Train & Pole / Relative Speed – Clean Notes

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1. Train crossing a Pole / Standing Man

Formula: Time = L/x​

• L = Length of train


• x = Speed of train

Explanation: Pole/man is stationary → only train moves. : মানুহ/খুঁটা স্থিৰ থাকে → কেৱল ট্ৰেইন গতি কৰে।

2. Train crossing a Platform

Formula: Time = L + P / x​

• P = Length of platform

Explanation: Train covers its own length + platform length. : ট্ৰেইনে নিজৰ দৈৰ্ঘ্য + প্লাটফৰ্মৰ দৈৰ্ঘ্য পাৰ কৰে।

3. Train crossing a Moving Man (Same Direction)

Given:

• Train speed = x km/hr


• Man speed = y km/hr


• Condition: x > y

Formula: Time = L / x - y​

Explanation: Same direction → subtract speeds. : একেদিশে গতি → গতি বিয়োগ (x - y)

4. Train crossing a Moving Man (Opposite Direction)

Formula: Time = L / x + y​

Explanation: Opposite direction → add speeds. : বিপৰীত দিশ → গতি যোগ (x + y)

5. Train crossing a Man sitting in another Train

Opposite Direction: Time = L / x + y​

Same Direction: Time = L / x - y​

Explanation: Man is inside another train → use relative speed. : মানুহটো আন ট্ৰেইনত আছে → আপেক্ষিক গতি ব্যৱহাৰ কৰিব লাগে।

6. Two Trains crossing each other

Speeds = x km/hr and y km/hr
Lengths = L₁, L₂

Opposite Direction: Time = L / x + y​​

Same Direction: Time = L /  x - y ​​

Explanation: Both trains move → total length = L₁ + L₂ : দুয়োখন ট্ৰেইন গতি কৰে → মুঠ দৈৰ্ঘ্য = L₁ + L₂

Revision (Exam Trick)

• Pole/Man → L/x


• Platform → (L + P)/x


• Same direction → x − y


• Opposite direction → x + y


• Two trains → L₁ + L₂

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Train Problems – PYQs (SSC/Railway Level)

Q1. A train 200 m long crosses a pole in 10 sec. Find speed. Option: (a) 72 km/h (b) 54 km/h (c) 60 km/h (d) 80 km/h

Ans: (a) 72 km/h

Solⁿ : Speed = 200/10 = 20 m/s = 72 km/h : গতি = 200/10 = 20 m/s = 72 km/h

Q2. A train crosses a platform 300 m long in 20 sec. Train length = 200 m. Find speed. Option : (a) 72 (b) 90 (c) 80 (d) 60

Ans: (b) 90 km/h
Solⁿ : Distance = 200 + 300 = 500 m → Speed = 500/20 = 25 m/s = 90 km/h :  দূৰত্ব = 500 m → গতি = 25 m/s = 90 km/h

Q3. A train crosses a man in 8 sec and a pole in 10 sec. Length ? Option: (a) 80 (b) 100 (c) 120 (d) 160

Ans: (b) 100 m
Solⁿ : Length = speed × time = same → 100 m : দৈৰ্ঘ্য = গতি × সময় = 100 m

Q4. Two trains 100 m & 150 m cross each other in 10 sec. Opposite direction. Find relative speed. Option: (a) 25 (b) 20 (c) 30 (d) 15

Ans: (a) 25 m/s
Solⁿ : Speed = (100+150)/10 = 25 m/s :  গতি = 250/10 = 25 m/s

Q5. A train passes a man running at 6 km/h in 12 sec. Train speed = 54 km/h. Length ?

Ans: 160 m
Solⁿ : Relative speed = 54 - 6 = 48 km/h = 13.33 m/s, Length = 13.33 × 12 ≈ 160 m : আপেক্ষিক গতি = 48 km/h → দৈৰ্ঘ্য = 160 m

Q6. A train 120 m crosses another train of 180 m in 10 sec (same direction). Find speed diff.

Ans: 30 m/s
Solⁿ : Speed = (120+180)/10 = 30 m/s : গতি = 300/10 = 30 m/s

Q7. A train crosses a pole in 6 sec and platform (120 m) in 10 sec. Find length.

Ans: 180 m
Solⁿ : Speed = L/6 → (L+120)/10 → solve → L=180 :  সমীকৰণ সমাধান কৰি L = 180 m

Q8. A 150 m train at 54 km/h crosses a man. Time ?

Ans: 10 sec
Solⁿ : Speed = 15 m/s → Time = 150/15 = 10 sec : সময় = 150/15 = 10 ছেকেণ্ড

Q9. Two trains 200 m & 300 m, opposite direction, speed 54 & 36 km/h. Time ?

Ans: 20 sec
Solⁿ : Speed = 15+10 = 25 m/s → Time = 500/25 = 20 sec : সময় = 20 ছেকেণ্ড

Q10. Train crosses a man in 5 sec and another man in opposite direction in 3 sec. Ratio speed ?

Ans: 5:3
Solⁿ : Speed ∝ 1/time → 5:3 : গতি ∝ 1/সময় → 5:3

Q11. A train crosses a pole in 12 sec at 72 km/h. Length?

Ans: 240 m
Solⁿ : Speed = 20 m/s → Length = 20×12 = 240 :  দৈৰ্ঘ্য = 240 m

Q12. Train 100 m crosses platform 200 m in 15 sec. Speed?

Ans: 72 km/h
Solⁿ :  Distance = 300 → Speed = 20 m/s = 72 km/h :  গতি = 72 km/h

Q13. Two trains equal length cross in 12 sec. Speed 60 & 40 km/h. Length?

Ans: 200 m each
Solⁿ : Speed = 100 km/h = 27.78 m/s → 2L/12 → L=200 :  দৈৰ্ঘ্য = 200 m

Q14. Train crosses man in 8 sec. Speed doubled → time?

Ans: 4 sec
Solⁿ : Time inversely proportional :  সময় ∝ 1/গতি

Q15. Train crosses pole in 10 sec, platform in 30 sec. Platform length = 240 m. Train length?

Ans: 120 m
Solⁿ : Solve equations → L=120,  L = 120 m

Q16. Two trains 120 m & 180 m, opposite direction, cross in 6 sec. Speed ?

Ans: 50 m/s
Solⁿ : Speed = 300/6 = 50 m/s,  গতি = 50 m/s

Q17. Train crosses man at 5 km/h in 10 sec, train speed 65 km/h. Length ?

Ans: 166.7 m
Solⁿ : Relative speed = 60 km/h = 16.67 m/s → L = 166.7,  দৈৰ্ঘ্য ≈ 166.7 m

Q18. Train crosses bridge 100 m in 15 sec, train length 200 m. Speed ?

Ans: 72 km/h
Solⁿ : Distance = 300 → Speed = 20 m/s :  গতি = 72 km/h

Q19. Train crosses pole in 20 sec, speed 36 km/h. Length ?

Ans: 200 m
Solⁿ : Speed = 10 m/s → L = 200 :  দৈৰ্ঘ্য = 200 m

Q20. Two trains same direction, speeds 72 & 54 km/h, cross in 20 sec. Total length?

Ans: 100 m
Solⁿ : Relative speed = 18 km/h = 5 m/s → L = 5×20 = 100 :  মুঠ দৈৰ্ঘ্য = 100 m

Tips

Always convert km/h → m/s (× 5/18)
Use Relative Speed
Remember: Same direction → subtract, Opposite direction → add