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:
- 31
- 34
- 33
- 32
The Correct Option is D
Approach Solution - 1
Let the present ages of Harish's two sons be \( x \) and \( y \).
Then, the sum of the ages of his two sons is \( x + y \).
According to the problem:
1. The present age of Harish is 8 times the sum of the ages of his two sons.
\( H = 8(x + y) \)
2. After 8 years, Harish's age will be twice the sum of the ages of his two sons.
\( H + 8 = 2(x + y + 16) \)
Solve these equations:
From Equation (1):
\( H = 8(x + y) \)
Substitute into Equation (2):
\( 8(x + y) + 8 = 2(x + y + 16) \)
Expand and simplify:
\( 8(x + y) + 8 = 2x + 2y + 32 \)
\( 8x + 8y + 8 = 2x + 2y + 32 \)
Rearrange terms:
\( 8x + 8y - 2x - 2y = 32 - 8 \)
\( 6x + 6y = 24 \)
Divide by 6:
\( x + y = 4 \)
Substitute \( x + y = 4 \) back into the first equation:
\( H = 8(x + y) = 8 \times 4 = 32 \)
Thus, the present age of Harish is 32 years.
Approach Solution -2
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, \(H = 8 \times 4 = 32\).
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