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 200 metres long passes another train 150 metres long, moving in the same direction. The first train travels at 60 km/h and the second train travels at 40 km/h. How long will it take for the first train to completely pass the second train?
Practice 2easy
A train travels 240 km in 4 hours at a constant speed. What is the speed of the train in km/h?
Practice 3easy
Train A travels at 72 km/h. How long will it take to cover 360 km?
Practice 4easy
Two trains start from the same station at the same time. Train X travels at 48 km/h and Train Y travels at 60 km/h in the same direction. After 3 hours, what is the distance between them?
Practice 5easy
A train 150 metres long passes a stationary pole in 10 seconds. What is the speed of the train in m/s?
Practice 6easy
Train P and Train Q are moving towards each other on parallel tracks. Train P travels at 50 km/h and Train Q travels at 40 km/h. If they are initially 270 km apart, in how many hours will they meet?
Practice 7medium
Train A and Train B are running in the same direction on parallel tracks. Train A is 200 metres long and travels at 80 km/h. Train B is 150 metres long and travels at 60 km/h. How much time (in seconds) will it take for Train A to completely overtake Train B?
Practice 8medium
Train A and Train B are running on parallel tracks. Train A is 240 metres long and crosses a stationary pole in 12 seconds. Train B is 180 metres long and crosses the same pole in 9 seconds. How much time (in seconds) will it take for the two trains to completely pass each other when running in opposite directions?
Practice 9medium
Train X crosses a 150-metre platform in 18 seconds and a 250-metre platform in 26 seconds. What is the speed of Train X (in km/h)?
Practice 10medium
Two trains start simultaneously from stations A and B, which are 480 km apart. Train P travels from A to B at 60 km/h, while Train Q travels from B to A at 40 km/h. After how many hours will they meet?
Practice 11medium
A train 320 metres long is running at 45 km/h. A man standing on a platform watches the train pass. How long does it take for the entire train to pass the man (in seconds)?
Practice 12hard
A train 150 metres long crosses a platform 250 metres long in 20 seconds. Another train 120 metres long travels at twice the speed of the first train. How long will the second train take to cross the same platform?
Practice 13hard
Two trains start from the same station at the same time. Train P travels towards the north at 72 km/h, while Train Q travels towards the south at 48 km/h. After how much time will they be 360 km apart?
Practice 14hard
Train A and Train B start simultaneously from stations P and Q respectively, which are 480 km apart. Train A travels towards Q at 60 km/h, while Train B travels towards P at 40 km/h. At what time will they meet, and how far will Train A have travelled by then?
Practice 15hard
A train travels from City A to City B, a distance of 360 km. For the first 120 km, it travels at 60 km/h. For the next 180 km, it travels at 90 km/h. For the remaining distance, it travels at 120 km/h. What is the average speed of the train for the entire journey?
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