Problems on Trains
Problems on Trains
A train question is a speed-distance question where the train's own length is part of the distance. When a train crosses something, the distance covered = length of the train + length of what it crosses (zero for a pole or a man). The speed is the relative speed if the other object is moving.
1. Crossing Rules
| Train crosses | Distance | Speed |
|---|---|---|
| Pole, tree, signal post, standing man | Length of train L | Train speed |
| Platform, bridge, tunnel of length P | L + P | Train speed |
| Man walking or cyclist (same direction at v) | L | Train speed − v |
| Man walking towards the train at v | L | Train speed + v |
| Another train (length L₂), opposite directions | L + L₂ | Sum of speeds |
| Another train (length L₂), same direction | L + L₂ | Difference of speeds |
Time = (sum of lengths)/(relative speed) Use metres and m/s together (× 5/18 for km/h)
Two crossings at the same speed (pole in t₁, platform P in t₂): speed = P/(t₂ − t₁), length = speed × t₁
✗ Train crosses a 240 m platform in 30 s, so speed = 240/30 | ✓ Distance is train + platform: (L + 240)/30
✗ Two trains at 72 and 54 km/h, same direction, relative speed 126 km/h | ✓ Same direction subtracts: 18 km/h = 5 m/s
हिंदी नोट: ट्रेन जब किसी चीज़ को पार करती है तो दूरी = ट्रेन की लंबाई + उस चीज़ की लंबाई होती है। खंभे या खड़े आदमी की लंबाई शून्य मानी जाती है। दूसरी वस्तु चल रही हो तो सापेक्ष चाल लीजिए।
Exam Pointer: Verified NTPC patterns: crossing a pole (December 2020, June 2022 CBT-2), pole and platform at the same speed (June 2022 CBT-2), two trains in opposite directions (January 2021) and overtaking in the same direction (June 2025 and March 2026 Graduate CBT-1). Crossing a moving man had no verified NTPC shift and is tagged syllabus-based.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Crossing a pole or a standing object
[PYQ: NTPC CBT-1 29-Dec-2020 Shift-2 | NTPC CBT-2 15-Jun-2022 Shift-3]
EXAM LEVEL
Q. A train running at 54 km/h crosses a pole in 12 seconds. Find its length.
54 km/h = 15 m/s. Length = 15 × 12 = 180 m.
Answer: 180 m
EXAMATLAS LEVEL
Q. A train running at 90 km/h crosses a signal post in 15 seconds. How long will it take to cross a 625 m long bridge?
90 km/h = 25 m/s, so the train is 25 × 15 = 375 m long. To cross the bridge it covers 375 + 625 = 1,000 m, taking 1,000/25 = 40 seconds.
Answer: 40 seconds
Pattern 2: Platform, bridge and the two-crossings method
[PYQ: NTPC CBT-2 12-Jun-2022 Shift-1]
EXAM LEVEL
Q. A 360 m long train running at 72 km/h crosses a 240 m platform. How long does it take?
Distance = 360 + 240 = 600 m, speed = 20 m/s, time = 30 seconds.
Answer: 30 seconds
EXAMATLAS LEVEL
Q. A train crosses a pole in 12 seconds and a 330 m long platform in 27 seconds. Find its length and speed in km/h.
The extra 15 seconds are spent covering the platform, so speed = 330/15 = 22 m/s = 79.2 km/h. Length = 22 × 12 = 264 m.
Answer: 264 m; 79.2 km/h
Pattern 3: Two trains in opposite directions
[PYQ: NTPC CBT-1 4-Jan-2021 Shift-1]
EXAM LEVEL
Q. Two trains 150 m and 200 m long run on parallel tracks in opposite directions at 50 km/h and 76 km/h. How long do they take to cross each other?
Relative speed = 126 km/h = 35 m/s. Total length = 350 m. Time = 10 seconds.
Answer: 10 seconds
EXAMATLAS LEVEL
Q. Two trains of equal length, running at 46 km/h and 62 km/h in opposite directions, cross each other in 12 seconds. Find the length of each, and the time they would take to cross if running in the same direction.
Relative speed = 108 km/h = 30 m/s, so the total length = 30 × 12 = 360 m and each train is 180 m. Same direction: relative speed = 16 km/h = 40/9 m/s, time = 360 ÷ 40/9 = 81 seconds.
Answer: 180 m each; 81 seconds
Pattern 4: Overtaking in the same direction
[PYQ: NTPC Graduate CBT-1 21-Jun-2025 Shift-2 | NTPC Graduate CBT-1 18-Mar-2026 Shift-3]
EXAM LEVEL
Q. Trains 100 m and 150 m long run in the same direction at 72 km/h and 54 km/h. How long does the faster one take to pass the slower one completely?
Relative speed = 18 km/h = 5 m/s. Distance = 250 m. Time = 50 seconds.
Answer: 50 seconds
EXAMATLAS LEVEL
Q. A 240 m long train overtakes a 180 m long goods train moving at 36 km/h in the same direction in 36 seconds. Find the speed of the faster train.
Relative speed = (240 + 180)/36 = 35/3 m/s = 42 km/h. Speed of the faster train = 36 + 42 = 78 km/h.
Answer: 78 km/h
Pattern 5: Crossing a moving man or cyclist
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. A 210 m long train running at 60 km/h passes a man walking at 3 km/h towards the train. How long does it take?
Relative speed = 63 km/h = 17.5 m/s. Time = 210/17.5 = 12 seconds.
Answer: 12 seconds
EXAMATLAS LEVEL
Q. A train passes two men walking in the same direction as the train at 2 km/h and 4 km/h in 9 seconds and 10 seconds respectively. Find the speed and length of the train.
Length is the same both times: (v − 2) × 5/18 × 9 = (v − 4) × 5/18 × 10, so 9v − 18 = 10v − 40 and v = 22 km/h. Length = 20 × 5/18 × 9 = 50 m.
Answer: 22 km/h; 50 m
60-Second Revision
- Distance = train length + length crossed (0 for pole or man).
- Opposite directions add speeds, same direction subtract.
- Pole t₁ and platform t₂: speed = platform/(t₂ − t₁).
- Work in metres and m/s: km/h × 5/18.