Question

A and B possess books in the ratio of 3 : 4. B and C possess them in the ratio 2 : 3. If C gives 20 books to A, then A, B and C possess books in the ratio 4 : 4 : 5. Find how many books A, B and C originally had?

• A. 30, 40, 60
• B. 60, 80, 100
• C. 60, 80, 120
• D. 40, 40, 50

Answer 1

Answer:

C. 60, 80, 120

Given:

A and B possess books in a ratio of 3 : 4.

B and C possess them in the ratio 2 : 3.

If C gives 20 books to A, then A, B, and C possess books in the ratio 4 : 4 : 5.

Calculation:

The ratio of the number of books of A to B = 3 : 4

The ratio of the number of books of B to C = 2 : 3 = 4 : 6

Hence, the ratio of the number of books of A, B to C

⇒ 3 : 4 : 6

Let's suppose, A, B, and C originally had 3k, 4k, and 6k books respectively.

According to the question,

(3k + 20) : 4k = 4 : 4 (Taking A and B only)

⇒ 12k + 80 = 16k

⇒ 4k = 80

⇒ k = 20

Now, A, B, and C originally had $(3\times{20})$ i.e. 60, $(4\times{20})$ i.e. 80, and $(6\times{20})$ i.e. 120 books respectively.

∴ A, B and C originally had 60, 80, and 120 books respectively.