A train crosses a 250 m long platform in 15 seconds, while it crosses a pole in 2.5 seconds. What is the length of the train?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 50 m
To pass a pole, a train covers only its own length; to pass a platform it covers its own length plus the platform. The speed is the same in both cases. Let the length of the train be \(L\) m.
Speed from the pole \(\displaystyle =\frac{L}{2.5}\)
Speed from the platform \(\displaystyle =\frac{L+250}{15}\)
\(\displaystyle \frac{L}{2.5}=\frac{L+250}{15}\), so \(6L=L+250\)
\(5L=250\), so \(L=50\) m
Shortcut: The extra 250 m of the platform takes the extra time.
Extra time \(=15-2.5=12.5\) s, so speed \(=250\div12.5=20\) m/s
Length of the train \(=20\times2.5=50\) m