Question

Now, the age of the Father and that of his Son are in the ratio 7 : 2. After 10 years, the ratio will become 9 : 4. The present age of the son is (in years)

• A. 25
• B. 10
• C. 15
• D. 8

Answer 1

The Correct Option is B

Let the present age of the son be \( 2x \) and the father be \( 7x \). After 10 years, their ages will be \( 2x + 10 \) and \( 7x + 10 \). 
The ratio after 10 years is given as \( \frac{7x + 10}{2x + 10} = \frac{9}{4} \). 
Solve this equation: \[ 4(7x + 10) = 9(2x + 10) \] \[ 28x + 40 = 18x + 90 \quad \Rightarrow \quad 10x = 50 \quad \Rightarrow \quad x = 5 \] The present age of the son is \( 2x = 10 \). 
For age-related ratio problems, set up an equation based on the given ratio and solve for the unknown variable.