A train leaves Meerut at 5 a.m. and reaches Delhi at 9 a.m. Another train…

2024

A train leaves Meerut at 5 a.m. and reaches Delhi at 9 a.m. Another train leaves Delhi at 7 a.m. and reaches Meerut at 10.30 a.m. At what time do the two trains travel in order to cross each other ?

  1. A.

    7.56 am

  2. B.

    8.00 pm

  3. C.

    12 am

  4. D.

    6 pm

Attempted by 6 students.

Show answer & explanation

Correct answer: A

Solution:

  1. Let the total distance between Meerut and Delhi be x.

  2. Speed of the train from Meerut = x/4 (it takes 4 hours from 5:00 a.m. to 9:00 a.m.). Speed of the train from Delhi = x/3.5 (it takes 3.5 hours from 7:00 a.m. to 10:30 a.m.).

  3. By 7:00 a.m. the first train has been running for 2 hours, so it covers (x/4)×2 = x/2. Thus the remaining distance between the trains at 7:00 a.m. is x/2.

  4. Their combined (relative) speed = x/4 + x/3.5 = x(1/4 + 2/7) = x(15/28).

  5. Time to meet after 7:00 a.m. = (distance to cover)/(relative speed) = (x/2) / (15x/28) = (1/2) × (28/15) = 14/15 hour = 56 minutes.

  6. Therefore they cross at 7:00 a.m. + 56 minutes = 7:56 a.m.

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