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Since there is no external force acting on the system of two masses M and 5M. Thus the centre of mass of the system will remain unaltered.
Considering mass M to be initially at the origin, The CM will be
X = (0×M + 5M×12R)/(5M+M)
=> X = 10R
Thus CM is at a distance 10R which remains unchanged before and after collision.
At collision the centre of the spherical masses will be 3R apart from each other
Now let the collision take place at a distance x from the origin
After collision
=> {mx + 5m(x+3R)}/6m = 10R
=> 6x + 15R = 60R
=> 6x = 45R
=> x = 7.5R
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