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Problems on Trains Questions with Solutions

Train problems are Time-Speed-Distance with one extra twist: the train itself has a length, so "crossing" something means covering that length too — a pole, a platform, or another train. Here’s the concept, four fully worked examples covering each standard scenario, and a few to try yourself.

The concept, quickly

  • Crossing a stationary point (a pole, a man, a signal) means the train covers a distance equal to its OWN length — treat the point as having zero length.
  • Crossing a platform (or bridge) means the train covers a distance equal to its own length PLUS the platform’s length — the whole train must clear the whole platform.
  • Two trains crossing each other: use relative speed (sum of speeds if opposite directions, difference if same direction), and the distance to cover is the SUM of both train lengths — the same rule as objects, just with two lengths now.
  • Always convert km/hr to m/s (× 5/18) before working with lengths in metres and time in seconds — mixing units is the most common mistake here.

Worked examples

1. A train 180 m long is running at 54 km/hr. How long will it take to cross a man standing on the platform?

Solution

  1. Convert speed to m/s: 54 × 5/18 = 15 m/s.
  2. Crossing a man (a point) means covering a distance equal to the train’s own length: 180 m.
  3. Time = Distance / Speed = 180 / 15 = 12 seconds.

Answer: 12 seconds

2. A train 150 m long running at 72 km/hr crosses a platform in 25 seconds. Find the length of the platform.

Solution

  1. Convert speed to m/s: 72 × 5/18 = 20 m/s.
  2. Distance covered in 25 seconds = 20 × 25 = 500 m.
  3. This distance is the train’s length plus the platform’s length, so platform length = 500 − 150 = 350 m.

Answer: 350 m

3. Two trains, 120 m and 180 m long, run on parallel tracks in the SAME direction at 72 km/hr and 54 km/hr. Find the time for the faster train to completely cross the slower one.

Solution

  1. Same direction, so relative speed = difference of speeds = 72 − 54 = 18 km/hr.
  2. Convert to m/s: 18 × 5/18 = 5 m/s.
  3. Distance to cover = sum of both lengths = 120 + 180 = 300 m.
  4. Time = Distance / Speed = 300 / 5 = 60 seconds.

Answer: 60 seconds

4. Two trains, 140 m and 160 m long, run on parallel tracks in OPPOSITE directions at 60 km/hr and 48 km/hr. Find the time for them to cross each other.

Solution

  1. Opposite directions, so relative speed = sum of speeds = 60 + 48 = 108 km/hr.
  2. Convert to m/s: 108 × 5/18 = 30 m/s.
  3. Distance to cover = sum of both lengths = 140 + 160 = 300 m.
  4. Time = Distance / Speed = 300 / 30 = 10 seconds.

Answer: 10 seconds

Try these yourself

Identify which of the four scenarios applies, then check against the answer.

1. A train 200 m long is running at 90 km/hr. How long will it take to cross a lamp post?

Answer: 8 seconds

2. A train 250 m long running at 108 km/hr crosses a platform in 30 seconds. Find the length of the platform.

Answer: 650 m

3. Two trains, 100 m and 140 m long, run on parallel tracks in the same direction at 63 km/hr and 45 km/hr. Find the time for the faster train to completely cross the slower one.

Answer: 48 seconds

Where this comes up

Problems on Trains is a dedicated, frequently tested sub-topic within the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk.

Practice more Problems on Trains questions

This page covers the concept and a handful of worked examples. Pariksha Saathi has full topic-wise practice sets for Problems on Trains (and every other Quant/Reasoning/English topic) with instant scoring and explanations — free, no account required.

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