Multiple choice

CAT [1997] After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how much percentage above the cost price does he mark his goods?

  1. 28.56%

  2. 35%

  3. 22.22%

  4. 18%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let CP = 100. Gain = 14.28% (1/7), so SP = 114.28. Discount = 11.11% (1/9). Let MP be x. x * (1 - 1/9) = 114.28 => x * 8/9 = 114.28 => x = 114.28 * 9 / 8 = 128.56. Markup = 28.56%.

AI explanation

Convert the given percentages into their fractional equivalents, where an 11.11% discount is 1/9 and a 14.28% gain is 1/7. Let the cost price be 1, so the selling price becomes 1 + 1/7 = 8/7. The selling price is also equal to the marked price multiplied by (1 - 1/9), so 8/7 = marked price * 8/9, which gives the marked price = 9/7. The markup percentage above the cost price is calculated as ((9/7) - 1) / 1 * 100, which equals 2/7 * 100 = 28.56%.

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