Episode 8 — Aptitude and Reasoning / 8.12 — Problems on Trains
8.12 Quick Revision -- Problems on Trains
The Master Rule
+-----------------------------------------------------+
| |
| Time = (Sum of relevant lengths) / Relative speed |
| |
+-----------------------------------------------------+
What Distance to Use
+-------------------------------------------------------+
| Scenario | Distance |
|-----------------------------|--------------------------|
| Train crosses pole/man | L_train |
| Train crosses platform | L_train + L_platform |
| Train crosses bridge/tunnel | L_train + L_bridge |
| Two trains cross each other | L_train1 + L_train2 |
| Train crosses man on | |
| another train | L_crossing_train ONLY |
| Man on train sees platform | L_platform ONLY |
+-------------------------------------------------------+
What Speed to Use
+-----------------------------------------------+
| Scenario | Relative Speed |
|-----------------------|------------------------|
| Stationary object | S_train |
| Same direction | |S1 - S2| |
| Opposite direction | S1 + S2 |
+-----------------------------------------------+
Unit Conversion (Must Memorize)
km/h to m/s: x 5/18
m/s to km/h: x 18/5
36 km/h = 10 m/s 72 km/h = 20 m/s
54 km/h = 15 m/s 90 km/h = 25 m/s
108 km/h = 30 m/s
Key Formulas
1. Pole: T = L / S
2. Platform: T = (L + P) / S
3. Two trains: T = (L1 + L2) / S_relative
4. Man on train sees other train: T = L_other / S_relative
Two-Equation Shortcut
Crosses pole in T1, platform (length P) in T2:
Speed = P / (T2 - T1)
Length = Speed x T1
"Man on Train" Trap
"Train crosses a man" --> Distance = Train length ONLY
"Two trains cross each other" --> Distance = BOTH lengths added
This is the #1 most tested distinction!
Opposite vs Same Direction
OPPOSITE: Faster crossing (SUM of speeds)
SAME: Slower crossing (DIFFERENCE of speeds)
Opposite direction crossing time is always LESS than
same direction crossing time for the same trains.
Fence-Post Rule
n poles = (n - 1) gaps
Distance = (n - 1) x gap_length
Speed Reasoning Checklist
[ ] Convert km/h to m/s FIRST
[ ] Identify WHAT crosses WHAT
[ ] Determine total distance (train length? both lengths? platform?)
[ ] Determine direction (same or opposite?)
[ ] Calculate relative speed
[ ] Apply T = Distance / Speed
[ ] Convert answer back if needed (seconds to minutes, m/s to km/h)
Common Mistakes
1. Forgetting to add train length to platform length
2. Using SUM instead of DIFFERENCE for same direction (or vice versa)
3. Mixing km/h and m/s in the same equation
4. Adding both lengths when a man (point) is the observer
5. Forgetting fence-post counting (n posts = n-1 gaps)
Part of Section 8.12: Problems on Trains