You might find it useful to compare this situation with this thread from a couple of months ago.
The 60W bulb example I used there shows how the resistance of the filament in a 240V bulb has to be four times greater than that of a 120V bulb if the power is to remain at 60W.
Your present problem is just looking at this same basic equation from the opposite direction, i.e. what happens to power if the resistance is kept constant.
