If two number are in the ratio 2 : 3 and the ratio becomes 3 : 4 when 8 is added to both the numbers, then the sum of the two numbers is = ?

Answer: Option D

Let the 2 number be (2x, 3x)
According to the question,
$$\begin{array}{rl}& \Rightarrow \frac{2x+8}{3x+8}=\frac{3}{4}\\ & \Rightarrow 8x+32=9x+24\\ & \Rightarrow x=8\end{array}$$
Therefore, the sum of the two numbers is
= 2x + 3x = 5x
= 5 × 8 = 40