The age of Sushil 6 years ago was three times the age of Snehal. 6 years hence, the age of Sushil would be `5/3`times that of Snehal.What is the present age of Snehal ?

Options

A. 14 years
B. 22years
C. 18 years
D. None of these

Answer

To solve the problem, we need to set up equations based on the information given about Sushil and Snehal's ages. Let's denote Snehal's present age as \( x \) years.

### Step-by-Step Solution:

1. **Define the ages**:
- Let Snehal's present age be \( x \).
- Therefore, Snehal's age 6 years ago was \( x - 6 \).
- Let Sushil's present age be \( y \).
- Therefore, Sushil's age 6 years ago was \( y - 6 \).

2. **Set up the first equation**:
- According to the problem, Sushil's age 6 years ago was three times Snehal's age 6 years ago. This gives us the equation:
\[ y - 6 = 3(x - 6) \]

3. **Simplify the first equation**:
- Expanding the equation:
\[ y - 6 = 3x - 18 \]
- Rearranging gives:
\[ y = 3x - 12 \quad \text{(Equation 1)} \]

4. **Set up the second equation**:
- The problem also states that 6 years hence, Sushil's age will be \( \frac{5}{3} \) times Snehal's age at that time. Therefore, we can write:
\[ y + 6 = \frac{5}{3}(x + 6) \]

5. **Simplify the second equation**:
- Expanding the equation:
\[ y + 6 = \frac{5}{3}x + 10 \]
- Rearranging gives:
\[ y = \frac{5}{3}x + 4 \quad \text{(Equation 2)} \]

6. **Substitute Equation 1 into Equation 2**:
- We can substitute \( y \) from Equation 1 into Equation 2:
\[ 3x - 12 = \frac{5}{3}x + 4 \]

7. **Clear the fraction**:
- Multiply through by 3 to eliminate the fraction:
\[ 9x - 36 = 5x + 12 \]

8. **Rearrange to solve for \( x \)**:
- Bringing all terms involving \( x \) to one side and constant terms to the other:
\[ 9x - 5x = 12 + 36 \]
\[ 4x = 48 \]
\[ x = 12 \]

9. **Conclusion**:
- The present age of Snehal is \( 12 \) years.

### Final Answer:
The present age of Snehal is **12 years**.