Discussion
A train running at 54 kmph takes 20 seconds to pass a platform. Next it takes 12 seconds to pass a man walking at 6 kmph in the same direction in which the train is going. Then the length of the train and the length of the platform is:
Answer: D
The train is 160 m long and the platform is 140 m: (160, 140m).
Convert the speeds to m/s: 54 km/h is 15 m/s and 6 km/h is 5/3 m/s. Passing a man walking the same way uses the relative speed.
\[ \begin{aligned} \text{relative} &= 15 - \tfrac{5}{3} = \tfrac{40}{3}\ \text{m/s} \\ \text{train} &= \tfrac{40}{3} \times 12 = 160\ \text{m} \end{aligned} \]
\[ \begin{aligned} \text{train + platform} &= 15 \times 20 = 300 \\ \text{platform} &= 300 - 160 = 140\ \text{m} \end{aligned} \]
All four options agree on 160 m for the train, so the question turns on the platform. 120, 130 and 150 m would need the train to cover 280, 290 or 310 m in 20 seconds, which is not 15 m/s.
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