Can any body help me understand the physics of a block of mass m sliding on a friction-less ramp kept on a friction-less horizontal table?

Consider a ramp of mass M, which has velocity V, and the block with mass m and velocity v.

Since there are no horizontal external forces, conserve horizontal momentum:
MV = mv
If your ultimate goal is to solve for V (the speed of the ramp), then rewrite as
v = MV/m

Since there are no losses, conserve energy:
mgΔh = ½MV² + ½mv² → where Δh is the change in height of the block
and substitute for v.
mgΔh = ½MV² + ½m(MV/m)² = ½MV² + ½MV²(M/m) = ½MV²(1 + M/m)
V² = 2mgΔh / M(1 + M/m)
which can be rearranged in a number of ways.

Consider that Δh might be expressed in terms of the angle of the incline:
Δh = ΔL*sinΘ → where L is the distance the block travels on the incline.

Does that help?