A man of mass m stands at the left end of a uniform plank of length L and mass M, which lies on a frictionaless surface of ice. If the man walks to the other end of the plank, then by what distance does the plank slide on the ice?

Explanation

The net external force on the system (man `+` plank) is zero (their weights are balanced by the normal reaction on the sled and the ice is frictionless). The cenre or mass of the system is to be at the same position during their movements. Obviously, the plank will shift towards left.
Let the displacement of plank relative to ground `=x`
The displacement of man relative to ground `=-(L-x)`
Moments of masses about `C.M.=0`
`Mx-m(L-x)=0`
`impliesMx=m(L-x)`
`impliesx=(mL)/(m+M)`
As a shortcut remember the distance moved by bodies w.r.t ground is in the inverse ratio of their masses.