# CAT Questions | CAT Arithmetic

###### CAT Quantitative Aptitude | CAT Speed time distance & Races

A CAT Speed time distance & Races is one of the most commonly tested topics in CAT exam. Questions from CAT speed time distance and Races have appeared consistently in the CAT exam for the last several years. Speed Time Distance and Races is a very interesting topic, as it is relatable in real life scenarios. CAT exam also does not only check for formulaic knowledge in this idea, but also for strang fundamentals and application of the concepts involved. Races as an idea is built on CAT Speed time distance, Ratio proportions. One can usually expect 3-4 questions from these ideas in the CAT exam. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

1. #### CAT Races: Circular Races

Two friends A and B simultaneously start running around a circular track . They run in the same direction. A travels at 6 m/s and B runs at b m/s. If they cross each other at exactly two points on the circular track and b is a natural number less than 30, how many values can b take?

1. 3
2. 4
3. 7
4. 5

2. #### CAT Races: Races in a square

Consider a square ABCD. EFGH is another square obtained by joining the midpoints of the sides of the square ABCD where E, F , G amd H are the midpoints of AB, BC, CD and DA respectively. Lakshman and Kanika start from points B and D respectively at speeds ‘l’ kmph and ‘k’ kmph respectively and travel towards each other along the sides of the square ABCD. Jagadeesh starts from Point E and travels along the Square EFGH in the anti-clockwise direction at ‘j’ kmph. Lakshman and Kanika meet for the second time at H where Jagadeesh also meets them for the first time. If l : k : j is 1: 3 : 5√2 then the distance travelled by Jagadeesh is

1. 7.5 × √2 times the side of the square ABCD
2. 7.5 × √2 times the side of the square EFGH
3. 7.5 times the side of the square ABCD
4. 7.5 times the side of the square EFGH

3. #### CAT Time Speed and Distance: Cars

Three cars leave A for B in equal time intervals. They reach B simultaneously and then leave for Point C which is 240 km away from B. The first car arrives at C an hour after the second car. The third car, having reached C, immediately turns back and heads towards B. The first and the third car meet a point that is 80 km away from C. What is the difference between the speed of the first and the third car?

1. 60 kmph
2. 20 kmph
3. 40 kmph
4. 80 kmph

4. #### CAT Races: Circular Races

Three friends A, B and C decide to run around a circular track. They start at the same time and run in the same direction. A is the quickest and when A finishes a lap, it is seen that C is as much behind B as B is behind A. When A completes 3 laps, C is the exact same position on the circular track as B was when A finished 1 lap. Find the ratio of the speeds of A, B and C?

1. 5 : 4 : 2
2. 4 : 3 : 2
3. 5 : 4 : 3
4. 3 : 2 : 1

5. #### CAT Time Speed and Distance: Speed Change

Mr. X decides to travel from Delhi to Gurgaon at a uniform speed and decides to reach Gurgaon after T hr. After 30 km, there is some engine malfunction and the speed of the car becomes (4/5)th of the original speed. So, he travels the rest of the distance at a constant speed (4/5)th of the original speed and reaches Gurgaon 45 minutes late. Had the same thing happened after he travelled 48 km, he would have reached only 36 minutes late. What is the distance between Delhi and Gurgaon?

1. 90 km
2. 120 km
3. 20 km
4. 40 km

6. #### CAT Time Speed and Distance: Meeting point

Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?

1. 60
2. 36
3. 24
4. 48

7. #### CAT Races: Race in a pool

A swimming pool is of length 50 m. A and B enter a 300 m race starting simultaneously at one end of the pool at speeds of 3 m/s and 5 m/s. How many times will they meet while travelling in opposite directions before B completes the race?

1. Twice
2. Thrice
3. Once
4. 5 Times

8. #### CAT Time Speed and Distance: Relative Speed

Car A trails car B by 50 meters. Car B travels at 45km/hr. Car C travels from the opposite direction at 54km/hr. Car C is at a distance of 220 meters from Car B. If car A decides to overtake Car B before cars B and C cross each other, what is the minimum speed at which car A must travel?

1. 36 km/hr
2. 45 km/hr
3. 67.5 km/hr
4. 18 km/hr

9. #### CAT Races: Circular Races

A and B stand at distinct points of a circular race track of length 120m. They run at speeds of a m/s and b m/s respectively. They meet for the first time 16 seconds after they start the race and for the second time 40 seconds from the time they start the race. Now, if B had started in the opposite direction to the one he had originally started, they would have meet for the first time after 40 seconds. If B is quicker than A, find B’s speed.

