A cyclist was riding alongside a railway track at a steady speed of 12 km/hr. A train running at a speed of 84 km/hr coming from behind the cyclist crosses him in 13.5 seconds. What is the length of the train?

  1. 240 m
  2. 270 m
  3. 320 m
  4. 360 m

Answer (Detailed Solution Below)

Option 2 : 270 m
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Detailed Solution

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∵ The train and cyclist are moving in the same direction,

Relative speed = 84 – 12 = 72 km/hr. = 72 × 5/18 = 20 m/sec.

Now, time taken to cross cyclist = Length of train/relative speed

⇒ 13.5 = Length of train/20

∴ Length of train = 20 × 13.5 = 270 m

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