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A person standing on a railway platform noticed that a train took 21 seconds to completely pass through the platform which was 84 m long and it took 9 seconds to pass him. What was the speed of the train?

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25.2 km / hr

32.4 km / hr

50.4 km / hr

75.6 km / hr

answer is A.

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Detailed Solution

Let the train's length be x meters. Next, the train's speed as it passes through the platform

= \frac{x + 84}{21} m / \sec

Speed of the train in passing the man

= \frac{x}{9} m / \sec

Given that both speeds are equal,

\begin{matrix} \frac{x + 84}{21} = \frac{x}{9} \Rightarrow 9 x + 756 = 21 x \\ \Rightarrow 12 x = 756 \\ \Rightarrow x = \frac{756}{12} = 63 m \end{matrix}

Since, Speed of the train

= \frac{\frac{(63 + 84)}{21} m}{\sec}

= \frac{7 m}{\sec}

= 7 \times \frac{\frac{18}{5} km}{hr}

= 25.2 km / hr .

Option 1 is correct.

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