1. 3 m/s
2. 4 m/s
3. 5 m/s
4. 8 m/s

10. #### CAT Time Speed and Distance: Boats and Streams

City A to City B is a downstream journey on a stream which flows at a speed of 5km/hr. Boats P and Q run a shuttle service between the two cities that are 300 kms apart. Boat P, which starts from City A has a still-water speed of 25km/hr, while boat Q, which starts from city B at the same time has a still-water speed of 15km/hr. When will the two boats meet for the first time? (this part is easy) When and where will they meet for the second time?

1. 7.5 hours and 15 hours
2. 7.5 hours and 18 hours
3. 8 hours and 18 hours
4. 7.5 hours and 20 hours

11. #### CAT Time Speed and Distance: Relative Speed

Cities M and N are 600km apart. Bus A starts from city M towards N at 9AM and bus B starts from city N towards M at the same time. Bus A travels the first one-third of the distance at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmph. Bus B travels the first one-third of the total time taken at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmph. When and where will the two buses cross each other?

1. 300 kms from M
2. 280 kms from M
3. 305 kms from M
4. 295 kms from M

12. #### CAT Time Speed and Distance: Relative Speed

A car of length 4m wants to overtake a trailer truck of length 20m travelling at 36km/hr within 10 seconds. At what speed should the car travel?

1. 12 m/s
2. 14.8 m/s
3. 12.4 m/s
4. 7.6 m/s

13. #### CAT Time Speed and Distance: Relative Speed

Train A travelling at 63 kmph takes 27 to sec to cross Train B when travelling in opposite direction whereas it takes 162 seconds to overtake it when travelling in the same direction. If the length of train B is 500 meters, find the length of Train A.

1. 400 m
2. 810 m
3. 500 m
4. 310 m

14. #### CAT Races: Dead Heat

P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the next 8 seconds, 6 m/s for the next 8 and so on. Q cycles at a constant speed of 6.5 m/s throughout. If P and Q had to cycle for a 436 m race, how much lead in terms of distance, can P give Q and still finish at the same time as Q?

1. 43.4 m
2. 56.6 m
3. 46 m
4. P cannot give a lead as Q is always ahead of P

15. #### CAT Time Speed and Distance: Ratio of speeds

A bus starts from a bus stop P and goes to another bus stop Q. In between P and Q, there is a bridge AB of certain length. A man is standing at a point C on the bridge such that AC:CB = 1:3. When the bus starts at P and if the man starts running towards A, he will meet the bus at A. But if he runs towards B, the bus will overtake him at B. Which of the following is true?

1. Bus travels 3x times faster than the man
2. Bus travels 2x times faster than the man
3. The bus and the man travel at the same speed
4. 4x the speed of the man is equal to 3x the speed of the bus

16. #### CAT Time Speed and Distance: Fuel consumption

Ramesh takes 6.5 hours to go from city A to city B at 3 different speeds 30 kmph, 45 kmph, and 60 kmph covering the same distance with each speed. The respective mileages per liter of fuel are 11 km, 14 km and 18 km for the above speeds. Ramesh's friend Arun is an efficient driver and wants to minimise his friend's car's fuel consumption. So he decides to drive Ramesh's car one day from city A to city B. How much fuel will he be able to save?

1. 4.2 liters
2. 4.5 liters
3. 0.7 liters
4. 0.3 liters

17. #### CAT Races: Speed in a race

Amar, Akbar and Antony decide to have a 'x' m race. Antony completes the race 14 m ahead of Amar. Akbar finishes 20 m ahead of Antony and 32 m ahead of Amar. What is Amar’s speed?

1. 9/10th of Antony's speed
2. 5/8th of Akbar's speed
3. 14/15th of Antony's speed
4. 10/7th of Akbar's speed

18. #### CAT Time Speed and Distance: Distance between two points

Tom, Jerry and Bill start from point A at the same time in their cars to go to B. Tom reaches point B first and turns back and meets Jerry at a distance of 9 miles from B. When Jerry reaches B, he too turns back and meets Bill at a distance of 7 miles from B. If 3 times the speed with which Tom drives his car is equal to 5 times Bill’s speed, what could be the distance between the points A and B?

