Discussion
Given below are two statements:
Statement I : A 200 m long train is running at the speed of 30 km/hr. The time taken by the train to pass a man standing near the railway line is 12 seconds.
Statement II : Two trains of equal length take 20 seconds and 30 seconds respectively to cross a telegraph post. If the length of each train is 180 metres, then the two trains will cross each other travelling in opposite direction in 20 seconds.
In the light of the above statements, choose the correct answer from the options given below:
Answer: B
Both Statement I and Statement II are false.
Statement I: \(30 \text{ km/h} = 30 \times \tfrac{5}{18} = \tfrac{25}{3}\) m/s, so passing a man takes \(200 \div \tfrac{25}{3} = 24\) seconds, not 12.
Statement II: the speeds are \(180/20 = 9\) m/s and \(180/30 = 6\) m/s. In opposite directions they close at 15 m/s and must cover both lengths:
\[ \frac{180 + 180}{9 + 6} = \frac{360}{15} = 24 \text{ s} \]
So the time is 24 seconds, not 20. Both statements are false, which rules out every option calling either one true.
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