Multiple choice

Akash jogs at a speed of 10 km per hour along a railway track. The Rajdhani Express of length 100 m, running in the same direction at a speed of 40 km per hour, is 200 m behind him. Find the time (in seconds) taken by the train to cross Akash.

  1. 12

  2. 18

  3. 24

  4. 36
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D Correct answer
Explanation

Relative speed = 40 - 10 = 30 km/hr = 30 * (5/18) m/s = 25/3 m/s. Distance to cover = 200 m. Time = 200 / (25/3) = 200 * 3 / 25 = 24 seconds.

AI explanation

Using the relative speed formula for objects moving in the same direction, the train's speed relative to Akash is 40 km/hr - 10 km/hr = 30 km/hr. Converting this to m/s gives 30 * 5/18 = 25/3 m/s. The total distance the train must cover to pass Akash includes its own length and the 200 m gap, totaling 100 m + 200 m = 300 m. Applying the time formula, the time taken is 300 m / (25/3 m/s) = 36 seconds.

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