Step 1: Understanding the Concept:
This problem can be translated into a set of linear algebraic equations. A crucial factor to keep in mind when tracking ages over time is that when $N$ years pass, every single individual grows older by $N$ years. Therefore, the sum of the ages of two sons will increase by $2 \times N$ years over an $N$-year interval.
Step 2: Key Formula or Approach:
Let Harish's present age be $H$, and let the combined present sum of his two sons' ages be $S$.
- Condition 1 (Present): $H = 8S$
- Condition 2 (After 8 years): Harish's age becomes $H + 8$, and the sum of his two sons' ages becomes $S + 8 + 8 = S + 16$.
- Equation 2: $H + 8 = 2(S + 16)$
Step 3: Detailed Explanation:
From the first condition, we establish our first relation:
\[ H = 8S \quad \text{--- (Equation 1)} \]
From the second condition, we set up the equation for their future ages:
\[ H + 8 = 2(S + 16) \]
Expand the right side of the equation:
\[ H + 8 = 2S + 32 \]
Subtract 8 from both sides to isolate $H$:
\[ H = 2S + 24 \quad \text{--- (Equation 2)} \]
Now, equate Equation 1 and Equation 2 to solve for $S$:
\[ 8S = 2S + 24 \]
Subtract $2S$ from both sides:
\[ 6S = 24 \]
\[ S = 4 \]
Now substitute $S = 4$ back into Equation 1 to find Harish's present age ($H$):
\[ H = 8 \times 4 = 32 \]
Step 4: Final Answer:
The present age of Harish is 32 years.