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1. 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 ?

A. 5 : 2

B. 2 : 1

C. 11 : 7

D. 13 : 9

Solution:

Let the man's age be 7x years ,
Then son's age = 3x years

\begin{aligned} ∴ 7 x \times 3 x = 756 \\ \Rightarrow 21 x^{2} = 756 \\ \Rightarrow x^{2} = 756 \\ \Rightarrow x^{2} = 36 \\ \Rightarrow x = 6 \end{aligned}

The ratio of their ages after 6 years

\begin{aligned} = (7 x + 6) : (3 x + 6) \\ = (7 \times 6 + 6) : (3 \times 6 + 6) \\ = 48 : 24 \\ = 2 : 1 \end{aligned}

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