Trains Problems
Key Concepts & Formulas
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Relative Speed (Opposite direction) | S₁ + S₂ km/h (add speeds when trains move towards each other) |
| 2 | Relative Speed (Same direction) | |
| 3 | Time to cross a pole/stationary object | Time = Length of train / Speed (no platform length added) |
| 4 | Time to cross a platform/bridge | Time = (Length of train + Length of platform) / Speed |
| 5 | Convert km/h → m/s | Multiply by 5/18 (e.g. 72 km/h = 20 m/s) |
| 6 | Convert m/s → km/h | Multiply by 18/5 (e.g. 15 m/s = 54 km/h) |
| 7 | Overtaking / Passing | Distance to cover = sum of train lengths; use relative speed |
10 Practice MCQs
1. A 180 m train running at 54 km/h crosses a pole in how many seconds?
**Answer:** 12 s **Solution:** 54 km/h = 15 m/s; time = 180 / 15 = 12 s **Shortcut tip:** km/h → m/s (×5/18) instantly gives 15 m/s **Concept tag:** Pole crossing, unit conversion2. A 200 m train takes 40 s to pass a 400 m platform. Speed in km/h is:
**Answer:** 54 km/h **Solution:** Total distance = 600 m; speed = 600/40 = 15 m/s = 15×18/5 = 54 km/h **Shortcut tip:** 15 m/s is the “magic number” for 54 km/h **Concept tag:** Platform crossing3. Two trains (120 m & 180 m) run opposite at 60 km/h & 48 km/h. Crossing time?
**Answer:** 10 s **Solution:** Relative speed = 108 km/h = 30 m/s; total length = 300 m; time = 300/30 = 10 s **Shortcut tip:** 108 km/h is exactly 30 m/s **Concept tag:** Opposite-direction relative speed4. Faster train (72 km/h) overtakes slower (54 km/h) in same direction in 60 s. Length of slower train?
**Answer:** 300 m **Solution:** Relative speed = 18 km/h = 5 m/s; distance = 5×60 = 300 m **Shortcut tip:** 18 km/h = 5 m/s (memorise) **Concept tag:** Overtaking, same direction5. A train crosses a man running 6 km/h opposite in 8 s. Train length 200 m; find train speed.
**Answer:** 84 km/h **Solution:** Relative speed = 200/8 = 25 m/s = 90 km/h; train speed = 90 – 6 = 84 km/h **Shortcut tip:** Relative speed minus man’s speed gives train speed **Concept tag:** Relative motion with man6. How long will a 300 m train take to pass through a 1.2 km tunnel at 72 km/h?
**Answer:** 75 s **Solution:** 72 km/h = 20 m/s; distance = 1500 m; time = 1500/20 = 75 s **Shortcut tip:** Add lengths first, then divide by speed **Concept tag:** Tunnel crossing7. A train running at 90 km/h crosses a platform in 30 s. If platform is 400 m, train length is:
**Answer:** 350 m **Solution:** 90 km/h = 25 m/s; total distance = 25×30 = 750 m; train = 750 – 400 = 350 m **Shortcut tip:** Distance – platform = train **Concept tag:** Platform8. Two trains start at same time from P & Q (360 km apart) at 50 km/h & 40 km/h towards each other. Meeting point distance from P?
**Answer:** 200 km **Solution:** Time to meet = 360/(50+40) = 4 h; distance from P = 50×4 = 200 km **Shortcut tip:** Use speed ratio 5:4; divide 360 in 5:4 → 200:160 **Concept tag:** Meeting point9. A train takes 25 s to pass a 500 m bridge and 15 s to pass a signal pole. Length of train?
**Answer:** 750 m **Solution:** Let length L m; (L+500)/25 = L/15 → 3L+1500 = 5L → L = 750 m **Shortcut tip:** Equate speeds from both cases **Concept tag:** Two-scene equation10. Speed of train in m/s if it passes a 200 m platform in 36 s and a man in 20 s?
**Answer:** 10 m/s **Solution:** Let L = length, S = speed; L/S = 20 → L = 20S; (20S+200)/S = 36 → 20S+200 = 36S → S = 10 m/s **Shortcut tip:** Difference in distances = 200 m; difference in times = 16 s → speed = 200/16 = 12.5 m/s (cross-check) **Concept tag:** Two-scene equation5 Previous Year Questions
[RRB NTPC 2021] A 270 m train at 60 km/h crosses a 330 m bridge. Time?
**Answer:** 36 s **Solution:** 60 km/h = 50/3 m/s; distance = 600 m; time = 600×3/50 = 36 s **Shortcut tip:** 600 m at 50/3 m/s → 600×3/50 = 36 **Concept tag:** Bridge[RRB Group-D 2019] Two trains (140 m & 160 m) run same direction 54 & 36 km/h. Overtaking time?
**Answer:** 60 s **Solution:** Relative 18 km/h = 5 m/s; distance 300 m; time 300/5 = 60 s **Shortcut tip:** 18 km/h = 5 m/s **Concept tag:** Same-direction overtake[RRB ALP 2018] A train passes a platform in 45 s and a pole in 15 s. Platform 600 m. Train length?
**Answer:** 300 m **Solution:** Speed same; L/15 = (L+600)/45 → 3L = L+600 → L = 300 m **Shortcut tip:** 3:1 time ratio → 1:3 length ratio → train = ½ platform **Concept tag:** Pole vs platform[RRB NTPC 2017] Train at 90 km/h crosses a 200 m platform in 24 s. Train length?
**Answer:** 400 m **Solution:** 90 km/h = 25 m/s; total = 25×24 = 600 m; train = 600 – 200 = 400 m **Shortcut tip:** 25 m/s × 24 = 600 **Concept tag:** Platform[RRB JE 2015] Two trains 108 km/h & 72 km/h opposite direction, each 250 m. Crossing time?
**Answer:** 10 s **Solution:** Relative 180 km/h = 50 m/s; total length 500 m; time 500/50 = 10 s **Shortcut tip:** 180 km/h = 50 m/s **Concept tag:** Opposite-directionSpeed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| 18 km/h → m/s | 5 m/s (memorise) | 36 km/h = 10 m/s |
| 72 km/h → m/s | 20 m/s (divide by 3.6) | 90 km/h = 25 m/s |
| Opposite direction | Speeds add → km/h or m/s | 60+48 = 108 km/h |
| Same direction overtake | Subtract speeds; distance = sum of lengths | 72–54 = 18 km/h = 5 m/s |
| Platform vs pole | Platform extra time × speed = platform length | Extra 20 s at 15 m/s → 300 m platform |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Forgetting to add train length | Focus only on platform | Always add train + obstacle lengths |
| Using wrong relative direction | Mix up +/– for same/opposite | Opposite → add; same → subtract |
| Leaving units mixed | km/h with metres | Convert to m/s first |
| Ignoring unitary time | 25 m/s × 30 s = 750 m (correct) | Write units in every line |
Quick Revision Flashcards
| Front | Back |
|---|---|
| 54 km/h in m/s | 15 m/s |
| 15 m/s in km/h | 54 km/h |
| Relative speed opposite 60 & 48 km/h | 108 km/h = 30 m/s |
| Relative speed same direction 60 & 48 km/h | 12 km/h = 3.33 m/s |
| Time formula for pole | t = L / S |
| Time formula for platform | t = (L_train + L_platform) / S |
| Magic number 18 km/h | 5 m/s |
| 72 km/h | 20 m/s |
| Convert km/h → m/s | × 5/18 |
| Convert m/s → km/h | × 18/5 |
BETA
