Answer to Question #75717 in Classical Mechanics for ADP

Question

Three men A, B & C of mass 40kg, 50kg & 60kg are standing on a plank of mass 90kg, which is kept on a smooth horizontal plane. B sits in the middle of the plane and A and C sit 2 metres away on opposite sides. If A & C exchange their positions then mass B will shift how many meters and in which direction?Ans: 1/3to the right.

Doubt:
A)Why can't we put the coordinate of 50kg mass as a variable in the Centre of Mass (CM) formula and then equate the two equations?
The answer comes out to be 8/5 that way.
B)The earlier CM is at 1/6 and as forces are only internal, the CM should not shift.
The new CM (considering 50kg at 0) comes to be -1/6. Stating that the CM shifted by 1/3 to the right.
To bring back the CM to 1/6, 50kg will move. What my doubt is why would the 50kg mass move to 1/3? And when we put 1/3 as coordinate for 50kg mass,the CM doesn't come out to be 1/6.

Thank you.