Multiple choice

A trader gives 25% discount on his articles and still makes a profit of 25%. Find his profit per cent, if he sells his articles at their marked price.

  1. $\displaystyle 66\frac{2}{3}\%$
  2. $\displaystyle 68\frac{2}{3}\%$
  3. $\displaystyle 66\frac{1}{3}\%$
  4. $\displaystyle 16\frac{2}{3}\%$
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A Correct answer
Explanation

Let the cost price be 100. Since profit is 25%, the selling price is 125. A 25% discount on the marked price (MP) means 0.75 * MP = 125, so MP = 125 / 0.75 = 500/3. Selling at MP means selling at 500/3. Profit = (500/3 - 100) / 100 = 200/3 = 66 2/3%.

AI explanation

Assume the marked price is Rs. 100. Applying the successive discount formula, the selling price is 100 - 25 = Rs. 75. Since this yields a 25% profit, the cost price is (75 / 125) * 100 = Rs. 60. If the trader sells at the marked price of Rs. 100 instead, the new profit is 100 - 60 = Rs. 40. Using the profit percentage formula, (40 / 60) * 100 equals 66 2/3%.

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