Renuka got married 8 years ago. Today here age is `1 1/3` times her age at the time of marriage. Her daughter's age is 1/8 times her age. He daughter's age is :

Options

A. 3 years
B. 4 years
C. 6 years
D. 8 years

Answer

To solve the problem step by step, let's break it down:

1. **Define Renuka's current age**:
Let Renuka's current age be \( x \) years.

2. **Determine Renuka's age at the time of marriage**:
Since Renuka got married 8 years ago, her age at that time would be \( x - 8 \) years.

3. **Set up the equation based on the given information**:
According to the problem, Renuka's current age is \( \frac{4}{3} \) times her age at the time of marriage. Therefore, we can write the equation:
\[ x = \frac{4}{3}(x - 8) \]

4. **Multiply both sides by 3 to eliminate the fraction**:
\[ 3x = 4(x - 8) \]

5. **Distribute the 4 on the right side**:
\[ 3x = 4x - 32 \]

6. **Rearrange the equation to isolate \( x \)**:
Subtract \( 4x \) from both sides:
\[ 3x - 4x = -32 \]
This simplifies to:
\[ -x = -32 \]
Therefore:
\[ x = 32 \]

7. **Calculate Renuka's daughter's age**:
The problem states that her daughter's age is \( \frac{1}{8} \) times Renuka's current age. So, we calculate:
\[ \text{Daughter's age} = \frac{1}{8} \times x = \frac{1}{8} \times 32 = 4 \]

8. **Final answer**:
Renuka's daughter's age is **4 years**.