The ratio of a man's age and his son's age is 7 : 3 and the product of their ages is 756. The ratio of their ages after 6 years will be ?

Answer: Option B

Let the man's age be 7x years ,
Then son's age = 3x years
$$\begin{array}{rl}& \therefore \text{7}x\times 3x=756\\ & \Rightarrow 21x^2=756\\ & \Rightarrow x^2=756\\ & \Rightarrow x^2=36\\ & \Rightarrow x=6\end{array}$$
The ratio of their ages after 6 years
$$\begin{array}{rl}& \text{ = }\left(7x+6\right):\left(3x+6\right)\\ & =\left(7\times 6+6\right):\left(3\times 6+6\right)\\ & =48:24\\ & =2:1\end{array}$$