Hello,

The energy initially stored by the capacitor is (1/2 C*V^2) or( Q^2 / 2*C) 

When the plate separation is doubled, the charge remains constant and the capacitance is halved. The work done in separating the plates is the difference in energy stored:this is

Q^2 / 2*0.5*C - Q^2 / 2*CT

This represents double the initial energy less the initial energy. The work done in adding this energy is Q^2 / 2*C.that is answer is option B

Hope this helps......