Eight years ago, the ratio of ages of A and B was 5 : 4. The ratio of their present ages is 6 : 5. What will be the sum (in years) of the ages of A and B after 7 years from now?

Answer: Option C

Let the income of A and B be 8 years ago = 5x, 4x
$$\begin{array}{rl}& \frac{\text{A}}{\text{B}}=\frac{5x+8}{4x+8}=\frac{6}{5}\\ & 25x+40=24x+48\\ & x=8\\ & \frac{\text{A}}{\text{B}}=\frac{5x+8+7}{4x+8+7}\\ & =\frac{5\times 8+15}{4\times 8+15}\\ & =\frac{55}{47}\end{array}$$
Sum of ages of A and B = A + B = 55 + 47 = 102