Two persons of masses 55 kg and 65 kg respectively are at the opposite ends of a boat. The length of the boat is 3.0 m and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sita with him. If the boat is in still water the centre of mass of the system shifts by

If we take boat and both persons as a system, there is no external force acting on the system. The center of mass of the system is initially are rest and will be at rest as there is no external force acting on it to displace center of mass. Hence there is no shifting of center of mass.