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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:

A. 45 m

B. 50 m

C. 54 m

D. 72 m

Correct Answer : B.


2 kmph = 2 x 518 m/sec = 59 m/sec.   4 kmph = 4 x 518 m/sec = 109 m/sec.Let the length of the train be x metres and its speed by y m/sec.  Then, xy-59 = 9 and xy-109= 10. Therefore 9y - 5 = x and 10(9y - 10) = 9x  ⇒ 9y - x = 5 and 90y - 9x = 100.  On solving, we get: x = 50.  Therefore Length of the train is 50 m.

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