Two blocks are in contact on a frictionless table. One block has mass 'm' and the other has '2m'. A force 'F' is applied on '2m' as shown in the figure. Now the same force 'F' is applied from the right on 'm'. In the two cases respectively, the ratio of force of the contact between the two blocks will be:

If 'F' is the applied force, then acceleration of the system = a = $\frac{F}{3m}$

Case -1: When we apply the force from the right, the force applied on the block 2m will be $\frac{F}{3m}\times 2m$= $\frac{2F}{3}$.This will be the force on the contact then.
 

Case- 2: Now when we apply the force from the left, the force applied on the block 'm' = $m\times a = m \times \frac{F}{3m}$ = $\frac{F}{3}$. This will be the force in the contact.

So, the ratio is $\frac{2F}{3} : \frac{F}{3}$ = $2 : 1$

Hence, option (C) is correct.