📑 Topics on this page (Jump to Topic):
📌 1. Basic Formulas
📘 Formulas:
- Distance = speed × time
- 1 km/h = 5/18 m/s; 1 m/s = 18/5 km/h
- Equal distances at speeds x, y → average speed = 2xy/(x + y)
- For fixed distance speed ∝ 1/time; speed ratio a:b → time ratio b:a
| m/s | |
|---|---|
| 18 | 5 |
| 36 | 10 |
| 54 | 15 |
| 72 | 20 |
| 90 | 25 |
| 108 | 30 |
📌 2. Relative Speed & Special Cases
- Same direction: relative speed = x − y; opposite: x + y.
- Late/early: t₁ late at speed x, t₂ early at y → distance = xy(t₁ + t₂)/(y − x).
- Walking at a/b of usual speed makes him t min late → usual time = a·t/(b − a).
⚠️ Exam Traps:
- Match the units — never mix metres with km/h.
- Average speed ≠ simple average of speeds.
📌 3. Practice MCQs
📝 Practice MCQs (prepared by SF Prep — not PYQs)
Q1. 5 m/s is equal to how many km/h? Practice
Correct answer: (B)
Solution: 5 × 18/5 = 18 km/h.
Solution: 5 × 18/5 = 18 km/h.
Q2. A car travels at 72 km/h for 4 hours. The distance covered is: Practice
Correct answer: (C)
Solution: Distance = 72 × 4 = 288 km.
Solution: Distance = 72 × 4 = 288 km.
Q3. A man covers three equal distances at 10, 20 and 60 km/h. His average speed is: Practice
Correct answer: (D)
Solution: Average = 3/(1/10 + 1/20 + 1/60) = 18 km/h.
Solution: Average = 3/(1/10 + 1/20 + 1/60) = 18 km/h.
Q4. Two towns are 240 km apart. Two cars start at the same time towards each other at 30 km/h and 50 km/h. After how many hours will they meet? Practice
Correct answer: (A)
Solution: Opposite directions → relative speed = 30 + 50 = 80; time = 240/80 = 3 hours.
Solution: Opposite directions → relative speed = 30 + 50 = 80; time = 240/80 = 3 hours.
Q5. A thief runs at 10 km/h. 2 hour(s) later a policeman starts chasing him at 12 km/h. In how many hours will the policeman catch him? Practice
Correct answer: (B)
Solution: Thief's lead = 10 × 2 = 20 km; relative speed = 12 − 10 = 2; time = 20/2 = 10 hours.
Solution: Thief's lead = 10 × 2 = 20 km; relative speed = 12 − 10 = 2; time = 20/2 = 10 hours.
Q6. A student walking at 4 km/h reaches school 10 minutes late; at 6 km/h he reaches 10 minutes early. The distance to school is: Practice
Correct answer: (C)
Solution: d = xy(t₁ + t₂)/(y − x) = 4×6×(20/60)/2 = 4 km.
Solution: d = xy(t₁ + t₂)/(y − x) = 4×6×(20/60)/2 = 4 km.
Q7. Walking at 4/5 of his usual speed, a man reaches office 15 minutes late. His usual time is: Practice
Correct answer: (D)
Solution: Speed 4/5 → time 5/4 times; extra (5−4)/4 × T = 15 → T = 60 minutes.
Solution: Speed 4/5 → time 5/4 times; extra (5−4)/4 × T = 15 → T = 60 minutes.
Q8. The speeds of A and B are in the ratio 4 : 5. If A covers a distance in 40 minutes, how long will B take for the same distance? Practice
Correct answer: (A)
Solution: Time ∝ 1/speed → B = 40 × 4/5 = 32 minutes.
Solution: Time ∝ 1/speed → B = 40 × 4/5 = 32 minutes.
Q9. A car travels at 60 km/h for 2.5 hours. The distance covered is: Practice
Correct answer: (B)
Solution: Distance = 60 × 2.5 = 150 km.
Solution: Distance = 60 × 2.5 = 150 km.
