Time Speed and Distance Practice Set 1
Time, Speed and Distance is one of the most important Maths topics for Banking, SSC, Railway, and other competitive exams. To solve questions from this chapter quickly and accurately, it is essential to understand not only the basic formulas but also smart shortcuts and calculation techniques.
This practice set contains 10 important Time, Speed and Distance questions covering a variety of concepts, including Early & Late Arrival, Trains, Races, Circular Tracks, Boats & Streams, Average Speed, Stoppage Time, and Schedule Recovery.
If you are preparing for Banking and other competitive exams, you can also practice our Percentage Questions, Ratio and Proportion Questions, and Profit and Loss Questions practice sets.
Table of Contents
Q1. Early & Late Concept
Question
A person travels from his home to his office by car. If he drives at 30 km/h, he reaches the office 12 minutes late. If he drives at 40 km/h, he reaches the office 3 minutes early. What is the distance (in km) between his home and his office?
Shortcut Method
Difference in arrival time:
12 + 3 = 15 minutes
15 minutes = 1/4 hour
Let distance = D km.
Time difference:
D/30 − D/40 = 1/4
D × (1/30 − 1/40) = 1/4
D/120 = 1/4
D = 30 km
✅ Answer
30 km
Q2. Train & Relative Speed
Question
A train of length 200 m runs at a uniform speed of 54 km/h. How many seconds will the train take to completely pass a man running at 18 km/h in the direction opposite to that of the train?
Shortcut Method
Since the man is running in the opposite direction, relative speed will be added.
Relative speed:
54 + 18 = 72 km/h
Convert into m/s:
72 × 5/18 = 20 m/s
Time = Distance / Speed
Time = 200/20
Time = 10 seconds
✅ Answer
10 seconds
Q3. Race with Head Start
Question
In a 1000 m race, Runner A gives Runner B a head start of 100 m and still beats him by 100 seconds. If Runner A runs at a speed of 5 m/s, find the speed of Runner B (in m/s).
Shortcut Method
Runner A covers:
1000 m
Time taken by A:
1000/5 = 200 seconds
Runner B has a 100 m head start, so B has to cover:
1000 − 100 = 900 m
A beats B by 100 seconds.
Therefore, B’s time:
200 + 100 = 300 seconds
B’s speed:
900/300 = 3 m/s
✅ Answer
3 m/s
Q4. Circular Track
Question
Two runners P and Q start running simultaneously from the same point on a 600 m circular track in the same direction. The speed of P is 18 km/h and the speed of Q is 24 km/h. After how many seconds from the start will they meet together at the starting point for the first time?
Shortcut Method
Convert speeds into m/s.
P:
18 × 5/18 = 5 m/s
Q:
24 × 5/18 = 20/3 m/s
Time taken by P to complete one round:
600/5 = 120 seconds
Time taken by Q:
600/(20/3) = 90 seconds
They will both be at the starting point together after the LCM of 120 and 90.
LCM(120, 90) = 360 seconds
✅ Answer
360 seconds
Q5. Boats & Streams
Question
A motorboat travels 36 km downstream in a river and returns upstream to the starting point. The return upstream journey takes 1 hour 36 minutes longer than the downstream journey. If the speed of the river current is 3 km/h, find the speed of the motorboat in still water (in km/h).
Shortcut Method
Let the speed of the motorboat in still water be v km/h.
Downstream speed:
v + 3
Upstream speed:
v − 3
Difference in time:
1 hour 36 minutes = 1.6 hours
Therefore:
36/(v − 3) − 36/(v + 3) = 1.6
36 × 6 / (v² − 9) = 1.6
216/(v² − 9) = 1.6
v² − 9 = 135
v² = 144
v = 12 km/h
✅ Answer
12 km/h
Q6. Two Trains
Question
Two railway stations P and Q are 340 km apart on a straight track. Train A leaves station P towards Q at 6:00 AM at a constant speed of 40 km/h. Train B leaves station Q towards P at 7:00 AM at a constant speed of 60 km/h. At what distance (in km) from station P will the two trains cross each other?
Shortcut Method
From 6:00 AM to 7:00 AM, Train A travels:
40 × 1 = 40 km
Remaining distance:
340 − 40 = 300 km
Now both trains move towards each other.
Combined speed:
40 + 60 = 100 km/h
Time to meet:
300/100 = 3 hours
Distance travelled by Train A after 7:00 AM:
40 × 3 = 120 km
Therefore, distance from P:
40 + 120 = 160 km
✅ Answer
160 km
Q7. Stoppage Time
Question
A bus travels a total distance of 240 km between two cities. While moving, it maintains a uniform speed of 60 km/h. Due to scheduled halts at intermediate stations, the total journey takes 5 hours. How many minutes in total did the bus spend halting at the stations?
