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There is a force acting on the boy = m g
                       where g is called acceleration due to gravity.

Work done by the boy against the force of gravity is given by the product of Force and distance traveled (vertically) or, height climbed.

Work done = m g h
In order to do this work, the boy spends some of his internal energy.

2) Work done to bring the boy to the height h is same = m g h.
   This work is done by the motor running the lift. The boy gains from it.

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