Question

The present age of Harish is 8 times the sum of the ages of his two sons. After 8 years, his age will be twice the sum of the ages of his two sons. The present age of Harish (in years) is:

• A. 31
• B. 34
• C. 33
• D. 32

Answer 1

The Correct Option is D

Let Harish's present age be \(H\) and the sum of the present ages of his two sons be \(S\). We are given that \(H = 8S\).

After 8 years, Harish's age will be \(H + 8\), and the sum of the ages of his two sons will be \(S + 8 + 8 = S + 16\). 

We are given that \(H + 8 = 2(S + 16)\).

Substituting \(H = 8S\) into the second equation, we get \(8S + 8 = 2(S + 16)\).

\(8S + 8 = 2S + 32\)

\(6S = 24\)

\(S = 4\)

Therefore, \(H = 8 \times 4 = 32\).

Answer 2

Let the sum of the sons' ages be $x$. 

Harish's age is $8x$. 

After 8 years: $8x + 8 = 2(x + 16) \Rightarrow 8x + 8 = 2x + 32 \Rightarrow 6x = 24 \Rightarrow x = 4$. 

Harish's current age is $8 \times 4 = 32$.