A train and two people — Aptitude Question
A train and two people: A train passes two people walking in the same direction at 2 km/h and 4 km/h in 9 and 10… Answer and worked solution on CodeKairo.
- Topic: Time, Speed & Distance
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 135 seconds
Question
A train passes two people walking in the same direction at 2 km/h and 4 km/h in 9 and 10 seconds respectively. What is the speed of the train?
Options
- 20 km/h
- 22 km/h
- 24 km/h
- 26 km/h
Show the answer and the worked solution
Correct answer: B. 22 km/h
Worked solution
- Length L = 9(v − 2) × 5/18 = 10(v − 4) × 5/18.
- Cancelling 5/18: 9(v − 2) = 10(v − 4) → 9v − 18 = 10v − 40.
- v = 22 km/h.
Answer: 22 km/h.
The idea
The train's length is the invariant. Write it twice using the two relative speeds and equate; the unit conversion cancels out entirely.
Shortcut. Back-substitute: at 22 km/h the relative speeds are 20 and 18 km/h, and 20 × 9 = 18 × 10 = 180 — the lengths agree with no unit conversion.
Common trap. 24 km/h — a rough check nearly works (22 × 9 = 198 against 20 × 10 = 200), so it looks right; only 22 km/h makes the two lengths exactly equal.