The ratio of present ages of P and Q is 5:8. Three years later their ages will be in ratio 8:11. What is the present age (in years) of Q?

Options

A. 5
B. 11
C. 14
D. 8

Explanation

To solve the problem, we need to find the present age of Q given the ratio of the present ages of P and Q and their ages in the future.

### Step-by-Step Solution:

1. **Define the Present Ages:**
Let the present age of P be \( 5x \) and the present age of Q be \( 8x \), where \( x \) is a common multiplier.

2. **Set Up the Future Age Ratio:**
In 3 years, the age of P will be \( 5x + 3 \) and the age of Q will be \( 8x + 3 \). According to the problem, the ratio of their ages after 3 years will be \( 8:11 \).

This gives us the equation:
\[ \frac{5x + 3}{8x + 3} = \frac{8}{11} \]

3. **Cross Multiply to Eliminate the Fraction:**
Cross multiplying gives:
\[ 11(5x + 3) = 8(8x + 3) \]

4. **Expand Both Sides:**
Expanding both sides results in:
\[ 55x + 33 = 64x + 24 \]

5. **Rearrange the Equation:**
To isolate \( x \), we move all terms involving \( x \) to one side and constant terms to the other side:
\[ 55x - 64x = 24 - 33 \]
This simplifies to:
\[ -9x = -9 \]

6. **Solve for \( x \):**
Dividing both sides by -9 gives:
\[ x = 1 \]

7. **Calculate Present Ages:**
Now we can find the present ages of P and Q:
- Present age of P: \( 5x = 5(1) = 5 \) years
- Present age of Q: \( 8x = 8(1) = 8 \) years

8. **Conclusion:**
Therefore, the present age of Q is \( 8 \) years.

### Final Answer:
The present age of Q is **8 years**.