📑 Topics on this page (Jump to Topic):
📌 1. Boats & Streams
📘 Formulas:
- Downstream D = b + s; upstream U = b − s
- Boat speed b = (D + U)/2; stream speed s = (D − U)/2
- Time to go d and return = d/(b + s) + d/(b − s)
⚠️ Exam Traps:
- "Speed in still water" = the boat's own speed b.
📌 2. Trains
| Crossing | Distance | Speed |
|---|---|---|
| Pole/standing man | Train length L | Train speed |
| Platform/bridge | L + P | Train speed |
| Another train (opposite) | L₁ + L₂ | S₁ + S₂ |
| Another train (same direction) | L₁ + L₂ | S₁ − S₂ |
| Moving man | L | S ± man's speed |
💡 Shortcut Trick: Do not forget to convert km/h to m/s: × 5/18. 72 km/h = 20 m/s.
📌 3. Practice MCQs
📝 Practice MCQs (prepared by SF Prep — not PYQs)
Q1. A boat goes downstream at 12 km/h and upstream at 8 km/h. The speed of the boat in still water is: Practice
Correct answer: (B)
Solution: b = (D + U)/2 = (12 + 8)/2 = 10 km/h.
Solution: b = (D + U)/2 = (12 + 8)/2 = 10 km/h.
Q2. A train running at 108 km/h crosses a pole in 9 seconds. The length of the train is: Practice
Correct answer: (C)
Solution: Speed = 108 × 5/18 = 30 m/s; length = 30 × 9 = 270 m.
Solution: Speed = 108 × 5/18 = 30 m/s; length = 30 × 9 = 270 m.
Q3. A boat's speed in still water is 18 km/h and the stream's is 6 km/h. It goes 36 km downstream and comes back. The total time taken is: Practice
Correct answer: (D)
Solution: 36/24 + 36/12 = 3/2 + 3 = 4.5 hours.
Solution: 36/24 + 36/12 = 3/2 + 3 = 4.5 hours.
Q4. In how many seconds will a 240 m long train running at 54 km/h cross a 180 m long platform? Practice
Correct answer: (A)
Solution: Distance = 240 + 180 = 420 m; speed = 15 m/s; time = 420/15 = 28 seconds.
Solution: Distance = 240 + 180 = 420 m; speed = 15 m/s; time = 420/15 = 28 seconds.
Q5. Two trains 150 m and 150 m long are running in the same direction at 54 km/h and 72 km/h. In how many seconds will they cross each other? Practice
Correct answer: (B)
Solution: Relative speed = 18 km/h = 5 m/s; time = 300/5 = 60 seconds.
Solution: Relative speed = 18 km/h = 5 m/s; time = 300/5 = 60 seconds.
Q6. A 200 m long train runs at 63 km/h. In how many seconds will it pass a man walking at 3 km/h in the same direction? Practice
Correct answer: (C)
Solution: Relative speed = 63 − 3 = 60 km/h = 50/3 m/s; time = 200/50/3 = 12 seconds.
Solution: Relative speed = 63 − 3 = 60 km/h = 50/3 m/s; time = 200/50/3 = 12 seconds.
Q7. A 200 m long train crosses a 150 m bridge in 15 seconds. The speed of the train in km/h is: Practice
Correct answer: (D)
Solution: Speed = (200 + 150)/15 = 70/3 m/s = 70/3 × 18/5 = 84 km/h.
Solution: Speed = (200 + 150)/15 = 70/3 m/s = 70/3 × 18/5 = 84 km/h.
Q8. A boatman covers 24 km upstream in 4 hours and the same distance downstream in 2 hours. His speed in still water is: Practice
Correct answer: (A)
Solution: U = 24/4 = 6, D = 24/2 = 12 → b = (12 + 6)/2 = 9 km/h.
Solution: U = 24/4 = 6, D = 24/2 = 12 → b = (12 + 6)/2 = 9 km/h.
Q9. A boat goes downstream at 16 km/h and upstream at 12 km/h. The speed of the boat in still water is: Practice
Correct answer: (B)
Solution: b = (D + U)/2 = (16 + 12)/2 = 14 km/h.
