Hi there,
Given that the transistor turns on in 100ns and takes 8us to turn off but you still have to maintain the correct duty cycle for inputs of 10 to 40vdc, the turn on and turn off time will limit the maximum frequency where you can achieve the right duty cycles for full range operation.
If you can reduce the turn off time, so much the better, but for this question they dont want you to do that, so you will be working with 8us and 100ns.
For example, you can not switch at 250kHz because the fastest the transistor can switch is around 125kHz, and that's even without providing the correct duty cycle, so there is no way you can switch that fast. The question is, what really is the maximum frequency you can obtain. It's your job to figure this out.
Count yourself lucky that they did not include an efficiency constraint in this question too...I would have