About Problems on Trains
Problems on trains are time and distance questions with one extra idea: a train has length. Passing a pole, a platform or another train means covering more than a point, so the distance in the formula is never simply the length of the track. Almost every question in this topic reduces to deciding two things — what distance is really being covered, and what the relative speed is.
What you need to understand
- A train passing a pole, a signal post, an electric pole or a standing man covers exactly its own length.
- A train passing a platform, bridge or tunnel covers its own length plus the length of the platform.
- Two trains moving in opposite directions approach each other at the sum of their speeds.
- Two trains moving in the same direction approach each other at the difference of their speeds.
- When a train passes a man who is walking, the man is not a point. The relative speed is the sum if they move in opposite directions and the difference if they move in the same direction.
- Distances in these questions are in metres and speeds are usually given in km/hr, so the conversion is part of the question, not an afterthought.
Formulas to remember
How to work through these questions
- Convert every speed to m/s at the start. Doing it early keeps the whole calculation in one set of units.
- Decide what distance the train actually covers: its own length alone, its length plus a platform, or its length plus another train.
- Decide the relative speed: the same train alone, the sum of two speeds, or the difference of two speeds.
- Divide the distance by the relative speed. If the question gives times and asks for a length or a speed, rearrange instead of guessing.
- Sanity-check the answer. A train should take longer to pass a platform than a pole, and two trains moving in opposite directions should cross faster than the same two moving in the same direction.
Mistakes that cost marks
- Forgetting to convert km/hr to m/s before dividing a distance in metres. This is the single most common error in the topic.
- Using only the length of the train when a platform is involved.
- Subtracting speeds when the trains move in opposite directions, or adding them when they move in the same direction.
- Treating a walking man as a stationary point and ignoring his speed.
- Assuming the answer must be a whole number and rounding an intermediate step.
Worked example
A train 240 m long is running at 72 km/hr. How long will it take to cross a platform 360 m long?
- Convert the speed: 72 km/hr = 72 x 5/18 = 20 m/s.
- Decide the distance. To clear the platform the train must cover its own length plus the length of the platform: 240 + 360 = 600 m.
- The train is alone on the track, so the relative speed is simply its own speed, 20 m/s.
- Time = distance / speed = 600 / 20 = 30 seconds.
Answer: 30 seconds
Practice questions with answers
A few Problems on Trains questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
A train of length 240 m is moving at 54 km/hr. Find the time it takes to pass a signal post.
Answer: Option B — with explanation
Speed = 54 km/hr = 54 x 5/18 = 15 m/s.
To pass a signal post the train covers its own length only, that is 240 m.
Time = distance / speed = 240 / 15 = 16 seconds.
Common mistakes
- used half the given speed: 32
- used twice the given speed: 8
- forgot to convert km/hr into m/s before dividing: 4.44
Question 2
A 560 m long train travelling at 126 km/hr crosses a platform of length 1050 m. How long does it take?
Answer: Option A — with explanation
Speed = 126 km/hr = 35 m/s.
To pass a platform the train must cover its own length plus the length of the platform = 560 + 1050 = 1610 m.
Time = 1610 / 35 = 46 seconds.
Common mistakes
- counted only the train's length and ignored the platform: 16
- forgot to convert km/hr into m/s: 12.78
- used only the length of the platform: 30
Question 3
Two trains of length 275 m and 675 m are moving in opposite directions at 180 km/hr and 162 km/hr. In how much time will they cross each other?
Answer: Option A — with explanation
When two trains move in opposite directions their relative speed is the sum of their speeds = 180 + 162 = 342 km/hr = 95 m/s.
The distance to be covered is the sum of their lengths = 275 + 675 = 950 m.
Time = 950 / 95 = 10 seconds.
Common mistakes
- forgot to convert km/hr into m/s: 2.78
- used the difference of the speeds instead of the sum: 190
- counted only one train's length: 2.89
Question 4
Two trains, 725 m and 175 m long, move in the same direction at 90 km/hr and 36 km/hr. Find the time the faster train needs to clear the slower one.
-
A
48.33
-
B
16.67
-
C
25.71
-
D
60
Answer: Option D — with explanation
Moving in the same direction, the relative speed is the difference of the speeds = 90 - 36 = 54 km/hr = 15 m/s.
The distance to be covered is the sum of the lengths = 725 + 175 = 900 m.
Time = 900 / 15 = 60 seconds.
Common mistakes
- counted only the faster train's length: 48.33
- added the speeds instead of subtracting them: 25.71
- forgot to convert km/hr into m/s: 16.67
Question 5
A man walking at 7.2 km/hr in the same direction is passed by a train of length 693 m running at 126 km/hr. How long does the train take to pass him?
-
A
19.8
-
B
21
-
C
5.5
-
D
18.73
Answer: Option B — with explanation
Speed of the train = 126 km/hr = 35 m/s and speed of the man = 36/5 km/hr = 2 m/s.
Both move in the same direction, so the relative speed is 35 - 2 = 33 m/s.
The train must cover its own length, 693 m. Time = 693 / 33 = 21 seconds.
Common mistakes
- ignored the man's speed completely: 19.8
- forgot to convert km/hr into m/s: 5.5
- used the wrong sign for the man's direction: 18.73
Frequently asked questions
What is the formula for a train crossing a platform?
Time = (length of the train + length of the platform) / speed of the train. The train has to clear its own length as well as the platform before it is fully across.
How do I know whether to add or subtract the speeds?
Add when the two trains move in opposite directions, because they close the gap faster. Subtract when they move in the same direction, because only the difference in speed closes the gap.
Is passing a pole the same as passing a platform?
No. A pole has no length worth counting, so the train only covers its own length. A platform has a real length, so it is added to the train.
Why do these questions use 5/18?
One kilometre is 1000 metres and one hour is 3600 seconds, so 1 km/hr is 1000/3600 = 5/18 m/s. Multiplying by 5/18 converts km/hr to m/s, and multiplying by 18/5 converts back.
Do problems on trains appear in bank and SSC exams?
Yes. They appear in the quantitative aptitude section of bank, SSC, railway and state government papers, and in most campus placement tests, usually as one or two questions.
