Multiple choice

A man buys a pair of gloves having the price of Rs. 150 at Rs. 105. He is given two successive discounts. If he receives the second discount of 12.5%, then find the percentage of the first discount.

  1. 12.5%

  2. 15%

  3. 20%

  4. 17.5%

  5. 18%
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C Correct answer
Explanation

Let the first discount be x%. The price after the first discount is 150 * (1 - x/100). After the second 12.5% discount, the price is 150 * (1 - x/100) * (1 - 0.125) = 105. Solving 150 * (1 - x/100) * 0.875 = 105 gives 1 - x/100 = 105 / (150 * 0.875) = 105 / 131.25 = 0.8. Thus, x = 20%.

AI explanation

The selling price after two successive discounts is 105 divided by 150, which equals 0.7. Since the second discount of 12.5% leaves a multiplier of 0.875, the first discount multiplier is 0.7 divided by 0.875, which equals 0.8. Therefore, the first discount is 1 minus 0.8, or 20%.

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