Multiple choice

A shopkeeper is selling a set of books whose minimum retail price is 30% more than the cost price. Then, he sold quarter of his books at a discount of 15%, and half of the books at the minimum retail price and the rest at a discount of 30%. Find his profit percentage.

  1. 15.375%

  2. 14.256%

  3. 15.265%

  4. 14.396%

  5. None of these
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A Correct answer
Explanation

Let cost price = 100. Retail price = 130. 1/4 sold at 15% discount (130 * 0.85 = 110.5). 1/2 sold at 130. 1/4 sold at 30% discount (130 * 0.7 = 91). Average selling price = (0.25 * 110.5) + (0.5 * 130) + (0.25 * 91) = 27.625 + 65 + 22.75 = 115.375. Profit = 15.375%.

AI explanation

Assume the cost price is Rs. 100 per book, making the minimum retail price Rs. 130. For a quarter of the books sold at a 15% discount, the selling price is 130 * 0.85 = Rs. 110.25; for half sold at the retail price, it is Rs. 130; and for the rest sold at a 30% discount, it is 130 * 0.70 = Rs. 91. The average selling price across these proportions is calculated as ((110.25 * 0.25) + (130 * 0.5) + (91 * 0.25)). Using this weighted average formula gives an overall selling price of Rs. 115.375, which against the Rs. 100 cost price results in a profit percentage of 15.375%.

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