Question

The present age of Harish is 8 times the sum of the ages of his two sons at present. After 8 years, his age will be 2 times the sum of the ages of his two sons. The present age of Harish (in years) is:

• A. 31
• B. 32
• C. 33
• D. 34

Hint:

Be careful with age problems involving multiple people.
After \( T \) years, the sum of the ages of \( N \) people increases by \( N \times T \), not just \( T \).
Here, since there are two sons, the sum of their ages increases by \( 2 \times 8 = 16 \). Avoiding this common trap is key to getting the correct answer.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This problem involves determining the present age of Harish using linear equations. We are given the relationships between Harish's age and the sum of his two sons' ages at two different time points: at present and 8 years in the future.

Step 2: Key Formula or Approach:
Let \( H \) represent the present age of Harish.
Let \( S \) represent the sum of the present ages of his two sons.
We establish two equations based on the conditions:
1. At present: \( H = 8S \).
2. After 8 years: Harish's age increases by 8 years, while each of his two sons also ages by 8 years. Thus, the sum of their ages increases by \( 2 \times 8 = 16 \) years.
The new relationship is:
\[ H + 8 = 2(S + 16) \]

Step 3: Detailed Explanation:
1. Let Harish's present age be \( H \) years.
2. Let the sum of the present ages of his two sons be \( S \) years.
3. According to the first condition:
\[ H = 8S \quad \text{--- (Equation 1)} \]
4. Now, let us consider the scenario after 8 years:
- Harish's age will be \( H + 8 \).
- The sum of the ages of his two sons will be \( S + 8 + 8 = S + 16 \) (since there are two sons, both ages increase by 8).
5. According to the second condition:
\[ H + 8 = 2(S + 16) \quad \text{--- (Equation 2)} \]
6. We can now solve these equations by substituting the value of \( H \) from Equation 1 into Equation 2:
\[ 8S + 8 = 2(S + 16) \]
7. Expanding the right side of the equation:
\[ 8S + 8 = 2S + 32 \]
8. Rearranging the terms to isolate the variable \( S \):
\[ 8S - 2S = 32 - 8 \]
\[ 6S = 24 \]
9. Dividing by 6, we get:
\[ S = 4 \]
10. Now, we find the present age of Harish by substituting \( S = 4 \) back into Equation 1:
\[ H = 8 \times 4 = 32\text{ years} \]

Step 4: Final Answer:
The present age of Harish is 32 years, which corresponds to option (B).