# 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 ?

• 15 : 2
• 22 : 1
• 311 : 7
• 413 : 9
Explanation:-

Solution:
Let the man's age be 7x years ,
Then son's age = 3x years
$\begin{array}{rl}& \therefore \text{7}x×3x=756\\ & ⇒21{x}^{2}=756\\ & ⇒{x}^{2}=756\\ & ⇒{x}^{2}=36\\ & ⇒x=6\end{array}$

The ratio of their ages after 6 years

$\begin{array}{rl}& \therefore \text{7}x×3x=756\\ & ⇒21{x}^{2}=756\\ & ⇒{x}^{2}=756\\ & ⇒{x}^{2}=36\\ & ⇒x=6\end{array}$