Multiple choice

A lamp post standing before the platform of a railway station is crossed by a train in 6 seconds. The same train crosses the 198 m long platform in 15 seconds. What is the length of the train?

  1. 132 m

  2. 164 m

  3. 152 m

  4. 148 m

  5. 128 m
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A Correct answer
Explanation

Let train length be L and speed be v. L/v = 6. (L + 198)/v = 15. Substituting L = 6v: (6v + 198)/v = 15. 6v + 198 = 15v. 9v = 198. v = 22 m/s. L = 6 * 22 = 132 m.

AI explanation

Let the length of the train be L and its speed be S. From the first scenario, L equals 6 times S. From the second scenario crossing the 198 m platform, L plus 198 equals 15 times S. Substituting the first equation into the second gives 6S plus 198 equals 15S, so 9S equals 198 and S equals 22 m/sec. Multiplying this speed by 6 seconds yields a train length of 132 m. The length of the train is 132 m.

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