bill equal to x - .35 * x = (1 - .35) * x = .65 * x.


the first discount of 20% on the bill makes the bill equal to x - .20 * x = .80 * x.


the second discount of 20% on the bill makes the bill equal to .80 * x - .20 * .80 * x which is equal to .80 * x - .16 * x which is equal to .64 * x.


the difference between a 35% discount on the original amount and two successive discounts of 20% on the original amount is .65 * x - .64 * x which is equal to .01 * x.


that difference is equal to 22, so you get .01 * x = 22.


solve for x to get x = 22/.01 = 2200.


the original amount was 2200.


a 35% discount on the original amount was .35 * 2200 = 770.


the discounted price was therefore 2200 - 7700 = 1430.


1430 is equal to 1430/2200 * 100 = 65% of the original cost, as we had calculated earlier.


a 20% discount on the original amount was .20 * 2200 = 440.


the first discounted price was therefore 2200 - 440 = 1760.


an additional discount of 20% on this amount was .20 * 1760 = 352.


the second discounted price was therefore 1760 - 352 = 1408.


1408 is equal to 1408 / 2200 * 100 = 64% of the original cost, as we had calculated earlier.


the difference between the 35% discounted price and the 20% on top of 20% discounted price is 1430 - 1408 = 22.


this confirms the solution is correct.


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2) A shopkeeper marks the prices of his goods at 25% higher than the original price. After that he allows a discount of 12%.

what profit or loss does he get?


let x equal the original price.


he marks it up by 25% which makes the marked price equal to x + .25 * x which is equal to 1.25 * x.


he gives a discount of 12% on this marked up price.


the discounted price is equal to 1.25 * x - .12 * 1.25 * x


simplify this to get the discounted price is equal to 1.25 * x - .15 * x.


combine like terms to get the discounted price is equal to 1.10 * x.


the original price was x.


the final discounted price off the marked up price is equal to 1.10 * x.


the difference is 1.10 * x - x which is equal to .10 * x.


thismeans the profit is equal to .10 * x which is equal to 10% of x which is equal to 10% of the original price.


to see if this makes sense, let x be any value.


i let x = 1000.


the marked up price is 1000 + .25 * 1000 = 1250.


a 12% discount on the marked price makes the discounted marked up price equal to 1250 - .12 * 1250 = 1100.


the original price was 1000.


the discounted marked up price was 1100.


the profit was 1100 - 1000 = 100 which is equal to 10% of the original price.


this confirms the solution was correct.


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