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1. A train travelling at 48 kmph crosses another train, having half of 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 railway platform is:

A. 200m

B. 300m

C. 350m

D. 400m

Solution:

Let the length of the train traveling at 48 kmph be 2x meters.
And length of the platform is y meters.

\begin{aligned} Relative speed of train \\ = (48 + 42) kmph \\ = \frac{90 \times 5}{18} \\ = 25 m / \sec \\ And 48 kmph \\ = \frac{48 \times 5}{18} \\ = \frac{40}{3} m / \sec \\ According to the question, \\ \frac{2 x + x}{25} = 12; \\ O r, 3 x = 12 \times 25 = 300 \\ O r, x = \frac{300}{3} = 100 m \\ Then, length of the train \\ = 2 x \\ = 100 \times 2 = 200 m \\ \frac{200 + y}{\frac{40}{3}} = 45 \\ 600 + 3 y = 40 \times 45 \\ Or, 3 y = 1800 - 600 \\ = 1200 \\ Or, y = \frac{1200}{3} = 400 m \\ Length of the platform \\ = 400 m \end{aligned}

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