1. 40 miles
2. 24 miles
3. 31 miles
4. 63 miles

19. #### CAT Time Speed and Distance: Starting Time

Kumar started from Chennai at x hrs y minutes and travelled to Vellore. He reached Vellore at y hrs z minutes. If the total travel time was z hrs and x minutes, his starting time in Chennai could have been ______ (Assume clock format to be 0 to 24 hrs).

1. 02:08 hrs
2. 13:03 hrs
3. 00:02 hrs
4. 12:01 hrs

20. #### CAT Time Speed and Distance: Increasing speed

When Sourav increases his speed from 20 Km/hr to 25 Km/hr, he takes one hour less than the usual time to cover a certain distance. What is the distance usually covered by him?

1. 125 km
2. 100 km
3. 80 km
4. 120 km

21. #### CAT Time Speed and Distance: Increasing speed

Distance between the office and the home of Alok is 100 Km. One day, he was late by an hour than the normal time to leave for the office, so he increased his speed by 5 Km/hr and reached office at the normal time. What is the changed speed of Alok?

1. 25 Km/hr
2. 20 Km/hr
3. 16 Km/hr
4. 50 Km/hr

22. #### CAT Time Speed and Distance: Increasing speed

Akash when going slower by 15 Km/hr, reaches late by 45 hours. If he goes faster by 10 Km/hr from his original speed, he reaches early by 20 hours than the original time. Find the distance he covers.

1. 8750 Km
2. 9750 Km
3. 1000 Km
4. 3750 Km

23. #### CAT Time Speed and Distance: Increasing speed

Raj was travelling to his hometown from Mumbai. He met with a small accident 80 Km away from Mumbai and continued the remaining journey at 4/5 of his original speed and reached his hometown 1 hour and 24 minutes late. If he had met with the accident 40 Km further, he would have been an hour late.

i) What is Raj's normal speed?
A) 20 Km/hr B) 15 Km/hr C) 30 Km/hr D) 25 Km/hr
ii) What is the distance between Mumbai and Raj's hometown?
A) 140 Km B) 200 Km C) 220 Km D) 250 Km

24. #### CAT Time Speed and Distance: Distance between two points

Two persons A and B start moving at each other from point P and Q respectively which are 1400 Km apart. Speed of A is 50 Km/hr and that of B is 20 Km/hr. How far is A from Q when he meets B for the 22nd time?

1. 1000 km
2. 400 km
3. 800 km
4. 1400 km

25. #### CAT Time Speed and Distance: Distance between two points

Two persons A and B start moving from point P towards Q which are 1400 Km apart. Speed of A is 50 Km/hr and that of B is 20 Km/hr. How far is A from Q when he meets B for the 22nd time?

1. 1000 Km
2. 600 Km
3. 800 Km
4. 1400 Km

26. #### CAT Time Speed and Distance: Relative Speed

Two trains A and B are 100 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.

1. 10 s
2. 6 s
3. 4 s
4. 8 s

27. #### CAT Time Speed and Distance: Relative Speed

Two trains left from two stations P and Q towards station Q and station P respectively. 3 hours after they met, they were 675 Km apart. First train arrived at its destination 16 hours after their meeting and the second train arrived at its destination 25 hours after their meeting. How long did it take for the first train to make the whole trip?

1. 18h
2. 36h
3. 25h
4. 48h

28. #### CAT Time Speed and Distance: Perpendicular directions

Arjun travels from A to B, a distance of 200 Km at the speed of 40 Km/hr. At the same time, Rakesh starts from point B at a speed of 20 Km/hr along a road which is perpendicular to AB. Find the time in which Arjun & Rakesh will be closer to each other?

1. 1.5 hr
2. 3.33 hr
3. 5 hr
4. 4 hr

29. ##### The following questions are from IPMAT Rohtak and Indore sample papers. If you want to take these questions as a mock please click below.

IPMAT Rohtak Sample Paper Mock
IPMAT Indore Sample Paper Mock

Please note that the explanation button will take you to the IPMAT solution page.

Directions (29-33): Study the data given below and answer the following questions. The pie charts shown below shows the distance covered by a boat moving upstream and downstream indifferent days of a week. And the table shows the speed of stream in km/hr. in different days of a week.

