यदि पिता एवं पुत्र की आयु का योग (वर्षो में) 65 है तथा उनकी आयु के अन्तर का दुगुना 50 वर्ष है तब पिता की आयु होगी -

Options

A. 45 वर्ष
B. 40 वर्ष
C. 50 वर्ष
D. 55 वर्ष

Answer

To solve the problem, we need to set up equations based on the information provided.

1. **Let the father's age be \( x \)** and the son's age be \( y \)**.
2. According to the problem, the sum of their ages is 65 years:
\[ x + y = 65 \quad \text{(Equation 1)} \]

3. The problem also states that the double of the difference of their ages is 50 years:
\[ 2(x - y) = 50 \quad \text{(Equation 2)} \]

4. We can simplify Equation 2:
\[ x - y = 25 \quad \text{(Divide both sides by 2)} \]

5. Now we have two equations:
- Equation 1: \( x + y = 65 \)
- Equation 2: \( x - y = 25 \)

6. We can solve these equations simultaneously. Let's add Equation 1 and Equation 2:
\[ (x + y) + (x - y) = 65 + 25 \]
This simplifies to:
\[ 2x = 90 \]

7. Now, divide both sides by 2 to find \( x \):
\[ x = 45 \]

8. Now that we have \( x \), we can find \( y \) using Equation 1:
\[ 45 + y = 65 \]
Subtract 45 from both sides:
\[ y = 20 \]

Thus, the father's age is \( 45 \) years.

### Summary of the Solution:
- Father's age \( x = 45 \)
- Son's age \( y = 20 \)