A body of mass 20 kg is at a height of 0.9 m. Calculate its potential energy and speed at the lowest point.

The potential energy at its position is $\boxed{\text{176.4 J}}$.

At the initial position, all energy is potential energy ($PE_i = mgh$, $KE_i = 0$). At the lowest point, all potential energy is converted to kinetic energy ($PE_f = 0$, $KE_f = \frac{1}{2}mv^2$).

The speed of the body when passing through the lowest point is $\boxed{\text{4.2 m/s}}$.

The work done by the crane is $\boxed{\text{58800 J}}$.

The power developed by the crane is $\boxed{\text{9.8 kW}}$.

$P_{in} = 12.5 \text{ kW} = 12.5 \times 1000 \text{ W} = 12500 \text{ W}$. The output power $P_{out}$ is the power developed by the crane, which is $9800 \text{ W}$ from part (b)(ii).

The efficiency of the crane is $\boxed{\text{78.4\%}}$.