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 at a constant speed. How long will it take to cover 360 km at the same speed?
Practice 2medium
Train A and Train B are moving towards each other on parallel tracks. Train A travels at 60 km/h and Train B travels at 40 km/h. If they are initially 300 km apart, in how many hours will they meet?
Practice 3hard
Two trains, A and 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 they meet, train A takes 4 more hours to reach Y, while train B takes 9 more hours to reach X. However, train A suddenly reduces its speed by 20% after meeting train B. At what time (in hours from the start) do the two trains actually meet?
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