A train goes from stations A to B. One day there Is a technical problem at the…

2024

A train goes from stations A to B. One day there Is a technical problem at the very beginning of the journey and hence the train travels at 3/5 of it’s original speed and so it arrives 2hours late. Had the problem occurred after 50 miles had been covered, the train would have arrived 40 minutes earlier. What is the distance between the two stations?

  1. A.

    150 miles

  2. B.

    210 miles

  3. C.

    200 miles

  4. D.

    180 miles

Attempted by 3 students.

Show answer & explanation

Correct answer: A

Answer: 150 miles

  1. Let the distance between A and B be d miles and the usual speed be x miles/hour. Usual time = d/x hours.

  2. First scenario (problem at the beginning): speed becomes 3x/5, so slow-trip time = d/(3x/5). The delay is 2 hours, so d/(3x/5) - d/x = 2.

    Simplify: (5d/3x) - d/x = 2 ⇒ (2d/3x) = 2 ⇒ d/x = 3.

  3. So the usual trip takes 3 hours. The fully slow trip (3x/5) takes (5/3)·3 = 5 hours, which is 2 hours longer than usual as given.

  4. Second scenario (problem after 50 miles): time = 50/x + (d-50)/(3x/5) = 50/x + 5(d-50)/(3x). This arrival is 40 minutes earlier than the fully-slow case, so it is late by 2 hours − 40 minutes = 80 minutes = 4/3 hours.

    Hence total time in this scenario = usual time + 4/3 = d/x + 4/3 = 3 + 4/3 = 13/3 hours.

  5. Set up the equation: 50/x + 5(d-50)/(3x) = 13/3. Substitute x = d/3 (from d/x = 3).

    Compute: 50/(d/3) + 5(d-50)/(3·(d/3)) = 150/d + 5(d-50)/d = (150 + 5d - 250)/d = (5d - 100)/d.

    So (5d - 100)/d = 13/3 ⇒ 5 - 100/d = 13/3 ⇒ -100/d = -2/3 ⇒ 100/d = 2/3 ⇒ d = 150.

  6. Therefore the distance between the two stations is 150 miles.

Explore the full course: Infosys Preparation