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Question 21 : A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another train leaves B at 10:30 am, heading towards A at a speed of 20 km/hr. The trains meet each other at

  1. 11 : 20 am
  2. 11 : 00 am
  3. 10 : 45 am
  4. 11 : 45 am

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Explanatory Answer

Let's represent the positions of the trains at 9:00 AM
Train Positions at 9:00 AM
Train from station B will not start till 10:30 AM, meanwhile train A starts from A at 9:00 AM, and travels for 1.5 hours at 40kmph speed. Therefore, by 10:30 AM, train A travels 1.5 × 40 = 60 km towards B.

The positions of the two trains at 10:30 AM will be
Train Positions at 9:00 AM
Now both the trains A and B have 90 - 60 = 30 km to cover between them.
The relative speed of the two trains will be 40 + 20 = 60kmph.
With a relative speed of 60kmph, the two trains cover 30km in half an hour.
Hence the two trains will meet at 11: 00 AM

The answer is, "11 : 00 am"

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