The ratio of the ages of A and B, 3 years ago, was 5 : 7. The ratio of their ages, 13 years from now, will be 9 : 11. If the present age of C is 11 years less than that of B, then the present age of C, in years, is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 20.
The ratio of the ages of A and B, 3 years ago = 5 : 7
Let the age of A and B three years ago be 5x and 7x, respectively.
So, (5x + 3 + 13)/(7x + 3 + 13) = 9/11
⇒ (5x + 16)/(7x + 16) = 9/11
⇒ 55x + 176 = 63x + 144
⇒ 8x = 32
⇒ x = 32/8 = 4
Present age of B = 7x + 3 = 7(4) + 3 = 28 + 3 = 31 years
Present age of C = 31 - 11 = 20 years
Therefore, the present age of C is 20 years.