Multiple choice

Mr. Colin bought $800$ books. He sold $65 \%$ of them at $Rs \ 15$ each, $60 \%$ of the remainder at a discount of $40 \%$ and the rest of the books at cost price. If he earned $Rs \ 1056$, find the cost price of each book.

  1. $Rs \ 10$
  2. $Rs \ 18$
  3. $Rs \ 12$
  4. $Rs\ 16$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP be x. Sales: 520 books at 15 (7800), 168 books at 60% of 15 * 0.6 = 5.4 (907.2), and 112 books at x. Total revenue is 8707.2 + 112x. Total cost is 800x. Profit = 8707.2 - 688x = 1056. Solving gives x = 12.

AI explanation

He sold 520 books at Rs. 15, 168 books at a 40% discount, and kept the remaining 112 books at cost price, meaning the total profit of Rs. 1056 comes only from the first two categories. The profit from the first category is 520 * (15 - CP) and from the second is 168 * (9 - CP), since their selling price is 15 * 0.60 = Rs. 9. Setting the sum of profits to 1056, 520 * 15 + 168 * 9 - 688 * CP = 1056, simplifying to 9312 - 688 * CP = 1056, which yields CP = 8256 / 688 = Rs. 12.

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