Present age of P is 45 years. 9 years hence ages of P and Q will be in ratio 6 : 7. What is the present age (in years) of Q?

Options

A. 64
B. 54
C. 63
D. 53

Explanation

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

1. **Identify the present age of P**:
The present age of P is given as 45 years.

2. **Determine the ages 9 years hence**:
In 9 years, P's age will be:
\[ 45 + 9 = 54 \text{ years} \]
Let the present age of Q be \( X \). In 9 years, Q's age will be:
\[ X + 9 \text{ years} \]

3. **Set up the ratio**:
According to the problem, the ratio of their ages in 9 years will be 6:7. Therefore, we can write the equation:
\[ \frac{54}{X + 9} = \frac{6}{7} \]

4. **Cross-multiply to eliminate the fraction**:
Cross-multiplying gives us:
\[ 54 \cdot 7 = 6 \cdot (X + 9) \]
Simplifying this, we get:
\[ 378 = 6X + 54 \]

5. **Rearrange the equation**:
To isolate \( X \), we subtract 54 from both sides:
\[ 378 - 54 = 6X \]
\[ 324 = 6X \]

6. **Solve for \( X \)**:
Now, divide both sides by 6:
\[ X = \frac{324}{6} = 54 \]

7. **Conclusion**:
The present age of Q is \( 54 \) years.