In this guide
Every railway exam asks train problems, and NTPC is no exception. They are ordinary speed and distance questions with one extra idea: the train has length. A car passing a lamp post is over in an instant. A 300 m train passing the same post takes several seconds, because the whole train has to go by.
Once you see what distance the train actually covers, every variety of the question uses the same few lines of working.
The one rule
While crossing something, a train covers its own length + the length of the object.
Why: picture the engine reaching the start of a platform. The crossing ends only when the last coach leaves the far end. By then the engine has travelled the platform's length and then the train's own length beyond it.
| Train crosses… | Distance to cover |
|---|---|
| A pole, signal post, tree or standing person | Length of the train |
| A platform, bridge or tunnel | Train length + platform length |
| A person walking or running | Train length (with relative speed) |
| Another train | Sum of both lengths (with relative speed) |
A pole or a person is treated as having no length, which is why only the train's length counts.
Units first
Speeds come in km/h and lengths in metres, so convert speed to m/s by multiplying by 5/18. The friendly values are worth knowing by heart:
| km/h | 36 | 54 | 72 | 90 | 108 |
|---|---|---|---|---|---|
| m/s | 10 | 15 | 20 | 25 | 30 |
If the answer is wanted in km/h, find m/s first and multiply by 18/5 at the end.
Relative speed
When two things are both moving, use the speed at which the gap between them changes.
| Direction | Relative speed |
|---|---|
| Opposite directions | Sum of speeds |
| Same direction | Difference of speeds |
This applies to a person too. A train passing a person who walks the same way needs a little longer than it would to pass a pole, because the person is moving away from it.
Two crossings: finding length and speed
A common NTPC pattern gives two crossing times and asks for the train's length or speed. The speed is the same in both crossings, so set up one equation:
L ÷ t₁ = (L + P) ÷ t₂
where t₁ is the time to cross a pole and t₂ the time to cross a platform of length P. The extra time (t₂ − t₁) is spent covering exactly the platform, so speed = P ÷ (t₂ − t₁). That is often the fastest route.
The meeting-time shortcut
Two trains start at the same time from two stations towards each other. After they meet, they take t₁ and t₂ hours to reach their destinations. Then:
Speed of first : speed of second = √t₂ : √t₁
Why: after meeting, each train must cover the stretch the other train covered before meeting. The faster train has less left to cover and covers it faster, so the time ratio is the square of the speed ratio, turned upside down.
Worked questions at NTPC level
Q1. A 150 m train runs at 54 km/h. How long does it take to cross a pole, and a 300 m platform?
54 km/h = 15 m/s.
Pole: 150 ÷ 15 = 10 seconds.
Platform: (150 + 300) ÷ 15 = 30 seconds.
Q2. A train crosses a pole in 12 seconds and a 240 m platform in 24 seconds. Find its length and speed.
The extra 12 seconds cover the 240 m platform, so speed = 240 ÷ 12 = 20 m/s = 72 km/h.
Length = 20 × 12 = 240 m.
Q3. Two trains, 120 m and 180 m long, run at 60 km/h and 48 km/h in opposite directions. How long do they take to cross each other?
Relative speed = 108 km/h = 30 m/s. Distance = 300 m.
Time = 300 ÷ 30 = 10 seconds.
Q4. The same two trains run in the same direction. How long does the faster train take to pass the slower one?
Relative speed = 12 km/h = 12 × 5/18 = 10/3 m/s.
Time = 300 ÷ 10/3 = 90 seconds.
Q5. A 110 m train at 60 km/h passes a person running at 6 km/h in the opposite direction. How long does it take?
Relative speed = 66 km/h = 66 × 5/18 = 55/3 m/s.
Time = 110 ÷ 55/3 = 6 seconds.
Q6. Two trains start at the same time from stations P and Q towards each other. After meeting, they take 9 hours and 16 hours to reach Q and P respectively. Find the ratio of their speeds.
Speed ratio = √16 : √9 = 4 : 3.
Common mistakes
- Forgetting the platform length. Crossing a platform is never train length alone.
- Adding speeds for the same direction. Overtaking uses the difference.
- Not converting km/h to m/s. Metres divided by km/h gives a wrong answer that is often among the options.
- Adding the person's length. A person, pole or signal counts as a point.
- Mixing up the meeting ratio. The first train's speed goes with the square root of the second train's time.
Practice set
- A 200 m train at 72 km/h crosses a pole. How long does it take?
- The same train crosses a 400 m platform. How long does it take?
- Trains of 100 m and 150 m run at 50 km/h and 40 km/h in opposite directions. How long do they take to cross each other?
- The same trains run in the same direction. How long does the faster one take to pass the slower one?
- A train crosses a pole in 15 seconds and a 300 m platform in 30 seconds. Find its length and speed.
- A 250 m train at 90 km/h crosses a bridge in 36 seconds. How long is the bridge?
- A 125 m train passes a person walking at 5 km/h in the same direction in 10 seconds. Find the train's speed.
- After meeting, two trains take 4 hours and 9 hours to reach their destinations. Find the ratio of their speeds.
Answers:
- 10 seconds. 72 km/h = 20 m/s; 200 ÷ 20.
- 30 seconds. 600 ÷ 20.
- 10 seconds. Relative speed 90 km/h = 25 m/s; 250 ÷ 25.
- 90 seconds. Relative speed 10 km/h = 25/9 m/s; 250 ÷ 25/9.
- 300 m and 72 km/h. Speed = 300 ÷ 15 = 20 m/s; length = 20 × 15.
- 650 m. 25 m/s × 36 = 900 m; 900 − 250.
- 50 km/h. Relative speed = 125 ÷ 10 = 12.5 m/s = 45 km/h; add the person's 5 km/h.
- 3 : 2. √9 : √4.
What to do next
- Draw a quick sketch for your first 10 questions: engine at the start, last coach at the end.
- Solve 20 mixed train questions and write "distance = … , relative speed = …" before any arithmetic.
- Practise five two-crossing questions using speed = P ÷ (t₂ − t₁).
- Revise time, speed and distance for average speed, and then try boats and streams.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Railway Recruitment Boards website .
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