30. #### IPMAT 2020 Sample Paper - IPM Rohtak Quants,Time Speed and Distance

If the time taken by boat to travel upstream on Wednesday is $$frac{6}{7}\\$ times than the time taken to travel downstream on Monday and the speed of boat in still water on Monday is 15 kmph then find the speed of boat in still water on Wednesday?$ speed of boat in still water is different for different days)

1. 52 kmph
2. 62 kmph
3. 42 kmph
4. 48 kmph
5. None of these

31. #### IPMAT 2020 Sample Paper - IPM Rohtak Quants,Time Speed and Distance

If the time taken by boat to travel upstream on Monday is 27$$frac{1}{5}\\$ hrs. more than the time taken by it to travel downstream on the same day, then find the speed of boat in still water on Monday ?$speed of boat in still water is same in upstream as in downstream)

1. 25 kmph
2. 18 kmph
3. 20 kmph
4. 15 kmph
5. None of these

32. #### IPMAT 2020 Sample Paper - IPM Rohtak Quants,Time Speed and Distance

If the speed of boat in still water on Saturday was 27 km/hr and the speed of boat in still water on Wednesday was 66$$frac{2}{3}\\$% more than that of Saturday and time taken to travel upstream on Wednesday is $\frac{16}{13}\\$ times than time taken by it to travel downstream on Saturday, then find the speed of stream$in kmph) on Saturday?

1. 2
2. 4
3. 9
4. 8
5. None of these

The speed of boat in still water on Saturday was 21 km/hr. and that on Sunday was 28$$frac{4}{7}\\$% more than that on Saturday, if the time taken by boat to travel upstream on Saturday is 2$\frac{1}{2}\\$ times the time taken to travel downstream on Sunday, then find the time taken by the boat to cover a distance of 125 km upstream on Saturday? 1. 6 hrs 45 min 2. 2 hrs 45 min 3. 4 hrs 30 min 4. 6 hrs 15 min 5. None of these 34. #### IPMAT 2020 Sample Paper - IPM Rohtak Quants,Time Speed and Distance If the time taken by boat to travel upstream on Friday is 30 hours more than the time taken by it to travel downstream on Wednesday and the speed of boat in still water on Friday is 17 kmph, then find the upstream speed of boat on Wednesday?$speed of boat in still water is different on different days)

1. 27 kmph
2. 22 kmph
3. 20 kmph
4. 25 kmph
5. None of these

35. #### IPMAT 2020 Sample Paper - IPM Rohtak Quants,Time Speed and Distance

Train A takes 45 minutes more than train B to travel 450 km. Due to engine trouble, speed of train B falls by a quarter. So it takes 30 minutes more than Train A to complete the same journey. Find the speed of Train A.

1. 120 km/hr
2. 110 km/hr
3. 100 km/hr
4. 90 km/hr

36. #### IPMAT 2020 Sample Paper - IPM Rohtak Quants,Time Speed and Distance

A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?

1. 40 minutes
2. 1 hour
3. 1 hr 15 min
4. 1 hr 30 min

37. #### IPMAT 2019 Question Paper - IPM Indore Quants,Time Speed and Distance

Two small insects, which are x metres apart, take u minutes to pass each other when they are flying towards each other, and v minutes to meet each other when they are flying in the same direction. Then, the ratio of the speed of the slower insect to that of the faster insect is

2. #### CAT 2017 Question Paper Slot 1 - Speed Time Distance

A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is:

1. √6 : √2
2. √7 : 2
3. 2√5 : 3
4. 3 : 2

3. #### CAT 2017 Question Paper Slot 2 - Races

In a 10 km race. A, B, and C, each running at uniform speed, get the gold, silver, and bronze medals, respectively. If A beats B by 1 km and B beats C by 1 km, then by how many metres does A beat C? [TITA]

4. #### CAT 2017 Question Paper Slot 2 - Speed Time Distance

Arun drove from home to his hostel at 60 miles per hour. While returning home he drove half way along the same route at a speed of 25 miles per hour and then took a bypass road which increased his driving distance by 5 miles, but allowed him to drive at 50 miles per hour along this bypass road. If his return journey took 30 minutes more than his onward journey, then the total distance travelled by him is:

1. 55 miles
2. 60 miles
3. 65 miles
4. 70 miles

5. #### CAT 2017 Question Paper Slot 2 - Speed Time Distance

A motorbike leaves point A at 1 pm and moves towards point B at a uniform speed. A car leaves point B at 2 pm and moves towards point A at a uniform speed which is double that of the motorbike. They meet at 3:40 pm at a point which is 168 km away from A. What is the distance, in km, between A and B?

