A takes 2 hours more than B to walk P km, but if A doubles his speed, then he can make it in one hour less than B. How much time does B require for walking P km?

B needs 4 hours.

Let B take t hours, so A takes t + 2 hours.

Doubling A's speed halves A's time: (t + 2)/2.

This equals t - 1: (t + 2)/2 = t - 1.

t + 2 = 2t - 2, so t = 4 hours.