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. 55 m

D. 60 m

View Answer

Correct Answer :
50 m

Explanation :

Converting km/hr to m/sec

2 kmph = 2 x (5/18) m/sec = (5/9) m/sec

4 kmph = 4 x (5/18) m/sec = (10/9) m/sec

Let the length of the train be a metres and its speed by b m/sec

Then, a / [ b - (5/9) ] = 9 and a / [ b - (10/9) ] = 10

=> 9b - 5 = a and 10(9b - 10) = 9a

=> 9b - a = 5 and 90b - 9a = 100

=> On Solving, we get a = 50

=> Length of the train is 50 m

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