Problems on Trains
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Solved Examples
Study MaterialSolved Examples – Problems on Trains
Solved examples help students understand the practical application of train concepts in competitive examinations. These examples are designed from basic to advanced level and cover important train problems frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, Defence, and placement aptitude tests.
Topics Covered in Solved Examples
- Train Crossing Pole Problems
- Train Crossing Platform Problems
- Two Trains Crossing Each Other
- Relative Speed Questions
- Train and Man Problems
- Opposite Direction Problems
- Same Direction Problems
- Bridge and Tunnel Problems
- Train Length Calculations
- Advanced Relative Speed Applications
Example 1: Train Crossing a Pole
Question: A train 180 meters long crosses a pole in 12 seconds. Find the speed of the train.
Solution:
Distance covered:
= Length of train
= 180 meters
Speed:
= Distance / Time
= 180/12
= 15 m/s
Convert into km/h:
= 15 × 18/5
= 54 km/h
Therefore:
Speed of train = 54 km/h
Example 2: Finding Train Length
Question: A train running at 72 km/h crosses a pole in 20 seconds. Find the length of the train.
Solution:
Convert speed into m/s:
= 72 × 5/18
= 20 m/s
Train length:
= Speed × Time
= 20 × 20
= 400 meters
Therefore:
Length of train = 400 meters
Example 3: Train Crossing a Platform
Question: A train 250 meters long crosses a platform 150 meters long in 20 seconds. Find the speed of the train.
Solution:
Total distance:
= 250 + 150
= 400 meters
Speed:
= 400/20
= 20 m/s
Convert into km/h:
= 20 × 18/5
= 72 km/h
Therefore:
Speed of train = 72 km/h
Example 4: Finding Platform Length
Question: A train 300 meters long running at 90 km/h crosses a platform in 24 seconds. Find the length of the platform.
Solution:
Convert speed:
= 90 × 5/18
= 25 m/s
Total distance:
= 25 × 24
= 600 meters
Platform length:
= 600 − 300
= 300 meters
Therefore:
Platform length = 300 meters
Example 5: Two Trains in Opposite Directions
Question: Two trains 150 m and 250 m long move in opposite directions at 54 km/h and 72 km/h. Find the time taken to cross each other.
Solution:
Total length:
= 150 + 250
= 400 meters
Relative speed:
= 54 + 72
= 126 km/h
Convert into m/s:
= 126 × 5/18
= 35 m/s
Time:
= 400/35
= 11.43 seconds
Therefore:
Required time ≈ 11.43 seconds
Example 6: Two Trains in Same Direction
Question: Two trains 180 m and 220 m long move in the same direction at 72 km/h and 54 km/h respectively. Find the time taken by the faster train to cross the slower train.
Solution:
Total length:
= 180 + 220
= 400 meters
Relative speed:
= 72 − 54
= 18 km/h
Convert into m/s:
= 18 × 5/18
= 5 m/s
Time:
= 400/5
= 80 seconds
Therefore:
Required time = 80 seconds
Example 7: Train Crossing a Man
Question: A train 240 meters long moving at 54 km/h crosses a standing man. Find the time taken.
Solution:
Convert speed:
= 54 × 5/18
= 15 m/s
Time:
= 240/15
= 16 seconds
Therefore:
Required time = 16 seconds
Example 8: Train Crossing a Walking Man
Question: A train 300 meters long moving at 72 km/h crosses a man walking at 6 km/h in the same direction. Find the time taken.
Solution:
Relative speed:
= 72 − 6
= 66 km/h
Convert into m/s:
= 66 × 5/18
= 18.33 m/s
Time:
= 300/18.33
≈ 16.36 seconds
Therefore:
Required time ≈ 16.36 seconds
Example 9: Opposite Direction Man Problem
Question: A train 200 meters long moving at 54 km/h crosses a man walking at 6 km/h in opposite direction. Find the time taken.
Solution:
Relative speed:
= 54 + 6
= 60 km/h
Convert into m/s:
= 60 × 5/18
= 16.67 m/s
Time:
= 200/16.67
≈ 12 seconds
Therefore:
Required time ≈ 12 seconds
Example 10: Train Crossing a Bridge
Question: A train 350 meters long crosses a bridge 250 meters long in 30 seconds. Find the speed of the train.
Solution:
Total distance:
= 350 + 250
= 600 meters
Speed:
= 600/30
= 20 m/s
Convert into km/h:
= 20 × 18/5
= 72 km/h
Therefore:
Speed of train = 72 km/h
Example 11: Finding Relative Speed
Question: Two trains move in opposite directions at 45 km/h and 55 km/h. Find relative speed.
Solution:
Relative speed:
= 45 + 55
= 100 km/h
Therefore:
Relative speed = 100 km/h
Example 12: Same Direction Relative Speed
Question: Two trains move in same direction at 80 km/h and 50 km/h. Find relative speed.
Solution:
Relative speed:
= 80 − 50
= 30 km/h
Therefore:
Relative speed = 30 km/h
Example 13: Advanced Crossing Problem
Question: A train crosses a pole in 18 seconds and a platform 180 meters long in 30 seconds. Find the length of the train.
Solution:
Let speed = s m/s
Train length:
= 18s
Crossing platform:
18s + 180 = 30s
12s = 180
s = 15 m/s
Train length:
= 18 × 15
= 270 meters
Therefore:
Length of train = 270 meters
Example 14: Two Trains Crossing a Pole
Question: Two trains 100 m and 150 m long moving in opposite directions at 36 km/h and 54 km/h respectively cross each other. Find the time taken.
Solution:
Total length:
= 100 + 150
= 250 meters
Relative speed:
= 36 + 54
= 90 km/h
Convert into m/s:
= 90 × 5/18
= 25 m/s
Time:
= 250/25
= 10 seconds
Therefore:
Required time = 10 seconds
Example 15: Platform and Speed Problem
Question: A train 400 meters long crosses a platform 200 meters long in 24 seconds. Find the speed of the train in km/h.
Solution:
Total distance:
= 400 + 200
= 600 meters
Speed:
= 600/24
= 25 m/s
Convert into km/h:
= 25 × 18/5
= 90 km/h
Therefore:
Speed of train = 90 km/h
Example 16: Relative Speed Ratio Problem
Question: Two trains cross a man in 20 seconds and 30 seconds respectively. Find the ratio of their speeds if both trains have equal length.
Solution:
For equal lengths:
Speed ratio:
= Inverse of time ratio
= 30 : 20
= 3 : 2
Therefore:
Required ratio = 3 : 2
Important Exam Tips
- Always convert km/h into m/s before solving.
- Use relative speed carefully.
- Memorize crossing formulas.
- Read direction carefully before selecting formula.
- Use total length in platform problems.
- Simplify calculations early.
- Verify units properly.
Practicing solved examples regularly improves conceptual clarity, logical thinking, and calculation speed in solving train-related aptitude questions in competitive examinations.