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1. A train, 240 m long, crosses a man walking alone the line in opposite direction at the rate of 3 kmph in 10 seconds. The speed of the train is?

A. 63 kmph

B. 75 kmph

C. 83.4 kmph

D. 86.4 kmph

Solution:

\begin{aligned} Speed of the train relative to man \\ = (\frac{240}{10}) m/sec \\ =  24 m/sec \\ = (24 \times \frac{18}{5}) km/sec \\ = \frac{432}{5} km/hr \\ Let the speed of the train be x kmph . \\ Then relative speed  = (x + 3) kmph \\ ∴ x + 3 = \frac{432}{5} \\ \Rightarrow x = \frac{432}{5} - 3 \\ \Rightarrow x = \frac{417}{5} \\ = 83.4 kmph \end{aligned}

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