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A retailer charges 25% more than his purchase price for any

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A retailer charges 25% more than his purchase price for any [#permalink] New post 30 Mar 2018, 02:17
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A retailer charges 25% more than his purchase price for any appliance he sells. When the retailer has a clearance sale, all appliances are marked 10% off. If the dealer sells a vacuum cleaner during a clearance sale, his profit (selling price minus purchase price) is what percent of his purchase price of the vacuum cleaner?

A. 10%

B. 12.5%

C. 15%

D. 17.5%

E. 20%
[Reveal] Spoiler: OA

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Re: A retailer charges 25% more than his purchase price for any [#permalink] New post 31 Mar 2018, 20:44
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let the purchase price (or cost price ) CP=x.
then Selling price is 25% more than cost price. SP=1.25x
during clearance, 10% OFF is offered. then the selling price after discount is = 1.25x-10% of 1.25x= 1.125x
profit = 1.125x-x =0.125x
profit%=0.125x/x *100% =12.5%

ans:B
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Re: A retailer charges 25% more than his purchase price for any [#permalink] New post 31 Mar 2018, 21:50
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Often, when per cents are given, they'll be easier to deal with if converted to fractions. In this case, since the dealer is making 25% profit, we can just think of that as 5/4 of the purchase price. A 10% off sale can be thought of as a "90% on" sale, which means in fraction form it's 9/10 of the selling price, which is 5/4 of the purchase price, so we should multiply these two fractions:

5x9
4x10

giving us 45/40 of the purchase price. Since this is 5/40ths over the purchase price, we can convert 5/40 into 12.5%. (The easiest way to do the arithmetic is to make the denominator into 100 by multiplying both the numerator and denominator by 2.5, giving us 12.5/100, which is 12.5%) Thus the answer is B.
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Re: A retailer charges 25% more than his purchase price for any   [#permalink] 31 Mar 2018, 21:50
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