At 40% of its usual speed, a train of length $L$ metres crosses a platform 320 metres long in 20 seconds. At its usual speed, the train crosses a pole in 4 seconds. What is the value of $L$?

260 meters
320 meters
540 meters
410 meters

Correct answer: 320 meters

Solution

When the train crosses a pole in 4 seconds, its usual speed is $L/4$ m/s. At 40% speed, the speed becomes $0.4\cdot L/4=L/10$ m/s. In 20 seconds, it covers $L+320$ metres, so $20\cdot (L/10)=L+320$, giving $2L=L+320$ and hence $L=320$ metres.

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