The height from which the ball falls gives it a potential energy which converts to kinetic energy as the ball falls down. When the ball finally hits the ground, all the potential energy has converted to kinetic energy. If we assume mass of ball as M kg, then
Mgh = (final kinetic energy)
120M = (final K.E.)
Ball loses 25% of (final K.E.), so initial energy with which it bounces back = 75% of (final K.E)
= (3/4) × 120M = 90M.
90M = Mgh
H= 9 metres.
There was a kinetic energy loss because you know, when the ball will bounce it'll create some sound and heat and vibrations on the floor, so the 25% of kinetic energy is lost there.