Shortcut Method
Time required while the bus is actually moving:
240/60 = 4 hours
Total journey time = 5 hours
Stoppage time:
5 − 4 = 1 hour
Convert into minutes:
1 × 60 = 60 minutes
✅ Answer
60 minutes
Q8. Average Speed
Question
A motorist covers the first one-third of a journey at 20 km/h, the second one-third at 30 km/h, and the remaining one-third at 60 km/h. What is the average speed of the motorist for the entire journey?
Shortcut Method
When equal distances are covered at different speeds:
Average Speed = Total Distance / Total Time
Assume total distance = 3 units.
Time taken:
First part = 1/20 hour
Second part = 1/30 hour
Third part = 1/60 hour
Total time:
1/20 + 1/30 + 1/60
= 3/60 + 2/60 + 1/60
= 6/60
= 1/10 hour
Average speed:
3 ÷ 1/10 = 30 km/h
✅ Answer
30 km/h
Q9. Breakdown & Schedule Recovery
Question
A car is scheduled to complete a journey at a uniform speed of 40 km/h. After travelling for 2 hours, the car breaks down and remains stopped for 30 minutes for repairs. The driver then increases his speed to 60 km/h for the remaining distance and reaches the destination exactly at the scheduled time. What is the total distance of the journey (in km)?
Shortcut Method
Let total distance = D km.
Scheduled time:
D/40
Actual time:
First 2 hours + 0.5 hour stoppage + remaining distance at 60 km/h
Remaining distance:
D − 40 × 2 = D − 80
Therefore:
D/40 = 2 + 0.5 + (D − 80)/60
Solving:
D/40 = 2.5 + (D − 80)/60
D = 140 km
✅ Answer
140 km
Q10. Post-Meeting Time Concept
Question
Two trains start at the exact same instant from stations X and Y towards each other. After passing each other, the first train takes 4 hours to reach station Y, while the second train takes 9 hours to reach station X. If the speed of the first train is 60 km/h, find the total distance between stations X and Y (in km).
Shortcut Method
First train takes 4 hours after meeting to reach Y.
Distance travelled by first train after meeting:
60 × 4 = 240 km
This 240 km is the distance covered by the second train before the meeting point.
Let speed of second train = v km/h.
Using the post-meeting relation:
Distance covered by first train before meeting / Distance covered by second train before meeting
= Speed of second train / Speed of first train
The first train’s distance before meeting is equal to the distance covered by the second train after meeting.
Second train takes 9 hours after meeting:
Distance = 9v
Therefore:
9v/240 = 60/v
9v² = 14400
v² = 1600
v = 40 km/h
Now:
Distance covered by first train before meeting:
9 × 40 = 360 km
Distance covered by second train before meeting:
240 km
Total distance:
360 + 240 = 600 km
✅ Answer
600 km
🎯 Practice Set Summary
| Q. No. | Concept | Answer |
|---|---|---|
| Q1 | Early & Late | 30 km |
| Q2 | Train & Relative Speed | 10 seconds |
| Q3 | Race with Head Start | 3 m/s |
| Q4 | Circular Track | 360 seconds |
| Q5 | Boats & Streams | 12 km/h |
| Q6 | Two Trains | 160 km |
| Q7 | Stoppage Time | 60 minutes |
| Q8 | Average Speed | 30 km/h |
| Q9 | Breakdown & Schedule Recovery | 140 km |
| Q10 | Post-Meeting Time Concept | 600 km |
🧠 Shortcut Trick of the Day
Equal Distance Average Speed
When equal distances are covered at different speeds, do not use the simple average.
Average Speed = Total Distance / Total Time
For three equal distances covered at speeds a, b, and c:
Average Speed = 3abc / (ab + bc + ca)
This shortcut can make calculations much faster in competitive exams. ⚡
🔥 Challenge Question
A man covers a certain distance at 40 km/h and reaches 15 minutes late. If he increases his speed to 50 km/h, he reaches 9 minutes early. Find the distance he has to travel.
Try solving it without looking for the answer! 🧠
❓ Frequently Asked Questions
What is Time, Speed and Distance?
Time, Speed & Distance is an important quantitative aptitude topic based on the relationship between distance, speed and time.
What is the basic formula of Time, Speed and Distance?
Distance = Speed × Time
Speed = Distance ÷ Time
Time = Distance ÷ Speed
Is Time, Speed and Distance important for banking exams?
Yes. Questions from trains, boats & streams, races, average speed, relative speed and time-based situations are commonly useful for banking and other competitive-exam preparation.
How can I improve my speed in Time, Speed and Distance questions?
Focus on unit conversion, relative speed, ratio-based shortcuts and repeated practice of different concepts rather than solving the same pattern repeatedly.
🚀 Final Words
Time, Speed and Distance questions become much easier when you understand the concept instead of memorising formulas.
Practice each question yourself first, then check the shortcut method. With regular practice, you can improve both calculation speed and accuracy. 💯
👉 Keep practising and stay connected with BrainQuro for more competitive exam Maths practice sets.
All the best for your preparation! 📚🔥
