Concept:Power is the rate of doing work. In climbing stairs, work done is equal to the potential energy gained (weight \( \times \) height).
Formula:$$ P = \frac{W}{t} = \frac{mgh}{t} $$
Solution:- Weight ratio: \( \frac{w_1}{w_2} = \frac{m_1 g}{m_2 g} = \frac{4}{5} \)
- Time ratio: \( \frac{t_1}{t_2} = \frac{5}{4} \)
- Since they climb the same stairs, height \( h \) is constant.
- \( \frac{P_1}{P_2} = \left( \frac{w_1}{w_2} \right) \times \left( \frac{t_2}{t_1} \right) \)
- Notice we must flip the time ratio because time is in the denominator: \( \frac{t_2}{t_1} = \frac{4}{5} \)
- \( \frac{P_1}{P_2} = \left(\frac{4}{5}\right) \times \left(\frac{4}{5}\right) = \frac{16}{25} \)
Why other options are incorrect:If you multiply the direct ratios without flipping time (4/5 * 5/4), you get 1 (Option A). If you flip weight instead of time, you get 25/16 (Option C).
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