1. Rules
| Train crosses | Distance covered |
|---|---|
| A pole, a man, a tree | Its own length |
| A platform, bridge, tunnel | Train length + platform length |
| Another train | Sum of both lengths (with relative speed) |
Relative speed: same direction = difference; opposite = sum. A man walking — treat as a point with his speed.
2. Solved examples
150 m train at 54 km/h (15 m/s) passes a pole in 10 s.
200 m train at 72 km/h crosses a 300 m platform: 500/20 = 25 s.
Two trains 120 m and 180 m at 50 and 40 km/h opposite → 300 m at 25 m/s = 12 s; same direction 300/(25/9) = 108 s.
Train passes a pole in 15 s and a 100 m platform in 25 s → speed = 100/10 = 10 m/s, length = 150 m.
Train at 63 km/h passes a man walking at 3 km/h in the same direction in 30 s → length = 60 × 5/18 × 30 = 500 m.
Two trains start from A and B, 300 km apart, at 60 and 40 km/h → meet after 3 h, 180 km from A.
Solved examples by question type
Each type that comes in the ASO paper, worked step by step. Try it yourself first, then read the solution.
Basic level
Example 1. A train 375 m long runs at 90 km/h. How long does it take to cross a pole?
(a) 30 s (b) 4.17 s (c) 15 s (d) 19 s
Answer: (c) 15 s
Solution: Speed = 90 × 5/18 = 25 m/s. Time = length/speed = 375/25 = 15 s.
ASO exam level
Example 2. A 250 m long train running at 54 km/h crosses a platform in 20 seconds. The length of the platform is:
(a) 50 m (b) 100 m (c) 300 m (d) 20 m
Answer: (a) 50 m
Solution: Distance in 20 s = 15 × 20 = 300 m = train + platform. Platform = 300 − 250 = 50 m.
Example 3. A 150 m long train running at 72 km/h crosses a platform in 24 seconds. The length of the platform is:
(a) 480 m (b) 330 m (c) 380 m (d) 300 m
Answer: (b) 330 m
Solution: Distance in 24 s = 20 × 24 = 480 m = train + platform. Platform = 480 − 150 = 330 m.
Example 4. A train 125 m long passes a man walking at 5 km/h in the opposite direction in 6 seconds. The speed of the train is:
(a) 80 km/h (b) 65 km/h (c) 70 km/h (d) 75 km/h
Answer: (c) 70 km/h
Solution: Relative speed = 125/6 m/s = 75 km/h = train + man. Train = 75 − 5 = 70 km/h. (Type asked in OPSC ASO 2025.)
Example 5. A train 125 m long passes a man walking at 5 km/h in the opposite direction in 5 seconds. The speed of the train is:
(a) 90 km/h (b) 85 km/h (c) 95 km/h (d) 80 km/h
Answer: (b) 85 km/h
Solution: Relative speed = 125/5 m/s = 90 km/h = train + man. Train = 90 − 5 = 85 km/h. (Type asked in OPSC ASO 2025.)
Example 6. A train 120 m long passes a man running at 9 km/h in the same direction in 12 seconds. The speed of the train is:
(a) 51 km/h (b) 36 km/h (c) 45 km/h (d) 27 km/h
Answer: (c) 45 km/h
Solution: Same direction: relative = train − man = 120/12 m/s = 36 km/h. Train = 36 + 9 = 45 km/h.
Example 7. A train 200 m long passes a man running at 9 km/h in the same direction in 10 seconds. The speed of the train is:
(a) 81 km/h (b) 72 km/h (c) 87 km/h (d) 63 km/h
Answer: (a) 81 km/h
Solution: Same direction: relative = train − man = 200/10 m/s = 72 km/h. Train = 72 + 9 = 81 km/h.
Example 8. Two trains 200 m and 250 m long run at 54 km/h and 36 km/h towards each other on parallel tracks. In how many seconds will they cross each other?
(a) 8 s (b) 90 s (c) 18 s (d) 21 s
Answer: (c) 18 s
Solution: Relative speed = 54 + 36 = 90 km/h = 25 m/s. Distance = 200 + 250 = 450 m. Time = 18 s.
Example 9. A 120 m long train at 90 km/h overtakes a 180 m long train running at 54 km/h in the same direction. How long does it take to pass it completely?
(a) 18 s (b) 30 s (c) 40 s (d) 7.5 s
Answer: (b) 30 s
Solution: Relative = 90 − 54 = 36 km/h = 10 m/s. Time = (120 + 180)/10 = 30 s.
Example 10. A 100 m long train at 60 km/h overtakes a 150 m long train running at 42 km/h in the same direction. How long does it take to pass it completely?
(a) 8.82 s (b) 60 s (c) 30 s (d) 50 s
Answer: (d) 50 s
Solution: Relative = 60 − 42 = 18 km/h = 5 m/s. Time = (100 + 150)/5 = 50 s.
Example 11. How long will a 240 m long train running at 54 km/h take to cross a 360 m long bridge?
(a) 24 s (b) 40 s (c) 16 s (d) 46 s
Answer: (b) 40 s
Solution: Distance = 240 + 360 = 600 m. Speed = 15 m/s. Time = 40 s.
Advanced level
Example 12. A train crosses a 100 m platform in 15 s and a 250 m platform in 20 s. The length of the train is:
(a) 600 m (b) 400 m (c) 325 m (d) 350 m
Answer: (d) 350 m
Solution: Extra 150 m takes 5 s → speed 30 m/s. Train = 30×15 − 100 = 350 m.
Example 13. A train crosses a 120 m platform in 15 s and a 270 m platform in 20 s. The length of the train is:
(a) 600 m (b) 380 m (c) 330 m (d) 305 m
Answer: (c) 330 m
Solution: Extra 150 m takes 5 s → speed 30 m/s. Train = 30×15 − 120 = 330 m.
Topic-wise practice for Trains (Quant): Crossing poles, platforms, bridges and other trains. Useful for OPSC ASO, OSSC, OSSSC and other Odisha exams.
Question types covered
- Train crossing a pole or man
- Train crossing a platform, bridge or tunnel
- Two trains crossing in the same or opposite direction
- Train crossing a moving man
- Finding the length of a train