A man of mass 50 kg stands on a crate of mass 200 kg. The rope attached to the crate passes over a pulley. What force must the man apply on the rope for the system to remain in equilibrium?

Man's mass: $m = 50$ kg
Crate's mass: $M = 200$ kg
Acceleration due to gravity: $g = 10$ m/s$^2$

Forces: weight $mg$ downward, normal force $N$ upward from crate, tension $T$ upward from rope.

Substitute $m = 50$ kg, $g = 10$ m/s$^2$:

$N + T = 500$ N
$N = 500 - T$ N

Forces: weight $Mg$ downward, normal force $N$ downward from man, tension $T$ upward from rope.

Substitute $M = 200$ kg, $g = 10$ m/s$^2$:

$T = 2000 + N$ N

$2T = 2500$ N
$T = 1250$ N

The required force is $\boxed{1250 N}$.