Shatabdi Express starts from Delhi at 12:15 pm and reaches Chandigarh at 2:45…

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Shatabdi Express starts from Delhi at 12:15 pm and reaches Chandigarh at 2:45 pm and Rajdhani express starts from Chandigarh at 12:30 and reach at Delhi at 2:30. What will be the time when both the trains will cross each other ?

  1. A.

    1:30 pm

  2. B.

    1:15 pm

  3. C.

    1:45 pm

  4. D.

    1:00 pm

Attempted by 13 students.

Show answer & explanation

Correct answer: A

Answer: 1:30 pm

Key idea: Find each train's speed from its total travel time, account for the 15-minute head start, then use relative speed to find meeting time.

  1. Let the distance between Delhi and Chandigarh be d km. Shatabdi: 12:15–2:45 = 2.5 hours, so speed = d/2.5 = 2d/5 km/h. Rajdhani: 12:30–2:30 = 2 hours, so speed = d/2 km/h.

  2. By 12:30 (when Rajdhani starts) Shatabdi has run 15 minutes = 0.25 h and covered distance = (2d/5)×0.25 = d/10. Remaining distance between them at 12:30 = d − d/10 = 9d/10.

  3. Their relative speed toward each other = 2d/5 + d/2 = (4d + 5d)/10 = 9d/10 km/h.

  4. Time to meet after 12:30 = (remaining distance)/(relative speed) = (9d/10)/(9d/10) = 1 hour.

Therefore they meet at 12:30 + 1 hour = 1:30 pm.

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