The sum of ages of father and his son is 40 yr and difference of their ages is 20 yr, then the age of the father will be

Options

A. 35 yr
B. 30 yr
C. 25 yr
D. 20 yr

Answer

To solve the problem step by step, we can follow these steps:

1. **Define the Variables**:
Let the age of the father be \( x \) years and the age of the son be \( y \) years.

2. **Set Up the Equations**:
We have two pieces of information:
- The sum of their ages is 40 years:
\[ x + y = 40 \quad \text{(1)} \]
- The difference of their ages is 20 years:
\[ x - y = 20 \quad \text{(2)} \]

3. **Add the Equations**:
To eliminate \( y \), we can add equations (1) and (2):
\[ (x + y) + (x - y) = 40 + 20 \]
This simplifies to:
\[ 2x = 60 \]

4. **Solve for \( x \)**:
Now, divide both sides by 2:
\[ x = \frac{60}{2} = 30 \]

5. **Conclusion**:
The age of the father is \( 30 \) years.