Well, the answer 1:2 is correct.

 

At the mid point, Let tension be T, force applied be F, and a be acceleration.

 

So, after drawing FBD, we get :

 

F-T=ma/2 [ we take mass as m/2 because, the net force on mid point is same

                 as the part of rope where the force F acts i.e mass of rope is m/2  ]

 

We know, F=ma

 

So, T is ma/2 at mid-point

 

So ratio is :

 

T:F = 1:2