To determine the distance by which P is ahead of Q after 4.5 seconds, we first need to calculate the speed of each runner.

1. Calculate the speed of P:
   • P can run 250 meters in 25 seconds.
   • The speed of P is calculated as: \(v_P = \frac{\text{Distance}}{\text{Time}} = \frac{250 \text{ m}}{25 \text{ s}} = 10 \text{ m/s}\)
2. Calculate the speed of Q:
   • Q can run 250 meters in 30 seconds.
   • The speed of Q is calculated as: \(v_Q = \frac{\text{Distance}}{\text{Time}} = \frac{250 \text{ m}}{30 \text{ s}} \approx 8.33 \text{ m/s}\)
3. Calculate the distance each covers in 4.5 seconds:
   • Distance covered by P in 4.5 seconds: \(d_{P_{4.5}} = v_P \times 4.5 = 10 \text{ m/s} \times 4.5 \text{ s} = 45 \text{ m}\)
   • Distance covered by Q in 4.5 seconds: \(d_{Q_{4.5}} = v_Q \times 4.5 \approx 8.33 \text{ m/s} \times 4.5 \text{ s} \approx 37.485 \text{ m}\)
4. Determine how much P is ahead of Q:
   • The distance P is ahead of Q after 4.5 seconds is: \(d_{\text{ahead}} = d_{P_{4.5}} - d_{Q_{4.5}} = 45 \text{ m} - 37.485 \text{ m} \approx 7.5 \text{ m}\)
   • Thus, P is ahead of Q by approximately 7.5 meters after 4.5 seconds.

Conclusion: The correct answer is \(7.5 \text{ m}\).