Multiple choice

Amit and Sumit are walking towards each other alongside a railway track. A train overtakes Amit in 20 seconds. After 10 minutes, it meets Sumit coming from the opposite direction. If the train passes Sumit in 18 seconds, then how long after the train has passed Sumit will they meet?

  1. 60 minutes

  2. 70 minutes

  3. 80 minutes

  4. 90 minutes

  5. 100 minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let train speed be V, Amit speed be A. Train passes Amit: (V-A)*20 = Length. Train passes Sumit: (V+S)*18 = Length. After 10 mins (600s), train meets Sumit. This is a relative speed problem. The time taken to meet is 90 minutes.

AI explanation

Let the train's length be L and its speed be T, while Amit and Sumit's speeds are A and S. From the crossing times, the relative speed of the train and Amit is L divided by 20, so T minus A equals L divided by 20; similarly, T plus S equals L divided by 18. The distance between Amit and Sumit 10 minutes before the train meets Sumit equals the distance Amit covers in 10 minutes plus the distance the train covers in 10 minutes, which is 10A plus 10T. This distance is also covered by Amit and Sumit walking towards each other, so using the relation 10A plus 10T equals 10A plus 10 multiplied by (18S divided by 2), the meeting time after the train passes Sumit is calculated as 90 minutes.

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