Problems on Trains
⚡ Unlock time-saving calculation tricks and mental math techniques. Solve complex problems in seconds with proven shortcut methods used by top performers.
Shortcut Techniques
Study MaterialShortcut Techniques – Problems on Trains
Shortcut techniques in Problems on Trains help candidates solve aptitude questions quickly and accurately in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, Defence, and placement examinations.
Most train problems are based on:
- Relative speed
- Train length
- Platform length
- Crossing time
- Unit conversion
- Opposite and same direction motion
Using shortcut techniques reduces lengthy calculations and improves solving speed significantly.
Why Learn Train Problem Shortcuts?
- Improves speed in competitive exams.
- Helps solve train crossing problems quickly.
- Reduces calculation mistakes.
- Useful in relative speed concepts.
- Improves accuracy and time management.
Shortcut #1: Memorize Basic Train Formula
Speed = Distance / Time
All train problems are based on this formula.
Shortcut #2: Pole Crossing Trick
When a train crosses:
- A pole
- A signal post
- A standing man
Only train length is considered.
Distance Covered = Length of Train
Formula:
Time = Train Length / Speed
✔ Pole has no length, so only train length matters.
Shortcut #3: Platform Crossing Trick
When a train crosses:
- Platform
- Bridge
- Tunnel
Total distance:
Distance = Train Length + Platform Length
Formula:
Time = (Train + Platform)/Speed
Shortcut #4: km/h to m/s Conversion Trick
To convert km/h into m/s:
Multiply by 5/18
Example:
72 km/h:
= 72 × 5/18
= 20 m/s
Shortcut #5: m/s to km/h Conversion Trick
To convert m/s into km/h:
Multiply by 18/5
Example:
25 m/s:
= 25 × 18/5
= 90 km/h
Shortcut #6: Relative Speed Rule
Opposite Directions
Relative Speed = Sum of Speeds
Same Direction
Relative Speed = Difference of Speeds
✔ Most train problems become easy using relative speed.
Shortcut #7: Two Trains Crossing in Opposite Directions
If:
- Lengths = a and b
- Speeds = u and v
Then:
Time = (a + b)/(u + v)
Shortcut #8: Two Trains Crossing in Same Direction
If:
- Lengths = a and b
- Speeds = u and v
Then:
Time = (a + b)/(u − v)
Shortcut #9: Direct Train Length Formula
If a train crosses a pole:
Train Length = Speed × Time
Example:
Speed = 20 m/s
Time = 15 s
Length:
= 20 × 15
= 300 m
Shortcut #10: Platform Length Formula
If train length is known:
Platform Length = Total Distance − Train Length
Shortcut #11: Relative Speed Memory Table
| Situation | Relative Speed |
|---|---|
| Opposite Directions | u + v |
| Same Direction | u − v |
Shortcut #12: Fast Unit Conversion Trick
Common speed conversions:
| km/h | m/s |
|---|---|
| 36 | 10 |
| 54 | 15 |
| 72 | 20 |
| 90 | 25 |
| 108 | 30 |
✔ Memorizing common conversions saves time in exams.
Shortcut #13: Same Time Ratio Trick
If two trains travel for the same time:
Distance Ratio = Speed Ratio
Shortcut #14: Crossing Man Walking Trick
If a man walks:
- In same direction → subtract speeds
- In opposite direction → add speeds
Shortcut #15: Quick Time Formula
For crossing problems:
Time = Total Distance / Relative Speed
Shortcut #16: Approximation Technique
In MCQs:
- Use approximation when answer options are far apart.
- Cancel common factors quickly.
- Simplify ratios before solving.
Shortcut #17: Opposite Direction Faster Crossing
When trains move in opposite directions:
Crossing time becomes smaller due to higher relative speed.
Shortcut #18: Same Direction Slower Crossing
When trains move in same direction:
Crossing time becomes larger due to smaller relative speed.
Shortcut #19: Train Crossing Formula Table
| Situation | Distance Covered |
|---|---|
| Pole | Train Length |
| Man | Train Length |
| Platform | Train + Platform |
| Bridge | Train + Bridge |
Shortcut #20: Important Formula Summary
| Concept | Formula |
|---|---|
| Speed | D/T |
| Distance | S × T |
| Time | D/S |
| Crossing Pole | L/S |
| Crossing Platform | (L+P)/S |
| Opposite Direction | u+v |
| Same Direction | u−v |
| km/h → m/s | × 5/18 |
| m/s → km/h | × 18/5 |
Important Exam Tips
- Always convert km/h into m/s before solving.
- Use relative speed carefully.
- Memorize common train formulas.
- Practice crossing problems regularly.
- Read direction carefully before selecting formula.
- Simplify calculations early.
- Verify final units properly.
Shortcut techniques in Problems on Trains help candidates improve calculation speed, reduce lengthy computations, and solve aptitude questions efficiently in competitive examinations.