Solution: b = (D + U)/2 = (16 + 12)/2 = 14 km/h.
Q10. A train running at 108 km/h crosses a pole in 15 seconds. The length of the train is: Practice
Correct answer: (C)
Solution: Speed = 108 × 5/18 = 30 m/s; length = 30 × 15 = 450 m.
Solution: Speed = 108 × 5/18 = 30 m/s; length = 30 × 15 = 450 m.
Q11. A boat's speed in still water is 9 km/h and the stream's is 3 km/h. It goes 72 km downstream and comes back. The total time taken is: Practice
Correct answer: (D)
Solution: 72/12 + 72/6 = 6 + 12 = 18 hours.
Solution: 72/12 + 72/6 = 6 + 12 = 18 hours.
Q12. Two trains 100 m and 150 m long are running in the same direction at 45 km/h and 63 km/h. In how many seconds will they cross each other? Practice
Correct answer: (A)
Solution: Relative speed = 18 km/h = 5 m/s; time = 250/5 = 50 seconds.
Solution: Relative speed = 18 km/h = 5 m/s; time = 250/5 = 50 seconds.
Q13. A 150 m long train runs at 45 km/h. In how many seconds will it pass a man walking at 9 km/h in the same direction? Practice
Correct answer: (B)
Solution: Relative speed = 45 − 9 = 36 km/h = 10 m/s; time = 150/10 = 15 seconds.
Solution: Relative speed = 45 − 9 = 36 km/h = 10 m/s; time = 150/10 = 15 seconds.
Q14. A 200 m long train crosses a 150 m bridge in 30 seconds. The speed of the train in km/h is: Practice
Correct answer: (C)
Solution: Speed = (200 + 150)/30 = 35/3 m/s = 35/3 × 18/5 = 42 km/h.
Solution: Speed = (200 + 150)/30 = 35/3 m/s = 35/3 × 18/5 = 42 km/h.
Q15. A boat goes downstream at 20 km/h and upstream at 10 km/h. The speed of the boat in still water is: Practice
Correct answer: (D)
Solution: b = (D + U)/2 = (20 + 10)/2 = 15 km/h.
Solution: b = (D + U)/2 = (20 + 10)/2 = 15 km/h.
Q16. A train running at 45 km/h crosses a pole in 20 seconds. The length of the train is: Practice
Correct answer: (A)
Solution: Speed = 45 × 5/18 = 25/2 m/s; length = 25/2 × 20 = 250 m.
Solution: Speed = 45 × 5/18 = 25/2 m/s; length = 25/2 × 20 = 250 m.
Q17. A boat's speed in still water is 12 km/h and the stream's is 4 km/h. It goes 32 km downstream and comes back. The total time taken is: Practice
Correct answer: (B)
Solution: 32/16 + 32/8 = 2 + 4 = 6 hours.
Solution: 32/16 + 32/8 = 2 + 4 = 6 hours.
Q18. In how many seconds will a 150 m long train running at 90 km/h cross a 200 m long platform? Practice
Correct answer: (C)
Solution: Distance = 150 + 200 = 350 m; speed = 25 m/s; time = 350/25 = 14 seconds.
Solution: Distance = 150 + 200 = 350 m; speed = 25 m/s; time = 350/25 = 14 seconds.
Q19. Two trains 150 m and 150 m long are running in the same direction at 45 km/h and 63 km/h. In how many seconds will they cross each other? Practice
Correct answer: (D)
Solution: Relative speed = 18 km/h = 5 m/s; time = 300/5 = 60 seconds.
Solution: Relative speed = 18 km/h = 5 m/s; time = 300/5 = 60 seconds.
Q20. A 125 m long train runs at 63 km/h. In how many seconds will it pass a man walking at 5 km/h in the same direction? Practice
Correct answer: (A)
Solution: Relative speed = 63 − 5 = 58 km/h = 145/9 m/s; time = 125/145/9 = 7.76 seconds.
Solution: Relative speed = 63 − 5 = 58 km/h = 145/9 m/s; time = 125/145/9 = 7.76 seconds.