# CAT Quantitative Ability Questions | CAT TIme, Speed, Distance and Work questions

Time,Speed, Distance And Work for CAT | CAT Past year TSD and TW Questions | Time, speed and Distance; Time, Work and Wages; Pipes and Cisterns; Calendar and Clocks; Problems on Trains, Boats, Aeroplane, Streams and Races.CAT/2023.3(Quantitative Ability)

### Question. 1

**Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be**

CAT/2023.3(Quantitative Ability)

### Question. 3

**Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is **

36

CAT/2023.2(Quantitative Ability)

### Question. 4

**Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe C to fill the empty tank is**

CAT/2023.2(Quantitative Ability)

### Question. 5

**Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, is**

CAT/2023.1(Quantitative Ability)

### Question. 8

**The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job. Then the number of days Sunil will take to finish the job working alone, is**

27

CAT/2023.1(Quantitative Ability)

### Question. 9

**Arvind travels from town A to town B, and Surbhi from town B to town A, both starting at the same time along the same route. After meeting each other, Arvind takes 6 hours to reach town B while Surbhi takes 24 hours to reach town A. If Arvind travelled at a speed of 54 km/h, then the distance, in km, between town A and town B is**

972

CAT/2022.3(Quantitative Ability)

### Question. 10

**Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards each other, is**

CAT/2022.3(Quantitative Ability)

### Question. 11

**Two ships are approaching a port along straight routes at constant speeds. Initially, the two ships and the port formed an equilateral triangle with sides of length 24 km. When the slower ship travelled 8 km, the triangle formed by the new positions of the two ships and the port became right-angled. When the faster ship reaches the port, the distance, in km, between the other ship and the port will be**

CAT/2022.3(Quantitative Ability)

### Question. 14

**Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three-day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, is**

11

CAT/2022.3(Quantitative Ability)

### Question. 15

**Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator is **

60

CAT/2022.2(Quantitative Ability)

### Question. 16

**Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 km per hour more than the other one, then the speed, in km per hour, of the slower ship is**

CAT/2022.2(Quantitative Ability)

### Question. 17

**Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is**

CAT/2022.1(Quantitative Ability)

### Question. 18

**Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is**

CAT/2021.1(Quantitative Ability)

### Question. 19

**Anu, Vinu, and Manu can complete work alone in 15 days, 12 days, and 20 days, respectively. Vinu works every day. Anu works only on alternate days starting from the first day while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is**

CAT/2021.1(Quantitative Ability)

### Question. 20

**The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is**

CAT/2021.1(Quantitative Ability)

### Question. 21

**Amar, Akbar, and Anthony are working on a project. Working together Amar and Akbar can complete the project in 1 year, Akbar and Anthony can complete in 16 months, Anthony and Amar can complete in 2 years. If the person who is neither the fastest nor the slowest works alone, the time in months he will take to complete the project is**

32

CAT/2021.1(Quantitative Ability)

### Question. 22

**Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160 m long and crosses a lamp post in 12 seconds. If the speed of the other train is 6 km/hr less than the faster one, its length, in m, is**

CAT/2021.2(Quantitative Ability)

### Question. 23

**Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tank becomes full at 10 pm. Instead, if pipe A is opened at 2 pm and pipe B is opened at 4 pm, then the tank becomes full at 6 pm. If pipe B is not opened at all, then the time, in minutes, taken to fill the tank is**

CAT/2021.2(Quantitative Ability)

### Question. 24

**Two trains A and B were moving in opposite directions, their speeds being in the ratio 5 : 3. The front end of A crossed the rear end of B 46 seconds after the front ends of the trains had crossed each other. It took another 69 seconds for the rear ends of the trains to cross each other. The ratio of length of train A to that of train B is**

CAT/2021.2(Quantitative Ability)

### Question. 25

**Anil can paint a house in 60 days while Bimal can paint it in 84 days. Anil starts painting and after 10 days, Bimal and Charu join him. Together, they complete the painting in 14 more days. If they are paid a total of ₹ 21000 for the job, then the share of Charu, in INR, proportionate to the work done by him, is**

CAT/2021.3(Quantitative Ability)

### Question. 26

**One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is**

CAT/2021.3(Quantitative Ability)

### Question. 27

**Mira and Amal walk along a circular track, starting from the same point at the same time. If they walk in the same direction, then in 45 minutes, Amal completes exactly 3 more rounds than Mira. If they walk in opposite directions, then they meet for the first time exactly after 3 minutes. The number of rounds Mira walks in one hour is**

CAT/2021.3(Quantitative Ability)

