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 second respectively. The length of the train is. (1) 45 metres (2) 40 metres (3) 54 metres (4) 50 metres

The correct answer is (4) 50 metres

Solution

Let the length of train be x km

Let the speed of the train be y km/hr

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

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

According to the given condition

 x/(y-2) = 9/(60*60)
x/(y-4) = 10/(60*60)

On combining both the equations we get
9y – 3600x = 18
and 10y – 3600x = 40
y-400x = 2

and y – 360x = 4
Therefore
40x = 2 

x = (2/40 *1000)m

= 50 metres

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