Time, Speed and Distance MCQs with Solutions for CUET, CLAT & IPMAT
Time, Speed and Distance – Complete Guide with Typewise Examples for CUET, CLAT & IPMAT
Time, Speed and Distance is one of the most important chapters in Quantitative Aptitude for competitive exams like CUET, CLAT and IPMAT. Every year multiple questions are asked from this topic because it tests calculation speed, conceptual clarity, and logical reasoning.
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In this detailed guide, we will cover:
- Basic Concepts & Formulas
- Unit Conversions
- Typewise Questions with Examples
- Shortcut Tricks
- Exam Preparation Strategy
If you master this chapter, you can easily score full marks in this section.
1. Basic Concept of Time, Speed and Distance
The relationship between time, speed, and distance is very simple.
Fundamental Formula:
Speed = Distance / Time
Distance = Speed × Time
Time = Distance / Speed
These three formulas are the base of the entire chapter.
2. Important Unit Conversions (Very Important for Exams)
1 km/hr = 5/18 m/s
1 m/s = 18/5 km/hr
💡 Trick:
To convert km/hr into m/s → Multiply by 5/18
To convert m/s into km/hr → Multiply by 18/5
Example:
72 km/hr = 72 × 5/18 = 20 m/s
3. Type 1 – Basic Formula Based Questions
Example 1:
A car travels 180 km in 3 hours. Find its speed.
Solution:
Speed = Distance / Time
= 180 / 3
= 60 km/hr
✔ Direct formula application.
4. Type 2 – Average Speed Questions
Average speed is often misunderstood.
Case 1: Equal Distance
Average Speed = (2 × S1 × S2) / (S1 + S2)
Example:
A man travels the same distance at 40 km/hr and 60 km/hr. Find average speed.
Average Speed = (2 × 40 × 60) / (40 + 60)
= 4800 / 100
= 48 km/hr
✔ Important for CUET and IPMAT.
Case 2: Equal Time
Average Speed = (S1 + S2) / 2
Example:
A person travels 2 hours at 50 km/hr and 2 hours at 70 km/hr.
Average Speed = (50 + 70) / 2
= 60 km/hr
5. Type 3 – Relative Speed Questions
Relative speed is used when two objects are moving.
Same Direction:
Relative Speed = S1 − S2
Opposite Direction:
Relative Speed = S1 + S2
Example:
Two cars move in opposite direction at 60 km/hr and 40 km/hr.
Relative Speed = 60 + 40 = 100 km/hr
If distance between them is 200 km:
Time = Distance / Relative Speed
= 200 / 100
= 2 hours
✔ Very common in CLAT and IPMAT.
6. Type 4 – Trains Problems
Train questions are frequently asked.
Case 1: Train crossing a pole
Time = Length of Train / Speed
Example:
A train 180 m long runs at 54 km/hr. Find time to cross a pole.
Step 1: Convert speed
54 × 5/18 = 15 m/s
Step 2:
Time = 180 / 15 = 12 seconds
Case 2: Train crossing a platform
Time = (Length of Train + Length of Platform) / Speed
Case 3: Two trains crossing each other
Use Relative Speed
Time = (Sum of Lengths) / Relative Speed
7. Type 5 – Boats and Streams
Very important for competitive exams.
Let:
Speed of boat in still water = B
Speed of stream = S
Downstream Speed = B + S
Upstream Speed = B − S
Example:
Downstream speed = 20 km/hr
Upstream speed = 12 km/hr
Boat Speed = (20 + 12) / 2 = 16 km/hr
Stream Speed = (20 − 12) / 2 = 4 km/hr
✔ Frequently asked in IPMAT.
8. Type 6 – Percentage Change in Speed
If speed increases by x%:
Time decreases by
x / (100 + x) × 100
If speed decreases by x%:
Time increases by
x / (100 − x) × 100
Example:
Speed increases by 25%.
Time decreases by
25 / 125 × 100
= 20%
✔ Shortcut-based question type.
9. Type 7 – Ratio Method
Speed and Time are inversely proportional.
If speed ratio = 2 : 3
Then time ratio = 3 : 2
Example:
If A travels at speed ratio 4:5 and takes 20 minutes, find time taken by second person.
Time ratio = 5:4
If first takes 20 minutes,
Second = (20 × 4) / 5
= 16 minutes
10. Most Important Question Types for CUET, CLAT & IPMAT
✔ Direct Formula Questions
✔ Average Speed
✔ Trains
✔ Boats & Streams
✔ Relative Speed
✔ Percentage Change
✔ Meeting Point Problems
11. Preparation Strategy for Exams
- Learn formulas thoroughly
- Practice 50–100 questions
- Focus on unit conversion
- Improve calculation speed
- Solve previous year papers
Time, Speed and Distance is a scoring topic. With regular practice, you can solve most questions within 30 seconds.