1. 364
2. 378
3. 380
4. 388

6. #### CAT 2018 Question Paper Slot 1 - Speed Time Distance

The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes four hours more than Narayan to reach B. Moreover, Partha reaches the mid-point of A and B two hours before Narayan reaches B. The speed of Partha, in km per hour, is

1. 6
2. 3
3. 4
4. 5

7. #### CAT 2018 Question Paper Slot 1 - Speed, Time and Distance

Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then the time, in minutes, taken by car 1 in reaching P from A is:[TITA]

8. #### CAT 2018 Question Paper Slot 1 - Speed Time Distance

Train T leaves station X for station Y at 3 pm. Train S, traveling at three quarters of the speed of T, leaves Y for X at 4 pm. The two trains pass each other at a station Z, where the distance between X and Z is three-fifths of that between X and Y. How many hours does train T take for its journey from X to Y? [TITA]

9. #### CAT 2018 Question Paper Slot 2 - Speed Time Distance

Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2 leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets Car 1 at Q, and Car 2 at P. If each car is moving in uniform speed then the ratio of the speed of Car 2 to that of Car 1 is

1. 1 : 4
2. 2 : 9
3. 1 : 2
4. 2 : 7

10. #### CAT 2018 Question Paper Slot 2 - Speed, Time and Distance

On a long stretch of east-west road, A and B are two points such that B is 350 km west of A. One car starts from A and another from B at the same time. If they move towards each other, then they meet after 1 hour. If they both move towards east, then they meet in 7 hrs. The difference between their speeds, in km per hour, is (TITA)

11. #### CAT 2018 Question Paper Slot 2 - Speed, Time and Distance

Points A and B are 150 km apart. Cars 1 and 2 travel from A to B, but car 2 starts from A when car 1 is already 20 km away from A. Each car travels at a speed of 100 kmph for the first 50 km, at 50 kmph for the next 50 km, and at 25 kmph for the last 50 km. The distance, in km, between car 2 and B when car 1 reaches B is (TITA)

12. #### CAT 2019 Question Paper Slot 1 - Speed, time and distance

Two cars travel the same distance starting at 10:00 am and 11:00 am, respectively, on the same day. They reach their common destination at the same point of time. If the first car travelled for at least 6 hours, then the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is

1. 20
2. 10
3. 35
4. 25

13. #### CAT 2019 Question Paper Slot 1 - Races

In a race of three horses, the first beat the second by 11 metres and the third by 90 metres. If the second beat the third by 80 metres, what was the length, in metres, of the racecourse? [TITA]

14. #### CAT 2019 Question Paper Slot 1 - Speed, time and distance

One can use three different transports which move at 10, 20, and 30 kmph, respectively. To reach from A to B, Amal took each mode of transport 1/3 of his total journey time, while Bimal took each mode of transport 1/3 of the total distance. The percentage by which Bimal’s travel time exceeds Amal’s travel time is nearest to

1. 22
2. 19
3. 21
4. 20

15. #### CAT 2019 Question Paper Slot 1 - Speed, time and distance

The wheels of bicycles A and B have radii 30 cm and 40 cm, respectively. While traveling a certain distance, each wheel of A required 5000 more revolutions than each wheel of B. If bicycle B traveled this distance in 45 minutes, then its speed, in km per hour, was

1. 18π
2. 16π
3. 12π
4. 14π

16. #### CAT 2019 Question Paper Slot 2 - Speed, Time & distance

A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motorcycle leaves A and moves towards B. Forty-five such motorcycles reach B by 11 am. All motorcycles have the same speed. If the cyclist had doubled his speed, how many motorcycles would have reached B by the time the cyclist reached B?

1. 22
2. 20
3. 15
4. 23

17. #### CAT 2019 Question Paper Slot 2 - Races

John jogs on track A at 6 kmph and Mary jogs on track B at 7.5 kmph. The total length of tracks A and B is 325 metres. While John makes 9 rounds of track A, Mary makes 5 rounds of track B. In how many seconds will Mary make one round of track A? [TITA]

18. #### CAT 2019 Question Paper Slot 2 - Speed, time & distance

Two ants A and B start from a point P on a circle at the same time, with A moving clock-wise and B moving anti-clockwise. They meet for the first time at 10:00 am when A has covered 60% of the track. If A returns to P at 10:12 am, then B returns to P at

1. 10:27 am
2. 10:25 am
3. 10:45 am
4. 10:18 am

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