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:

Question: 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

Answer: Option B

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,		x		= 9 and		x		= 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.