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Question:

A bookseller sells only three books – A, B and C – on Sundays and their Selling Price are in the ratio 4 : 5 : 6 respectively. The bookseller makes 10%, 20% and 30% profit on selling A, B and C respectively. If the bookseller made an overall profit of 20% on a Sunday when he sold at least one copy of each of the three books, then which of the following statements is definitely true regarding that day?

Explanation:

Let the Selling Price of a copy A, B and C be 4x, 5x and 6x respectively.

Let the Cost Price of a copy A, B and C be CA, CB and CC respectively.

Let the number of copies of A, B and C sold on that Sunday be a, b and c respectively.

∴ 1.1aC_A+ 1.2bC_B+ 1.3cC_C= 1.2(aC_A+ bC_B+ cC_C)

⇒ aC_A = cC_C

⇒ $\frac{a}{c} = \frac{C_{C}}{C_{A}}$ = $\frac{\frac{6 x}{1.3}}{\frac{4 x}{1.1}}$ > 1

Hence, option (b).

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