Discussion
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:
Answer: B
Let the speeds be \( a \) and \( b \) m/s. Crossing a man gives each length:
\[ L_{1} = 27a, \qquad L_{2} = 17b \]
Running opposite ways they cross in 23 seconds, covering both lengths at \( a + b \):
\[ \frac{27a + 17b}{a + b} = 23 \]
\[ 27a + 17b = 23a + 23b \quad\Longrightarrow\quad 4a = 6b \]
\[ \frac{a}{b} = \frac{3}{2} \quad\Longrightarrow\quad 3 : 2 \]
Neither actual speed is needed - the lengths cancel out into the ratio.
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