Dynamics

This in only an arithmetic problem, as it doesn't involve any dynamics prinicples.
Assume fuel is burnt at a constant rate by the aircraft engine, since the max range is 3200 miles with a speed of 400 mph, the time taken t is
t = 3200/400 hours = 8 hours
Now, when flying into a headwind, the speed of the aircraft is reduced to (400-50) mph = 350 mph
Time needed to cover the journey of 3200 miles = 3200/350 hours = 9.143 hours
Therefore, excess time of flight = (9.143 - 8) hours = 1.143 hours
But by reducing a passenger load, the time of flight can be lengthened by 10/400 hours = 0.025 hours
Hence, in order to cover an excessive flight time of 1.143 hours, the no. of passengers needs to be reduced
= 1.143/0.025 = 45.72
That is, the number of passengers carried by the aircraft
= 100 - 45.72 = 54.28
Therefore, a max of 54 passengers are allowed on the aircraft.