Multiple choice

A person, standing on a railway platform, noticed that a train took 21 seconds to completely cross the platform which is 84 m long, and it took 9 seconds in crossing it. The speed of the train is ______.

  1. 25.2 km/hr

  2. 32.4 km/hr

  3. 50.4 km/hr

  4. 75.64 km/hr
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A Correct answer
Explanation

The train takes 21 seconds to cross the platform (length 84m) and 9 seconds to cross a point (the person). Let L be the length of the train and V be the speed. L/V = 9, so L = 9V. (L + 84)/V = 21. Substituting L: (9V + 84)/V = 21, so 9V + 84 = 21V, 12V = 84, V = 7 m/s. Converting to km/hr: 7 * 18/5 = 25.2 km/hr.

AI explanation

Let L be the train length. By the crossing formula L = speed * time, we have L + 84 = speed * 21 and L = speed * 9. Subtracting the second equation from the first gives 84 = speed * 12, so the speed is 7 m/s. To convert to km/hr, multiply by 18/5, yielding 25.2 km/hr.

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