Q10. A man covers three equal distances at 15, 30 and 60 km/h. His average speed is: Practice
Correct answer: (C)
Solution: Average = 3/(1/15 + 1/30 + 1/60) = 25.71 km/h.
Solution: Average = 3/(1/15 + 1/30 + 1/60) = 25.71 km/h.
Q11. Two towns are 200 km apart. Two cars start at the same time towards each other at 45 km/h and 55 km/h. After how many hours will they meet? Practice
Correct answer: (D)
Solution: Opposite directions → relative speed = 45 + 55 = 100; time = 200/100 = 2 hours.
Solution: Opposite directions → relative speed = 45 + 55 = 100; time = 200/100 = 2 hours.
Q12. A thief runs at 36 km/h. 3 hour(s) later a policeman starts chasing him at 45 km/h. In how many hours will the policeman catch him? Practice
Correct answer: (A)
Solution: Thief's lead = 36 × 3 = 108 km; relative speed = 45 − 36 = 9; time = 108/9 = 12 hours.
Solution: Thief's lead = 36 × 3 = 108 km; relative speed = 45 − 36 = 9; time = 108/9 = 12 hours.
Q13. A student walking at 3 km/h reaches school 12 minutes late; at 4 km/h he reaches 8 minutes early. The distance to school is: Practice
Correct answer: (B)
Solution: d = xy(t₁ + t₂)/(y − x) = 3×4×(20/60)/1 = 4 km.
Solution: d = xy(t₁ + t₂)/(y − x) = 3×4×(20/60)/1 = 4 km.
Q14. Walking at 3/4 of his usual speed, a man reaches office 10 minutes late. His usual time is: Practice
Correct answer: (C)
Solution: Speed 3/4 → time 4/3 times; extra (4−3)/3 × T = 10 → T = 30 minutes.
Solution: Speed 3/4 → time 4/3 times; extra (4−3)/3 × T = 10 → T = 30 minutes.
Q15. The speeds of A and B are in the ratio 2 : 3. If A covers a distance in 20 minutes, how long will B take for the same distance? Practice
Correct answer: (D)
Solution: Time ∝ 1/speed → B = 20 × 2/3 = 13.33 minutes.
Solution: Time ∝ 1/speed → B = 20 × 2/3 = 13.33 minutes.
Q16. 25 m/s is equal to how many km/h? Practice
Correct answer: (A)
Solution: 25 × 18/5 = 90 km/h.
Solution: 25 × 18/5 = 90 km/h.
Q17. A man covers three equal distances at 20, 30 and 60 km/h. His average speed is: Practice
Correct answer: (B)
Solution: Average = 3/(1/20 + 1/30 + 1/60) = 30 km/h.
Solution: Average = 3/(1/20 + 1/30 + 1/60) = 30 km/h.
Q18. Two towns are 420 km apart. Two cars start at the same time towards each other at 35 km/h and 45 km/h. After how many hours will they meet? Practice
Correct answer: (C)
Solution: Opposite directions → relative speed = 35 + 45 = 80; time = 420/80 = 5.25 hours.
Solution: Opposite directions → relative speed = 35 + 45 = 80; time = 420/80 = 5.25 hours.
Q19. A thief runs at 20 km/h. 1 hour(s) later a policeman starts chasing him at 25 km/h. In how many hours will the policeman catch him? Practice
Correct answer: (D)
Solution: Thief's lead = 20 × 1 = 20 km; relative speed = 25 − 20 = 5; time = 20/5 = 4 hours.
Solution: Thief's lead = 20 × 1 = 20 km; relative speed = 25 − 20 = 5; time = 20/5 = 4 hours.
Q20. A student walking at 6 km/h reaches school 15 minutes late; at 8 km/h he reaches 5 minutes early. The distance to school is: Practice
Correct answer: (A)
Solution: d = xy(t₁ + t₂)/(y − x) = 6×8×(20/60)/2 = 8 km.
Solution: d = xy(t₁ + t₂)/(y − x) = 6×8×(20/60)/2 = 8 km.