4 years ago, the average age of Sakshi, Anjali and Samridhi was 32 years ,6 year ago the average age of Anjali and Samridhi was 30 years. Find the present age of Sakshi

Options

A. 50 years
B. 48 years
C. 36 years
D. 42 years

Answer

To solve the problem, we need to find the present age of Sakshi based on the information given about the average ages of Sakshi, Anjali, and Samridhi at different points in time.

### Step-by-Step Solution:

1. **Understanding the Given Information:**
- 4 years ago, the average age of Sakshi, Anjali, and Samridhi was 32 years.
- 6 years ago, the average age of Anjali and Samridhi was 30 years.

2. **Setting Up the Equations:**
- Let the present ages of Sakshi, Anjali, and Samridhi be \( S \), \( A \), and \( M \) respectively.
- From the first statement, 4 years ago, their ages were \( S - 4 \), \( A - 4 \), and \( M - 4 \).
- The average age 4 years ago can be expressed as:
\[ \frac{(S - 4) + (A - 4) + (M - 4)}{3} = 32 \]
- Simplifying this, we have:
\[ (S + A + M - 12) = 96 \quad \text{(since } 32 \times 3 = 96\text{)} \]
- Therefore, we can write:
\[ S + A + M = 108 \quad \text{(Equation 1)} \]

3. **Using the Second Statement:**
- From the second statement, 6 years ago, the ages of Anjali and Samridhi were \( A - 6 \) and \( M - 6 \).
- The average age of Anjali and Samridhi 6 years ago can be expressed as:
\[ \frac{(A - 6) + (M - 6)}{2} = 30 \]
- Simplifying this, we have:
\[ (A + M - 12) = 60 \quad \text{(since } 30 \times 2 = 60\text{)} \]
- Therefore, we can write:
\[ A + M = 72 \quad \text{(Equation 2)} \]

4. **Finding the Present Age of Sakshi:**
- Now we have two equations:
- Equation 1: \( S + A + M = 108 \)
- Equation 2: \( A + M = 72 \)
- We can substitute Equation 2 into Equation 1:
\[ S + 72 = 108 \]
- Solving for \( S \):
\[ S = 108 - 72 = 36 \]

5. **Conclusion:**
- The present age of Sakshi is \( \boxed{36} \) years.