Two particles having masses m and 2m are travelling along x-axis on a smooth surface with velocities u₁ and u₂, collide. If their velocities after collision are v₁ and v₂, then the ratio of velocities of their centre of mass before and after impact is

There are no net external forces operating on the system during a collision; all forces acting on the system are internal forces. 

As a result, acceleration is zero and the hit has no effect on COM's velocity.

The velocity of the centre of mass remains constant after a collision because there is no external force acting on the two mass systems. 

The velocity ratio before and after the impact is therefore 1:1.