The ages of A and B are presently in the ratio of 5 : 6 respectively. Six years hence, this ratio became 6 : 7 respectively. What was B's age 5 years ago ?

A. 25 years

B. 30 years

C. 31 years

D. 36 years

E. None of these

Answer: Option C

Solution(By Examveda Team)

Let A's age be 5x years.
Then, B's age = 6x years
$$\eqalign{ & \therefore \frac{{5x + 6}}{{6x + 6}} = \frac{6}{7} \cr & \Rightarrow 7\left( {5x + 6} \right) = 6\left( {6x + 6} \right) \cr & \Rightarrow 35x + 42 = 36x + 36 \cr & \Rightarrow x = 6 \cr} $$
B's age 5 years ago = (6x - 5) years
= (6 × 6 - 5) years
= 31 years