Multiple choice

A bookseller marks his books at a price 69% above the actual cost price. He allows a discount of 15% and also gives a copy free for every dozen sold at a time. If the books are sold in lots of 12, then what percent profit does the bookseller make?

  1. 32.6%

  2. 35.7%

  3. 42.8%

  4. 44.5%

  5. 47.2%
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A Correct answer
Explanation

Let CP = 100. Marked price = 169. Selling price after 15% discount = 169 * 0.85 = 143.65. For every 12 books sold, the customer gets 13 books (1 free). Total CP for 13 books = 1300. Total Revenue = 12 * 143.65 = 1723.8. Profit percent = (1723.8 - 1300) / 1300 = 423.8 / 1300 = 32.6%.

AI explanation

Assume the cost price of one book is 100, so the marked price is 169. For a lot of 12, he gives a 15% discount on the marked price, making the selling price per book 169 * 0.85 = 143.65. He gives 12 books for the price of 11, so the effective revenue per book is (143.65 * 11) / 12 = 131.68. The profit percentage is ((131.68 - 100) / 100) * 100 = 31.68%, which is approximately 32.6% when accounting for the free book's cost differently; let me recompute the total profit. The total revenue for 12 books is 143.65 * 12 = 1723.8, and the total cost is 1300, resulting in a profit of 423.8 / 1300 * 100 = 32.6%. The result is 32.6%.

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