UPSC Prelims 2010 Q27: Science & Technology – Physics
Two trains leave New Delhi at the same time. One travels north at 60 kmph and the other
travels south at 40 kmph. After how many hours will the trains be 150 km apart?
- (a) 3/2
- (b) 15/4
- (c) 3/4
- (d) 15/2
Answer: (a) 3/2
Explanation
Two trains moving apart: when are they 150 km apart?
One train travels north at 60 km/h, the other south at 40 km/h, starting from the same point at the same time.
| Step | Calculation |
|---|---|
| Combined separation speed | Since they move in opposite directions, their speeds add: 60 + 40 = 100 km/h |
| Distance to cover | 150 km apart |
| Time required | Time = Distance / Speed = 150 / 100 = 1.5 hours = 3/2 hours |
Why speeds add here:
| Point | Detail |
|---|---|
| Opposite directions | Relative speed = sum of individual speeds |
| Formula | Time = Separation distance / Combined speed |
Answer: (a) 3/2.
Why each option is right or wrong
- (a) CORRECT. Combined speed = 100 km/h; time = 150/100 = 3/2 hours.
- (b) Incorrect. 15/4 hours does not match the correct combined-speed calculation.
- (c) Incorrect. 3/4 hours would be too short a time for the trains to reach 150 km apart at this combined speed.
- (d) Incorrect. 15/2 hours overstates the actual time required.
Key point
Trains moving in opposite directions: relative speed = sum of speeds (60+40=100 km/h). Time to be 150 km apart = 150/100 = 3/2 hours.
Remember
Two trains, opposite directions, 60+40=100 km/h combined speed: time to be 150 km apart = 3/2 hours.
Common mistakes
- Forgetting that opposite-direction relative speed is the SUM, not the difference, of individual speeds.
- Making an arithmetic slip when dividing distance by combined speed.
- Confusing this with a 'catching up' (same-direction) problem, which uses the speed difference instead.
Exam tip
Opposite directions → ADD speeds for relative speed. Same direction (catching up) → SUBTRACT speeds.
Sources
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Time and Distance)
- Arun Sharma — How to Prepare for Quantitative Aptitude for the CAT (Time, Speed and Distance)