A train 180 m long passes a point in 12 s. Find the speed of the train.
- (a)45 km/h
- (b)54 km/h
- (c)60 km/h
- (d)72 km/h
Answer
Why
Correct — B.
Rule: passing a point, a train covers just its own length.
Distance = 180 m, time = 12 s
Speed = 180 ÷ 12 = 15 m/s
Convert: 15 × 18⁄5 = 54 km/h → option (b).
Why the others are wrong
- (a)45 km/h — 45 km/h is 12.5 m/s, which covers only 150 m in 12 s. The train is 180 m long, so it must be faster.
- (c)60 km/h — 60 km/h is 16⅔ m/s, which covers 200 m in 12 s, 20 m more than the train's length.
- (d)72 km/h — 72 km/h is 20 m/s, which covers 240 m in 12 s. That suits a 240 m train, not a 180 m one.
Concept
A train passing a point (a pole, a signal, a standing man) has cleared it when its tail reaches the point, so the distance covered is exactly the train's length. Passing a platform or bridge, the distance becomes train length + platform length.
Then convert. 1 km/h = 1000 m ÷ 3600 s = 5⁄18 m/s, so m/s × 18⁄5 gives km/h.
Multiplying by 18⁄5 is the same as multiplying by 3.6, which is quicker with decimals: 15 × 3.6 = 54.
Key facts
- Passing a point: distance = length of the train.
- Passing a platform or bridge: distance = train length + platform length.
- m/s to km/h: multiply by 18⁄5 (3.6). km/h to m/s: multiply by 5⁄18.
Study next
Common traps
- Stopping at 15 and forgetting to convert m/s to km/h
- Multiplying by 5⁄18 instead of 18⁄5, which gives about 4.2
21 Sep 2025, 16:00, Reasoning Q.23 sets the same case: a 120 m train crosses a man in 6 s, so 20 m/s, keyed 72 km/h.
24 Sep 2024, 12:30, Quant Q.5 extends it to two trains running towards each other, where both lengths add (132 + 108 = 240 m) and so do the speeds.
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