UPSC Prelims 2002 Q34: Science & Technology – Quantitative Aptitude
A train of length 150 metres, moving at a speed of 90 km/hr can cross a 200 - metre bridge in
- (a) 8 seconds
- (b) 14 seconds
- (c) 6 seconds
- (d) 15 seconds
Answer: (b) 14 seconds
Explanation
Time for a train to cross a bridge
| Quantity | Value |
|---|---|
| Length of the train | 150 m |
| Length of the bridge | 200 m |
| Distance to cover | 150 + 200 = 350 m |
| Speed | 90 km/hr = 90 × 5/18 = 25 m/s |
To cross the bridge, the train must travel its own length plus the bridge: 350 m. At a speed of 25 m/s, the time is 350 ÷ 25 = 14 seconds.
Answer: (b) 14 seconds.
Why each option is right or wrong
- (a) Incorrect. 8 seconds would cover only 200 m at 25 m/s.
- (b) CORRECT. 350 m ÷ 25 m/s = 14 seconds.
- (c) Incorrect. 6 seconds would cover only 150 m at 25 m/s.
- (d) Incorrect. 15 seconds would cover 375 m at 25 m/s.
Key point
Crossing time = (train length + bridge length) ÷ speed; convert km/hr to m/s by multiplying by 5/18.
Remember
90 km/hr = 25 m/s; distance = train + bridge.
Common mistakes
- Using only the bridge length (200 ÷ 25 = 8).
- Using only the train length (150 ÷ 25 = 6).
- Forgetting to convert 90 km/hr to 25 m/s.
Exam tip
Compute 350 ÷ 25 and compare with the options.
Sources
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Problems on Trains)
- Arun Sharma — How to Prepare for Quantitative Aptitude for the CAT (Time, Speed and Distance)