A train overtakes two persons who are walking in the same direction in which…

20242019

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

  1. A.

    45 m

  2. B.

    50 m

  3. C.

    54 m

  4. D.

    72 m

Attempted by 28 students.

Show answer & explanation

Correct answer: B

Concept

When a train overtakes a person moving in the SAME direction, the train covers its own length at the RELATIVE speed = (train speed - person speed). Time to pass = length / relative speed. Converting km/h to m/s uses the factor 5/18.

Application

  1. Let the train speed be x km/h and its length be L metres.

  2. Against the 2 km/h walker: relative speed = (x - 2) km/h, time = 9 s, so L = (x - 2) x (5/18) x 9.

  3. Against the 4 km/h walker: relative speed = (x - 4) km/h, time = 10 s, so L = (x - 4) x (5/18) x 10.

  4. Equate the two expressions for L: (x - 2) x 9 = (x - 4) x 10.

  5. Expand: 9x - 18 = 10x - 40, which gives x = 22 km/h.

  6. Substitute back: L = (22 - 2) x (5/18) x 9 = 20 x (5/18) x 9 = 50 metres.

Cross-check

Use the second equation independently: L = (22 - 4) x (5/18) x 10 = 18 x (5/18) x 10 = 5 x 10 = 50 metres. Both cases agree, so the length of the train is 50 m.

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