Renuka got married 8 years ago. Today her age is `1 1/3` times her age at the time of marriage. Her daughter's age is 1/8 times her age. Her 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, we will determine Renuka's current age and then find her daughter's age based on the information provided.

### Step 1: Define Renuka's current age
Let Renuka's current age be represented as \( X \).

### Step 2: Determine Renuka's age at the time of marriage
Since Renuka got married 8 years ago, her age at the time of marriage would be:
\[ X - 8 \]

### Step 3: Set up the equation based on the information given
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:
\[ X = \frac{4}{3}(X - 8) \]

### Step 4: Solve the equation
To eliminate the fraction, multiply both sides of the equation by 3:
\[ 3X = 4(X - 8) \]
Expanding the right side:
\[ 3X = 4X - 32 \]
Now, rearranging the equation to isolate \( X \):
\[ 3X - 4X = -32 \]
\[ -X = -32 \]
\[ X = 32 \]
So, Renuka's current age is 32 years.

### Step 5: Calculate Renuka's daughter's age
According to the problem, Renuka's daughter's age is \( \frac{1}{8} \) times Renuka's current age. Therefore, we can calculate her daughter's age as follows:
\[ \text{Daughter's age} = \frac{1}{8} \times 32 = 4 \]

### Conclusion
Renuka's daughter's age is 4 years.

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