One train overtaking another — Aptitude Question
One train overtaking another: Two trains 100 m and 150 m long run in the same direction at 72 km/h and 54 km/h. Answer and worked solution on CodeKairo.
- Topic: Time, Speed & Distance
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
Two trains 100 m and 150 m long run in the same direction at 72 km/h and 54 km/h. How long does the faster take to completely overtake the slower?
Options
- 30 s
- 40 s
- 50 s
- 60 s
Show the answer and the worked solution
Correct answer: C. 50 s
Worked solution
- Relative speed = 72 − 54 = 18 km/h = 5 m/s.
- Distance = 100 + 150 = 250 m.
- Time = 250 ÷ 5 = 50 s.
Answer: 50 s.
The idea
Overtaking uses the difference of speeds, which is small, so overtaking always takes far longer than crossing head-on.
Shortcut. The gap in speeds, 18 km/h, is exactly 5 m/s, so the 250 m of both trains takes 250 ÷ 5 = 50 s with no fractions.
Common trap. 30 s — counting only the slower train's 150 m (150 ÷ 5); the faster train must also clear its own 100 m to be completely past.