Problems on Trains
Problems on Trains
Train problems are a specialised application of Time, Speed & Distance. The key insight is that a train has length — so the distance covered when crossing an object equals the train's length plus the object's length. Unit conversion between km/h and m/s is essential in every train problem.
Key Idea
Distance = length of train + length of obstacle. Opposite directions: add speeds. Same direction: subtract speeds. Always match units — km/h to m/s using ×5/18.
Core Formulas
Cross pole/person
Time = Length of train / Speed of train
When train crosses a stationary point
Cross platform
Time = (L_train + L_platform) / Speed
When train crosses a platform or bridge
Opposite direction
Time to cross = (L₁ + L₂) / (S₁ + S₂)
Two trains coming towards each other
Same direction
Time to cross = (L₁ + L₂) / (S₁ − S₂)
Faster train overtaking slower train
Speed conversion
1 km/h = 5/18 m/s; 1 m/s = 18/5 km/h
Essential unit conversion for train problems
Relevant Exams
2–4 questions per exam in SSC CGL Tier 1 and RRB exams. Train problems are among the most frequently asked TSD applications. Three types: pole, platform, two trains.