### Question. 28

**Anil can paint a house in 12 days while Barun can paint it in 16 days. Anil, Barun, and Chandu undertake to paint the house for ₹ 24000 and the three of them together complete the painting in 6 days. If Chandu is paid in proportion to the work done by him, then the amount in INR received by him is**

3000

CAT/2020.1(Quantitative Ability)

### Question. 29

**A train travelled at one-thirds of its usual speed, and hence reached the destination 30 minutes after the scheduled time. On its return journey, the train initially travelled at its usual speed for 5 minutes but then stopped for 4 minutes for an emergency. The percentage by which the train must now increase its usual speed so as to reach the destination at the scheduled time, is nearest to**

CAT/2020.1(Quantitative Ability)

### Question. 30

**A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. After meeting each other, they take 45 minutes and 20 minutes, respectively, to complete their journeys. If Car 1 travels at the speed of 60 km/hr, then the speed of Car 2, in km/hr, is**

CAT/2020.1(Quantitative Ability)

### Question. 31

**Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to**

CAT/2020.2(Quantitative Ability)

### Question. 34

**The distance from B to C is thrice that from A to B. Two trains travel from A to C via B. The speed of train 2 is double that of train 1 while traveling from A to B and their speeds are interchanged while traveling from B to C. The ratio of the time taken by train 1 to that taken by train 2 in travelling from A to C is**

CAT/2020.2(Quantitative Ability)

### Question. 35

**Two circular tracks T1 and T2 of radii 100 m and 20 m, respectively touch at a point A. Starting from A at the same time, Ram and Rahim are walking on track T1 and track T2 at speeds 15 km/hr and 5 km/hr respectively. The number of full rounds that Ram will make before he meets Rahim again for the first time is**

CAT/2020.2(Quantitative Ability)

### Question. 36

**A and B are two points on a straight line. Ram runs from A to B while Rahim runs from B to A. After crossing each other, Ram and Rahim reach their destinations in one minutes and four minutes, respectively. If they start at the same time, then the ratio of Ram's speed to Rahim's speed is**

CAT/2020.2(Quantitative Ability)

### Question. 37

**John takes twice as much time as Jack to finish a job. Jack and Jim together take one-thirds of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them working together. In how many days will Jim finish the job working alone?**

CAT/2020.3(Quantitative Ability)

### Question. 38

**A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?**

40

CAT/2020.3(Quantitative Ability)

### Question. 39

**Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15 km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?**

CAT/2020.3(Quantitative Ability)

### Question. 41

**Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 km/hr. She is late by 6 minutes if she drives at 35 km/hr. One day, she covers two-thirds of her distance to office in one-thirds of her usual time to reach office, and then stops for 8 minutes. The speed, in km/hr, at which she should drive the remaining distance to reach office exactly on time is**

CAT/2019.1(Quantitative Ability)

### Question. 42

**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**

CAT/2019.1(Quantitative Ability)

### Question. 43

**At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?**

CAT/2019.1(Quantitative Ability)

### Question. 44

**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**

CAT/2019.1(Quantitative Ability)

### Question. 45

**Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days? **

13

CAT/2019.1(Quantitative Ability)

### Question. 46

**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**

CAT/2019.2(Quantitative Ability)

### Question. 47

**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?**

CAT/2019.2(Quantitative Ability)

### Question. 48

**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?**

48

CAT/2019.2(Quantitative Ability)

### Question. 49

Anil alone can do a job in 20 days while Sunil alone can do it in 40 days. Anil starts the job, and after 3 days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done 10% of the job, then in how many days was the job done?

CAT/2019.2(Quantitative Ability)

### Question. 51

**John gets Rs 57 per hour of regular work and Rs 114 per hour of overtime work. He works altogether 172 hours and his income from overtime hours is 15% of his income from regular hours. Then, for how many hours did he work overtime?**

12

CAT/2018.1(Quantitative Ability)

### Question. 52

**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**

CAT/2018.1(Quantitative Ability)

### Question. 53

**When they work alone, B needs 25% more time to ﬁnish a job than A does. They two ﬁnish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and ﬁnally B works alone to complete the remaining 5% of the job. In how many days can B alone ﬁnish the entire job?**

CAT/2018.1(Quantitative Ability)

### Question. 54

**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**

12

CAT/2018.1(Quantitative Ability)

### Question. 55

**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?**

15

CAT/2018.1(Quantitative Ability)

