Multiple choice

The total cost price of certain number of books is $450$. By selling the books at $50$ each, a profit equal to the cost price of $2$ books is made. Find the approximate number of books.

  1. $13$
  2. $11$
  3. $15$
  4. $25$
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B Correct answer
Explanation

Let n be the number of books. Total CP = 450. Selling Price = 50n. Profit = 50n - 450. Profit = 2 * (CP per book) = 2 * (450/n). So 50n - 450 = 900/n. 50n^2 - 450n - 900 = 0. n^2 - 9n - 18 = 0. Solving for n gives approximately 10.5, so 11 is the nearest integer.

AI explanation

Let the total number of books be n, making the total selling price 50 multiplied by n, which equals 50n rupees. The profit is the selling price minus the cost price, so 50n minus 450 equals the cost price of 2 books; assuming a uniform cost, the cost price of 2 books is 2 multiplied by (450 divided by n). Solving 50n minus 450 equals 900 divided by n results in the quadratic equation 50n squared minus 450n minus 900 equals 0, which simplifies to n squared minus 9n minus 18 equals 0. Factoring this gives (n minus 11)(n plus 2) equals 0, meaning n is 11 books.

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