Multiple choice

A train X starts from Meerut at 4 pm and reaches Ghaziabad at 5 pm. Another train Y starts from Ghaziabad at 4 pm and reaches Meerut at 5:30 pm. At what time will the two trains cross each other?

  1. 4.36 pm

  2. 4.42 pm

  3. 4.48 pm

  4. 4.50 pm

  5. 4.55 pm
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A Correct answer
Explanation

Train X speed = 1 distance unit/hour. Train Y speed = 1 distance unit/1.5 hours = 2/3 distance unit/hour. They start at the same time and distance is 1 unit. Relative speed = 1 + 2/3 = 5/3 units/hour. Time = Distance / Relative Speed = 1 / (5/3) = 3/5 hours = 36 minutes. They cross at 4:36 pm.

AI explanation

Let the distance between Meerut and Ghaziabad be D. Train X travels the distance in 1 hour, so its speed is D per hour. Train Y travels the distance in 1.5 hours, so its speed is D divided by 1.5, which equals 2D divided by 3 per hour. If they start moving towards each other at 4 pm, their relative speed is D plus 2D divided by 3, which equals 5D divided by 3 per hour. The time taken to meet is D divided by (5D divided by 3), which equals 3 divided by 5 hours, or 0.6 hours. Adding 0.6 hours (36 minutes) to 4 pm gives the meeting time of 4.36 pm.

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