Discussion
Two trains running in opposite direction 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 speed is
Answer: C
The ratio of their speeds is 3:2.
Let the speeds be \(x\) and \(y\). Passing a standing man, each train covers its own length, so the lengths are \(27x\) and \(17y\). Crossing each other in opposite directions, they cover the sum of their lengths at the sum of their speeds:
\[ \begin{aligned} \frac{27x + 17y}{x + y} &= 23 \\ 27x + 17y &= 23x + 23y \\ 4x = 6y &\Rightarrow x : y = 3 : 2 \end{aligned} \]
2:3 is the same ratio reversed; the working shows the train that takes 27 seconds to pass the man is the faster one, so it must also be much the longer. 1:3 and 3:4 do not satisfy the equation.
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