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Time, Speed and Distance – 30 MCQs with Detailed Explanation
1. A car travels 150 km in 3 hours. Find its speed.
A) 45 km/hr
B) 50 km/hr
C) 55 km/hr
D) 60 km/hr
Answer: B) 50 km/hr
Explanation:
Speed = Distance / Time
= 150 / 3 = 50 km/hr
2. A train 200 m long runs at 54 km/hr. Time to cross a pole?
A) 12 sec
B) 13 sec
C) 14 sec
D) 15 sec
Answer: B) 13 sec
Explanation:
54 × 5/18 = 15 m/s
Time = 200 / 15 = 13.33 ≈ 13 sec
3. A person travels same distance at 40 km/hr and 60 km/hr. Average speed?
A) 48
B) 50
C) 52
D) 45
Answer: A) 48 km/hr
Explanation:
Average speed (equal distance)
= (2×40×60)/(40+60)
= 4800/100 = 48
4. Two cars move in opposite direction at 70 and 50 km/hr. Relative speed?
A) 20
B) 100
C) 120
D) 110
Answer: C) 120 km/hr
Explanation:
Opposite direction → Add speeds
70 + 50 = 120
5. 72 km/hr in m/s?
A) 18
B) 20
C) 22
D) 25
Answer: B) 20 m/s
Explanation:
72 × 5/18 = 20 m/s
6. Downstream speed = 18 km/hr, Upstream = 10 km/hr. Boat speed?
A) 12
B) 14
C) 16
D) 15
Answer: B) 14 km/hr
Explanation:
Boat speed = (18+10)/2 = 14
7. Stream speed from above?
A) 4
B) 5
C) 3
D) 6
Answer: A) 4 km/hr
Explanation:
Stream speed = (18−10)/2 = 4
8. Speed increases by 25%. Time decreases by?
A) 20%
B) 25%
C) 15%
D) 18%
Answer: A) 20%
Explanation:
25/(100+25) ×100 = 20%
9. A train 120 m long crosses 180 m platform at 10 m/s. Time?
A) 25 sec
B) 30 sec
C) 35 sec
D) 28 sec
Answer: B) 30 sec
Explanation:
Total length = 120+180 = 300
Time = 300/10 = 30 sec
10. Two trains 150 m & 100 m move opposite at 60 & 40 km/hr. Time?
A) 9 sec
B) 10 sec
C) 12 sec
D) 8 sec
Answer: A) 9 sec
Explanation:
Relative speed = 100 km/hr
= 27.78 m/s
Total length = 250
Time = 250/27.78 ≈ 9 sec
11. 1 m/s equals?
A) 5/18 km/hr
B) 18/5 km/hr
C) 20/5 km/hr
D) 15/5 km/hr
Answer: B) 18/5 km/hr
12. Distance covered in 4 hours at 60 km/hr?
A) 200
B) 240
C) 220
D) 260
Answer: B) 240 km
Explanation:
Distance = Speed × Time
= 60×4 = 240
13. Speed ratio 3:4. Time ratio?
A) 3:4
B) 4:3
C) 9:16
D) 16:9
Answer: B) 4:3
Explanation:
Speed & Time inversely proportional
14. A man walks 5 km/hr for 2 hrs. Distance?
A) 12
B) 10
C) 8
D) 9
Answer: B) 10 km
15. Speed decreases by 20%. Time increases by?
A) 20%
B) 25%
C) 22%
D) 18%
Answer: B) 25%
Explanation:
20/(100−20)×100 = 25%
16. 90 km/hr into m/s?
A) 20
B) 22
C) 25
D) 18
Answer: C) 25 m/s
17. Distance 300 km, speed 75 km/hr. Time?
A) 5
B) 4
C) 6
D) 3
Answer: B) 4 hours
18. Two persons move same direction at 60 & 45 km/hr. Relative speed?
A) 15
B) 105
C) 25
D) 20
Answer: A) 15 km/hr
19. A 100 m train at 20 m/s crosses pole. Time?
A) 4
B) 5
C) 6
D) 3
Answer: B) 5 sec
20. Equal time speeds 30 & 50. Average speed?
A) 40
B) 38
C) 42
D) 45
Answer: A) 40 km/hr
21. 54 km/hr into m/s?
A) 14
B) 15
C) 16
D) 13
Answer: B) 15 m/s
22. Distance 180 km, time 4 hr. Speed?
A) 45
B) 50
C) 40
D) 55
Answer: A) 45 km/hr
23. Downstream 24, upstream 16. Stream speed?
A) 3
B) 4
C) 5
D) 6
Answer: B) 4 km/hr
24. Boat speed in above?
A) 20
B) 18
C) 16
D) 22
Answer: A) 20 km/hr
25. 36 km/hr in m/s?
A) 10
B) 12
C) 8
D) 15
Answer: A) 10 m/s
26. 15 m/s into km/hr?
A) 52
B) 54
C) 56
D) 50
Answer: B) 54 km/hr
27. Speed doubles. Time becomes?
A) Half
B) Double
C) Same
D) Triple
Answer: A) Half
28. Distance 400 km, speed 80 km/hr. Time?
A) 4
B) 6
C) 5
D) 3
Answer: C) 5 hours
29. Train 150 m, speed 30 m/s crosses 150 m bridge. Time?
A) 10
B) 8
C) 12
D) 6
Answer: A) 10 sec
Explanation:
Total length = 150+150 = 300
Time = 300/30 = 10 sec
30. A person covers half distance at 40 km/hr and remaining at 60 km/hr. Average speed?
A) 50
B) 48
C) 52
D) 45
Answer: B) 48 km/hr
Explanation:
Equal distance formula
= (2×40×60)/(40+60)
= 48
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