Question

A capacitor is charged to a potential difference of 12v it delivers 40% of its stored energy to a lamp what is the final potential difference across the capacitor

Answer 1

Call the capacitance C. 
Note the energy in a capacitor with voltage V is E =½CV². 

Initial energy = ½C(12)² = 72C 

40% of energy is delivered, so 60% remains.in the capacitor. 
Remaining energy = (60/100) x 72C =43.2C 

If the final potential difference is X, the energy stored is ½CX² 
½CX² = 43.2C 
X² = 2 x 43.2 = 86.4 
X = 9.3V