Length AB of the wedge shown in figure is rough and BC is smooth. A solid cylinder rolls without slipping from A to B.  If AB=BC, then ratio of translational kinetic energy to rotational kinetic energy when the cylinder reaches point C is :

 

For a cylinder  if $K_r$ is translational KE and $K_R$ is rotational KE

in case of pure rolling upto B: 

and 

After B: Rotational kinetic energy is constant however transitional kinetic energy increases.
At C: 

while 

 Alternative solution:
For journey from A to B, conserving energy we can write 

For solid cyliner, 

At B, rotational K.E, 

Also for journey from B to C, loss in P.E. is converted into additional translational K.E. so KE_T at C =