Two particles A and B initially at rest move towards each other under a mutual force of attraction. At the instant when the speed of A is V and the speed of B is 2v, the speed of the centre of mass of the system is

Since the particles are moving due to mutual attraction, which is an internal force, the velocity of the centre of mass wont change. Centre of mass is altered only when an external force acts on the system. Since, the particles are initially at rest, centre of mass's velocity will be zero initially and stays zero later on too.