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1. 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

A. 400 m

B. 450 m

C. 560 m

D. 600 m

Solution:

\begin{aligned} Let the length of the first train be x metres \\ Then, the length of the second train is \frac{x}{2} metres \\ Relative speed = (48 + 42) kmph \\ = (90 \times \frac{5}{18}) m/sec \\ = 25 m/sec \\ ∴ \frac{x + (x / 2)}{25} = 12 \\ o r \frac{3 x}{2} = 300 \\ o r x = 200 \\ ∴ Length of first train = 200 m \\ Let the length of platform be y metres \\ Speed of the first train \\ = (48 \times \frac{5}{18}) m/sec \\ = \frac{40}{3} m/sec \\ ∴ (200 + y) \times \frac{3}{40} = 45 \\ \Rightarrow 600 + 3 y = 1800 \\ \Rightarrow y = 400 m \end{aligned}

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