A boy of mass 20kg is standing on a 80kg free to move long cart. there is negligible friction

As there is no external force, so displacement of centre of mass of the cart + boy system parallel to the surface is zero.

∆x_cm=(m₁∆x₁+m₁∆x₁) / (m₁+m₂) 

0=(m₁∆x₁+m₁∆x₁) / (m₁+m₂) 

Let the boy moves towards the wall a distance 10 m and the cart moves away from the wall a distance x so,

displacement of man wrt ground towards the wall is ∆x₁=10-x

displacement of cart wrt ground towards the wall  is ∆x₂=-x

m₁∆x₁+m₁∆x₁=0

20(10-x)+80(-x)=0

100x=200

x=2m

displacement of man wrt ground towards the wall is ∆x₁=10-2=8m

Hence, the final distance of the boy from the wall will be X=25-8=17m