The average age of shikha and her huband Amit is `48` years. The average of shikha , Amit and their daughter Advika is `39` years. Find the age of Advika.

Options

A. `"21 years"`
B. `"22 years"`
C. `"23 years"`
D. `"24 years"`

Answer

To find the age of Advika, we can follow these steps:

1. **Define Variables**:
Let Shikha's age be \( x \), Amit's age be \( y \), and Advika's age be \( z \).

2. **Use the First Average**:
We know that the average age of Shikha and Amit is 48 years. This can be expressed mathematically as:
\[ \frac{x + y}{2} = 48 \]
To eliminate the fraction, we multiply both sides by 2:
\[ x + y = 96 \quad \text{(Equation 1)} \]

3. **Use the Second Average**:
The average age of Shikha, Amit, and Advika is 39 years. This can be expressed as:
\[ \frac{x + y + z}{3} = 39 \]
Again, we multiply both sides by 3 to eliminate the fraction:
\[ x + y + z = 117 \quad \text{(Equation 2)} \]

4. **Substitute Equation 1 into Equation 2**:
We can substitute the value of \( x + y \) from Equation 1 into Equation 2:
\[ 96 + z = 117 \]

5. **Solve for Advika's Age**:
To find \( z \), we subtract 96 from both sides:
\[ z = 117 - 96 \]
\[ z = 21 \]

Thus, the age of Advika is **21 years**.