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      Question

      Train A, running at 72 km/h, is 100 m long. It passes a

      platform of length 300 m in a certain time. Train B, running at 90 km/h in the opposite direction, is of unknown length. When the two trains are moving in opposite directions, they completely cross each other in 10 seconds. In how much time will Train B alone cross a platform of length 250 m?
      A 20 secs Correct Answer Incorrect Answer
      B 18 secs Correct Answer Incorrect Answer
      C 24 secs Correct Answer Incorrect Answer
      D 32 secs Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Convert speeds to m/s: Train A speed = 72 km/h = 72 × (5/18) = 20 m/s Train B speed = 90 km/h = 90 × (5/18) = 25 m/s Train A crossing the platform (to find/check length of A if needed): Distance covered = length of A + length of platform = 100 + 300 = 400 m Time = distance / speed = 400 / 20 = 20 s (consistent, no unknowns here). When A and B cross each other (opposite directions): Relative speed = 20 + 25 = 45 m/s Time = 10 s Distance covered = (length of A + length of B) ⇒ 100 + length of B = relative speed × time = 45 × 10 = 450 ⇒ length of B = 450 − 100 = 350 m Train B crossing a platform of length 250 m: Total distance = 350 + 250 = 600 m Speed of B = 25 m/s Time = 600 / 25 = 24 seconds

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