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:

45 m
50 m
54 m
72 m

Correct Answer: 50 m

Explanation:

2 kmph =	❨	2 x	5	❩	m/sec =	5	m/sec.
			18			9

4 kmph =	❨	4 x	5	❩	m/sec =	10	m/sec.
			18			9

Let the length of the train be x metres and its speed by y m/sec.

Then,

❨

❩

= 9 and

❨

❩

= 10.

y -	5
	9

y -	10
	9

∴ 9y - 5 = x and 10(9y - 10) = 9x

⟹ 9y - x = 5 and 90y - 9x = 100.

On solving, we get: x = 50.

∴ Length of the train is 50 m.

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