A train travelling at 48 kmph completely crosses another train having half its l

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Question
A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
Options
A. 400 m
B. 450 m
C. 560 m
D. 600 m

Correct Answer

400 m

Explanation
Let the length of the first train be x metres.

Then, the length of the second train is	❨	x	❩	metres.
		2

Relative speed = (48 + 42) kmph =	❨	90 x	5	❩	m/sec = 25 m/sec.
			18

∴	[x + (x/2)]	= 12 or	3x	= 300 or x = 200.
	25		2

∴ Length of first train = 200 m.

Let the length of platform be y metres.

Speed of the first train =	❨	48 x	5	❩	m/sec =	40	m/sec.
			18			3

∴ (200 + y) x	3	= 45
	40

⟹ 600 + 3y = 1800

⟹ y = 400 m.