Module 1 · Arithmetic
Chapter 12: Trains
Arithmetic
3 topics
What this chapter covers
The 3 topics below make up Trains on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
📚 Study this chapter
Notes, worked examples and hint-guided practice for every topic.
Start learning →
🎯 Topic tests
8 auto-graded questions per topic, pulled from the question bank.
Practice by topic →
📝 Chapter test
25 fresh mixed-difficulty questions, timed, with full solutions.
Take chapter test →
Formula Reference Sheet
This chapter
Core relations
| Crossing a point (pole/man/signal) | time = train length ÷ speed |
|---|---|
| Crossing a platform/bridge | time = (train length + platform length) ÷ speed |
| km/h to m/s | multiply by 5/18 |
| m/s to km/h | multiply by 18/5 |
| Speed | speed = distance ÷ time |
Two bodies in motion
| Relative speed — opposite directions | add the two speeds |
|---|---|
| Relative speed — same direction | subtract (faster − slower) |
| Two trains crossing each other | time = (L₁ + L₂) ÷ relative speed |
| Train crossing a moving man/train | distance = sum of relevant lengths, speed = relative |
| Two crossing times → lengths | use point-time × speed = own length |
CAT reference
🖩 Graphing Calculator