Multiple choice

An article is marked at 100% above its cost price. After allowing two successive discounts of 5% and 20% respectively on the marked price, it is sold at x% profit. What is the value of x?

  1. 48

  2. 75

  3. 72

  4. 52
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D Correct answer
Explanation

Let CP = 100, so MP = 200. Applying a 5% discount gives 190, and a 20% discount on 190 (38) results in a selling price of 152. The profit is 152 - 100 = 52, which is 52%.

AI explanation

Assume the cost price is 100, making the marked price 200 since it is marked 100% above cost. Using the equivalent single discount formula of 100 minus (D1 plus D2 minus D1 times D2 divided by 100), the discount is 100 minus (5 plus 20 minus 1), which equals 24%. The selling price is 200 times (1 minus 0.24), resulting in 152. This selling price of 152 represents a 52% profit on the cost price of 100. The value of x is 52.

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