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
🔑Essential Formulas
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
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Exam Patterns
What examiners ask — read before attempting PYQs
💡Remember
72 km/hr = 20 m/s (this conversion appears frequently)
✏️Worked Example 1
1
Distance covered = Length of train = 120m
2
Time taken = 8 seconds
3
Speed = Distance/Time = 120/8 = 15 m/s
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
Total distance = 100 + 150 = 250m
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.
Most common error: Forgetting to add platform length in crossing problems
📌 Exam Facts
Standard speed conversion factor from km/hr to m/s is 5/18
Standard speed conversion factor from m/s to km/hr is 18/5
When two trains move in opposite directions, relative speed equals sum of individual speeds
When two trains move in same direction, relative speed equals difference of individual speeds
Distance covered while crossing equals train length when crossing a pole or telegraph post
Distance covered while crossing platform equals train length plus platform length
72 km/hr equals exactly 20 m/s (frequently used in SSC problems)
Time taken by train to completely cross another train equals sum of lengths divided by relative speed
Questions Asked in Previous Exams
Real questions from SSC papers — 2015 to 2024 · Showing 3 of 8
Exam Q 12022Previous Year Pattern
Train A crosses a platform of length 150 m in 20 seconds. If the train's length is 250 m, what is the speed of Train A?
Exam Q 22022Previous Year Pattern
Two trains are moving towards each other on parallel tracks. Train X has a speed of 45 km/h and Train Y has a speed of 55 km/h. If they are 400 km apart, in how many hours will they meet?
Exam Q 32022Previous Year Pattern
A train of length 180 m passes a stationary pole in 9 seconds. How long will it take to pass another train of length 120 m moving in the opposite direction at the same speed?
💪 Practice Questions (5) · Showing 3
Q 1hard
Train A and Train B start simultaneously from stations X and Y respectively, which are 480 km apart. Train A travels towards Y at 60 km/h, while Train B travels towards X at 40 km/h. After how many hours will they meet, and at what distance from station X?
Q 2hard
A train 150 m long crosses a platform 250 m long in 20 seconds. Another train 120 m long crosses the same platform in 16 seconds. What is the difference in their speeds (in m/s)?
Q 3hard
Train X leaves station A at 8:00 AM travelling at 72 km/h. Train Y leaves the same station at 9:30 AM travelling at 90 km/h in the same direction. At what time will Train Y catch up with Train X?
🚀 60-Second Revision
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
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