Discussion
Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Answer: B
Two trains that meet and then take \( t_{1} \) and \( t_{2} \) to finish have speeds in the ratio
\[ \frac{v_{1}}{v_{2}} = \sqrt{\frac{t_{2}}{t_{1}}} \]
\[ = \sqrt{\frac{16}{9}} = \frac{4}{3} \quad\Longrightarrow\quad 4 : 3 \]
The square root is essential; taking the times directly would give 9 : 16, which is offered as the last option and is also the wrong way round.
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