### Question. 56

**Humans and robots can both perform a job but at diﬀerent eﬃciencies. Fifteen humans and ﬁve robots working together take thirty days to ﬁnish the job, whereas ﬁve humans and ﬁfteen robots working together take sixty days to ﬁnish it. How many days will ﬁfteen humans working together (without any robot) take to ﬁnish it?**

CAT/2018.1(Quantitative Ability)

### Question. 57

**A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?**

10

CAT/2018.2(Quantitative Ability)

### Question. 58

**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**

CAT/2018.2(Quantitative Ability)

### Question. 59

**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**

50

CAT/2018.2(Quantitative Ability)

### Question. 60

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

CAT/2018.2(Quantitative Ability)

### Question. 61

**A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?**

CAT/2018.2(Quantitative Ability)

### Question. 62

**Ramesh and Ganesh can together complete a work in 16 days. After seven days of working together, Ramesh got sick and his efficiency fell by 30%. As a result, they completed the work in 17 days instead of 16 days. If Ganesh had worked alone after Ramesh got sick, in how many days would he have completed the remaining work?**

CAT/2018.2(Quantitative Ability)

### Question. 63

**A water tank has inlets of two types A and B. All inlets of type A when open, bring in water at the same rate. All inlets of type B, when open, bring in water at the same rate. The empty tank is completely filled in 30 minutes if 10 inlets of type A and 45 inlets of type B are open, and in 1 hour if 8 inlets of type A and 18 inlets of type B are open. In how many minutes will the empty tank get completely filled if 7 inlets of type A and 27 inlets of type B are open?**

48

CAT/2017.1(Quantitative Ability)

### Question. 64

A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days. On Day 3, they are joined by another person of equal efficiency. Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job?

15

CAT/2017.1(Quantitative Ability)

### Question. 65

A man leaves his home and walks at a speed of 12 km per hour, reaching the railway station 10 minutes after the train had departed. If instead he had walked at a speed of 15 km per hour, he would have reached the station 10 minutes before the train's departure. The distance (in km) from his home to the railway station is:

20

CAT/2017.1(Quantitative Ability)

### Question. 66

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:

CAT/2017.2(Quantitative Ability)

### Question. 67

**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**

CAT/2017.2(Quantitative Ability)

### Question. 68

**A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours. If the outlet pipe is open then the inlet pipe fills the empty tank in 10 hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full?**

CAT/2017.2(Quantitative Ability)

### Question. 69

**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?**

CAT/2017.2(Quantitative Ability)

### Question. 70

**Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration. If this amount is shared by them in proportion to their work, then Kamal's share, in rupees, is**

CAT/2008(Quantitative Ability)

### Question. 71

**Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and northwest of B, with BC at 60° to AB. Also, C is located between south and southwest of A with AC at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to**

### Comprehension

**Directions for Questions 11 and 12: **

Answer the following questions based on the information given below:

Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on the same day.

Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west at 50 km per hour.

### Comprehension

**Directions for Questions 11 and 12: **

Answer the following questions based on the information given below:

Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on the same day.

Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west at 50 km per hour.

CAT/2006(Quantitative Ability)

### Question. 74

**Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40 and 60 km per hour respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?**

CAT/2005(Quantitative Ability)

### Question. 75

A chemical plant has four tanks (A, B, C and D) each containing 1000 litres of a chemical. The chemical is being pumped from one tank to another as follows :

From A to B @ 20 litres/minute

From C to A @ 90 litres/minute

From A to D @ 10 litres/minute

From C to D @ 50 litres/minute

From B to C @ 100 litres/minute

From D to B @ 110 litres/minute

Which tank gets emptied first, and how long does it take (in minutes) to get empty after pumping starts?

### Comprehension

**Directions for question: Answer the questions on the basis of the information given below**

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.

### Comprehension

**Directions for question: Answer the questions on the basis of the information given below**

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.

CAT/2004(Quantitative Ability)

### Question. 78

Karan and Arjun run a 100-metre race, where Karan beats Arjun by 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100-metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?

CAT/2004(Quantitative Ability)

### Question. 81

In nuts and bolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts. Another machine produces only bolts at the rate of 75 bolts per minute and needs to be cleaned for 10 minutes after production of every 1500 bolts. If both the machines start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?

CAT/2003(Quantitative Ability)

### Question. 82

In a 4000 metre race around a circular stadium having a circumference of 1000 metres, the fastest runner and the slowest runner reach the same point at the end of the 5th minute for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

A city has two perfectly circular concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR) . These are also four (straight line) chord roads form E1 , the east end point of OR to N2 , the north end point of IR; from N1 , the north end point of OR to W2 , the west end point of IR, from W1, the west end point of OR, to S2 , the south end point of IR; and from S1 , the south end point of OR to E2 , the east end point of IR. Traffic moves at a constant speed of 30 km/hr on the OR road, 20 km/hr on the IR road and 15√5 km/hr on all the chord roads.

