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1 : 3

3 : 2

3 : 4

None of these

B. 3 : 2

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27x metres,

and length of the second train = 17y metres.

$\therefore \frac{27x+17y}{x+y}=23\phantom{\rule{0ex}{0ex}}\Rightarrow 27x+17y=23x+23y\phantom{\rule{0ex}{0ex}}\Rightarrow 4x=6y\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{x}{y}=\frac{3}{2}.$