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1. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

A. 1 : 3

B. 3 : 2

C. 3 : 4

D. None of these

Solution:

\begin{aligned} Let the speeds of the two trains be x m/sec \\ and y m/sec respectively . \\ Then, length of the first train = 27 x metres, \\ and length of the second train = 17 y metres . \\ ∴ \frac{27 x + 17 y}{x + y} = 23 \\ \Rightarrow 27 x + 17 y = 23 x + 23 y \\ \Rightarrow 4 x = 6 y \\ \Rightarrow \frac{x}{y} = \frac{3}{2} \end{aligned}

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