Two trains cross each other — Aptitude Question
Two trains cross each other: Two trains, 120 m and 180 m long, run towards each other at 54 km/h and 36 km/h. Answer and worked solution on CodeKairo.
- Topic: Time, Speed & Distance
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
Two trains, 120 m and 180 m long, run towards each other at 54 km/h and 36 km/h. How long do they take to cross each other?
Options
- 10 s
- 12 s
- 15 s
- 18 s
Show the answer and the worked solution
Correct answer: B. 12 s
Worked solution
- Relative speed = 54 + 36 = 90 km/h = 90 × 5/18 = 25 m/s.
- Distance to clear = 120 + 180 = 300 m.
- Time = 300/25 = 12 s.
Answer: 12 s.
The idea
Opposite directions add speeds; same direction subtracts them. The distance is always the sum of both lengths when trains cross each other.
Shortcut. 54 km/h = 15 m/s and 36 km/h = 10 m/s are stock pairs, so the relative speed is 25 m/s and 300 m clears in 12 s.
Common trap. 10 s — converting 90 km/h by dividing by 3 instead of 3.6 (30 m/s); 90 × 5/18 is 25 m/s, giving 12 s.