UPSC Prelims 2010 Q33: Science & Technology – Quantitative Aptitude
Running at a speed of 60 km per hour, a train passed through a 1.5 km long tunnel in two
minutes. What is the length of the train?
- (a) 250 m
- (b) 500 m
- (c) 1000 m
- (d) 1500 m
Answer: (b) 500 m
Explanation
Finding train length from tunnel-crossing time
The train travels at 60 km/h and takes 2 minutes to completely pass through a 1.5 km tunnel.
| Step | Calculation |
|---|---|
| Convert speed | 60 km/h = 1 km/min |
| Total distance covered in 2 minutes | 1 km/min × 2 min = 2 km |
| This total distance | = tunnel length + train length (train must fully clear the tunnel) |
| Train length | 2 km − 1.5 km = 0.5 km = 500 m |
Why we add tunnel + train length:
| Point | Detail |
|---|---|
| 'Passing through' | Train enters until its rear end exits |
| Distance covered | Tunnel length + train's own length |
Answer: (b) 500 m.
Why each option is right or wrong
- (a) Incorrect. 250 m does not match the correct distance calculation based on the given speed and time.
- (b) CORRECT. Total distance (2 km) minus tunnel length (1.5 km) gives a train length of 500 m.
- (c) Incorrect. 1000 m overstates the train's length relative to the given data.
- (d) Incorrect. 1500 m would mean the train is as long as the tunnel itself, which doesn't match the calculation.
Key point
Distance covered while 'passing through' a tunnel = tunnel length + train length. Here, 2 km covered − 1.5 km tunnel = 500 m train length.
Remember
Train-tunnel problems: total distance covered = tunnel length + train length. Here, that gives a 500 m train.
Common mistakes
- Forgetting to add the train's own length to the tunnel length when calculating total distance covered.
- Making a unit conversion error between km/h and km/min.
- Treating the tunnel length alone as the total distance covered, ignoring the train's length.
Exam tip
'Train passes through tunnel' = distance covered equals TUNNEL LENGTH + TRAIN LENGTH. A standard trap in train-length problems.
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)