A man is 3 years older than his wife and four times as old as his son. If the son becomes 15 years old after 3 years. Then what is the present age of the wife?
एक आदमी अपनी पत्नी से 3 वर्ष बड़ा है और उसकी उम्र अपने बेटे की 4 गुना है। अगर बेटा 3 साल के बाद 15 वर्ष का हो जाता है, तो उसकी पत्नी की वर्तमान उम्र क्या है?

Options

A. 60 years/वर्ष
B. 51 years/वर्ष
C. 48 years/वर्ष
D. 45 years/वर्ष

Explanation

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

1. **Define Variables:**
Let the present age of the man be \( x \).
Since the man is 3 years older than his wife, the present age of the wife will be \( x - 3 \).
The man is also four times as old as his son, so we can denote the son's age as \( \frac{x}{4} \).

2. **Determine Son's Age in 3 Years:**
According to the problem, the son will be 15 years old after 3 years. Therefore, we can express this as:
\[ \frac{x}{4} + 3 = 15 \]

3. **Solve for \( x \):**
Rearranging the equation gives:
\[ \frac{x}{4} = 15 - 3 \]
\[ \frac{x}{4} = 12 \]
Now, multiply both sides by 4 to find \( x \):
\[ x = 12 \times 4 = 48 \]

4. **Calculate the Present Age of the Wife:**
Now that we have the age of the man, we can find the age of the wife:
\[ \text{Wife's age} = x - 3 = 48 - 3 = 45 \]

5. **Conclusion:**
Therefore, the present age of the wife is \( 45 \) years.