Core ConceptRead this first — the foundation of the topic
Core Concept
Train problems involve calculating time taken by trains to cross objects like poles, platforms, bridges, or other trains. The key is understanding that trains have length, unlike point objects
Key Rules
When a train crosses a stationary object like a pole, it travels a distance equal to its own length. When crossing a platform or bridge, it travels its own length plus the length of the platform/bridge. For two trains, use relative speed concept.
Formula BlockMemorise — at least one formula appears in every paper
Time = Distance/Speed
Speed = Distance/Time
Relative Speed (same direction) = |S1 - S2|
Relative Speed (opposite direction) = S1 + S2
Speed conversion: km/hr to m/s multiply by 5/18, m/s to km/hr multiply by 18/5
Exam PatternsWhat examiners ask — read before attempting PYQs
SSC CGL typically asks 1-2 train problems per paper. Common question types include trains crossing poles, platforms, bridges, and other trains. Questions often involve unit conversions and relative motion.
ShortcutsUse these to save 30–60 seconds per question
- The 5/18 Rule: To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5. Remember: 72 km/hr = 20 m/s (this conversion appears frequently).
Worked ExampleSolve this step-by-step before moving on
1
Step 1
Distance covered = Length of train = 120m
2
Step 2
Time taken = 8 seconds
3
Step 3
Speed = Distance/Time = 120/8 = 15 m/s
4
Step 4
Convert to km/hr = 15 × 18/5 = 54 km/hr
Answer: 54 km/hr
Worked Example 2: Two trains of lengths 100m and 150m are running in opposite directions at speeds 40 km/hr and 50 km/hr respectively. In how much time will they cross each other?
Relative speed = 100/9 + 125/9 = 225/9 = 25 m/s (opposite direction, so add)
3
Step 3
Total distance = 100 + 150 = 250m
4
Step 4
Time = Distance/Speed = 250/25 = 10 seconds
Answer: 10 seconds
Advanced Shortcut - Platform Formula: Time to cross platform = (Train length + Platform length)/Speed. This direct formula saves calculation steps in exams.
Most Common Trap: Students forget to add platform/bridge length when train crosses them. They only consider train length, leading to wrong answers. Always read whether the train crosses a pole (only train length) or platform/bridge (train length + platform/bridge length).
Another frequent mistake is wrong unit conversion. Practice the 5/18 conversion thoroughly. Many students confuse when to multiply or divide.
Speed-Distance-Time Shortcut: If train crosses pole in time T1 and platform in time T2, then platform length = speed × (T2 - T1). This eliminates the need to calculate train length first.
A train travels 240 km in 4 hours. What is the speed of the train?
Practice 2easy
Train A travels at 45 km/h and Train B travels at 55 km/h. If both trains start from the same point and travel in the same direction, how far apart will they be after 3 hours?
Practice 3easy
A train needs to cover 360 km. If it travels at 90 km/h, how much time will it take?
Practice 4medium
A train travels 240 km in 4 hours at a constant speed. What is the speed of the train?
Practice 5medium
A train moving at 72 km/h needs to cross a platform of length 150 m. If the train's length is 100 m, how long does it take to completely cross the platform?
Practice 6medium
Train A and Train B are moving towards each other on parallel tracks. Train A travels at 50 km/h and Train B at 40 km/h. They are 180 km apart. After how many hours will they meet?
Practice 7medium
A train crosses a stationary pole in 8 seconds. If the train's length is 240 m, what is its speed in km/h?
Practice 8hard
Train A of length 150 m travels at 60 km/h. Train B of length 100 m travels at 40 km/h in the opposite direction on a parallel track. How much time (in seconds) will it take for the two trains to completely pass each other?
60-Second Revision — Trains
Remember: Pole crossing uses only train length, platform crossing adds platform length
Formula: Speed conversion km/hr to m/s multiply by 5/18
Trap: Always check if crossing pole or platform - different distance calculations
Shortcut: 72 km/hr = 20 m/s conversion for quick calculations
Relative speed: Add for opposite direction, subtract for same direction
Two trains: Total distance = Length1 + Length2, use relative speed
Platform trick: Time difference method gives platform length directly