The speed of a train is 72 km/h and it crosses a platform in 25 seconds. If…
2025
The speed of a train is 72 km/h and it crosses a platform in 25 seconds. If the train crosses an athlete whose speed is 18 km/h running in same direction of train in 10 seconds, then find the length of platform (in meters)?
Answer: D. 350 — ConceptTo compare the time a train takes to pass different objects, convert all speeds to m/s and use Distance = Speed x Time. When a train passes a moving…
- A.
150
- B.
400
- C.
450
- D.
350
- E.
500
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Correct answer: D
Concept
To compare the time a train takes to pass different objects, convert all speeds to m/s and use Distance = Speed x Time. When a train passes a moving object travelling in the SAME direction, the relevant speed is the relative speed (train speed minus object speed). When it passes a point object (a person), the distance covered equals the train's own length; when it passes a platform, the distance covered equals train length plus platform length.
Application
Convert speeds: train 72 km/h = 72 x 5/18 = 20 m/s; athlete 18 km/h = 18 x 5/18 = 5 m/s.
Athlete runs in the same direction, so relative speed = 20 - 5 = 15 m/s.
Crossing the athlete (a point) covers exactly the train's length: length = relative speed x time = 15 x 10 = 150 m.
Crossing the platform, the train moves at its own 20 m/s for 25 s, covering 20 x 25 = 500 m, which equals train length + platform length.
Platform length = 500 - 150 = 350 m.
Cross-check
Reverse it: a 150 m train plus a 350 m platform is 500 m; at 20 m/s that takes 500/20 = 25 s, matching the given crossing time. So the platform is 350 m.