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:

1 : 3

3 : 2

3 : 4

None of these

Explanation:

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.

$\therefore \dfrac{27x + 17y}{x+ y} $= 23

$\Rightarrow$ 27$ x $ + 17$ y $ = 23$ x $ + 23$ y $

$\Rightarrow$ 4$ x $ = 6$ y $

$\Rightarrow \dfrac{x}{y} $=$ \dfrac{3}{2} $.