A shopkeeper offers two successive discounts of \(20\%\) each on a sweater and still makes a profit of \(60\%.\) By what

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A shopkeeper offers two successive discounts of \(20\%\) each on a sweater and still makes a profit of \(60\%.\) By what percentage did the shopkeeper mark-up the price of the sweater?

A) \(60\%\)

B) \(100\%\)

C) \(150\%\)

D) \(200\%\)

E) \(250\%\)

Answer: C

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When a price is reduced by 20%, it becomes 80%, or 0.8, of its original value. So if a price is discounted by 20% twice, it becomes (0.8)(0.8) = 0.64 of its original value. So if the pre-discount price of the sweater was $100, the post-discount price was $64. If the retailer still makes a 60% profit at this selling price, this selling price is 1.6 times the retailer's purchase price, and if that is p, we have 1.6p = 64, and p = 40. There's a clarity issue with the wording of the question, but presumably we want to know the percent markup on the sweater before the discounts were applied, and if the retailer bought the sweater for $40, and intended to sell it for $100, the markup, or percent increase in the price, was 150%.
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