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 ?

Answer: Option C

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