A train 120 meters long takes 6 seconds to cross a man. What is the speed of the train in km/h?
- (a)36
- (b)72
- (c)60
- (d)75
Answer
Why
Correct — B.
Rule: to pass a man, a train covers just its own length.
Distance = 120 m, time = 6 s
Speed = 120 ÷ 6 = 20 m/s
Convert: 20 × 18⁄5 = 72 km/h → option (b).
Why the others are wrong
- (a)36 — 36 km/h is 10 m/s, half the true speed. At 10 m/s the train would take 12 s, not 6, to pass the man.
- (c)60 — 60 km/h is about 16.7 m/s. At that speed 120 m takes 7.2 s, not 6.
- (d)75 — 75 km/h is about 20.8 m/s, a shade too fast: 120 m would take about 5.76 s, not 6.
Concept
A man by the track has no length worth counting, so the train has passed him once its whole length has gone by. Distance = train length.
Metres and seconds give m/s. To convert to km/h multiply by 18⁄5, because 1 m/s is 3600 m in an hour, which is 3.6 km/h.
The stem does not say the man is moving, so he is taken as standing still. If he walked, the speed relative to him would change and the working would need his speed too.
Key facts
- Passing a man or a pole: distance = length of the train.
- 1 m/s = 18⁄5 km/h = 3.6 km/h.
- Passing a platform or a bridge: distance = train length + platform length.
Study next
Common traps
- Multiplying by 5⁄18 instead of 18⁄5 when going from m/s to km/h, which gives about 5.6.
17 Sep 2025, 16:00, Reasoning Q.17 sets the same case: a 180 m train passes a point in 12 s, so 15 m/s, keyed 54 km/h.
24 Sep 2024, 12:30, Quant Q.5 extends it to two goods trains running towards each other, where the lengths add (132 + 108 = 240 m) and so do the speeds.
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