A crane 'A' lifts a heavy load in 5 seconds, whereas another crane 'B' does the same work in 2 seconds. Compare the power of crane 'A' to that of crane 'B'.

Let the work done by both cranes be 'W'

Given,

Time taken by crane A to do work, t₁ = 5 s

Time taken by crane B to do work, t₂ = 2 s

Power of crane A, P_A = $\frac{W}{t_1}$

Power of crane B, P_B = $\frac{W}{t_2}$

$$\begin{aligned}\frac{P_A}{P_B} = \frac{Wt_2}{Wt_1} \\[0.5em] \frac{P_A}{P_B} = \frac{t_2}{t_1} \\[0.5em] \frac{P_A}{P_B} = \frac{2}{5}\end{aligned}$$

P_A : P_B = 2 : 5