An express train travelling at 80 km/hr overtakes a goods train, twice as long and going at 40 km/hr on a parallel track, in 54 s. How long will the express train take to cross a platform of 400 m long?

Using the formula relative speed equals total distance divided by time, let the express train length be L; the goods train is 2L. Their relative speed for overtaking is 80 minus 40, which equals 40 km/hr or 100/9 m/s. The total distance of 3L crossed in 54 seconds means 3L equals 54 times 100/9, so L is 200 m. To cross a 400 m platform, the train must cover 600 m at its own speed of 80 km/hr, which is 200/9 m/s. The time taken is 600 divided by 200/9, which equals 27 seconds.

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