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

A city has two perfectly circular concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR) . These are also four (straight line) chord roads form E1 , the east end point of OR to N2 , the north end point of IR; from N1 , the north end point of OR to W2 , the west end point of IR, from W1, the west end point of OR, to S2 , the south end point of IR; and from S1 , the south end point of OR to E2 , the east end point of IR. Traffic moves at a constant speed of 30 km/hr on the OR road, 20 km/hr on the IR road and 15√5 km/hr on all the chord roads.

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

A city has two perfectly circular concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR) . These are also four (straight line) chord roads form E1 , the east end point of OR to N2 , the north end point of IR; from N1 , the north end point of OR to W2 , the west end point of IR, from W1, the west end point of OR, to S2 , the south end point of IR; and from S1 , the south end point of OR to E2 , the east end point of IR. Traffic moves at a constant speed of 30 km/hr on the OR road, 20 km/hr on the IR road and 15√5 km/hr on all the chord roads.

CAT/2003(Quantitative Ability)

### Question. 86

A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process, it takes 10 minutes for the angle of elevation to change from 45° to 60°. After how much more time will this car reach the base of the tower?

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

Consider three circular parks of equal size with centers at A1 , A2 and A3 respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed by the triangles A1A2A3 , B1 B2 B3 and C1 C2 C3 as shown. Three sprinters A, B and C begin running from points A1 , B1 and C1 respectively. Each sprinter traverses her respective triangular path clockwise and returns to her starting point

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

Consider three circular parks of equal size with centers at A1 , A2 and A3 respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed by the triangles A1A2A3 , B1 B2 B3 and C1 C2 C3 as shown. Three sprinters A, B and C begin running from points A1 , B1 and C1 respectively. Each sprinter traverses her respective triangular path clockwise and returns to her starting point

CAT/2003(Quantitative Ability)

### Question. 88

Sprinter A traverses distances A1 A2 , A2 A3 and A3 A1 at average speeds of 20, 30 and 15, respectively. B traverses her entire path at a uniform speed of (10 3 + 20). C traverses distances C1 C2 , C2 C3 and C3 C1 at average speeds of 40/3(√3 + 1 ), 40/3(√3 + 1) and 120, respectively. All speeds are in the same unit. Where would B and C be respectively when A finishes her sprint?

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

Consider three circular parks of equal size with centers at A1 , A2 and A3 respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed by the triangles A1A2A3 , B1 B2 B3 and C1 C2 C3 as shown. Three sprinters A, B and C begin running from points A1 , B1 and C1 respectively. Each sprinter traverses her respective triangular path clockwise and returns to her starting point

CAT/2003(Quantitative Ability)

### Question. 89

Sprinters A, B and C traverse their respective paths at uniform speeds of u, v and w respectively. It is known that u² : v² : w² is equal to Area A : Area B : Area C, where Area A, Area B and Area C are the areas of triangles A1 A2 A3 , B1 B2 B3 and C1 C2 C3 , respectively. Where would A and C be when B reaches point B3 ?

CAT/2003(Quantitative Ability)

### Question. 90

Two straight roads R1 and R2 diverge from a point A at an angle of 120°. Ram starts walking from point A along R1 at a uniform speed of 3 km/hr. Shyam starts walking at the same time from A along R2 at a uniform speed of 2 km/h. They continue walking for 4 hours along their respective roads and reach points B and C on R1 and R2 , respectively. There is a straight line path connecting B and C. Then Ram returns to point A after walking along the line segments BC and CA. Shyam also returns to A after walking along line segments CB and BA. Their speeds remain unchanged. The time interval (in hours) between Ram’s and shyam’s return to the point A is

CAT/2002(Quantitative Ability)

### Question. 91

6 technicians take total 10 hours to build a new server from Direct Computer, with each working at the same rate. If six technicians start to build the server at 11:00 am, and one technician per hour is added beginning at 5:00 pm, at what time will the server be complete?

CAT/2002(Quantitative Ability)

### Question. 92

3 small pumps and a large pump are filling a tank. Each of the three small pumps works at 2/3rd the rate of the large pump. If all 4 pumps work at the same time, they should fill the tank in what fraction of the time that it would have taken the large pump alone?

CAT/2002(Quantitative Ability)

### Question. 93

On a straight road XY, 100 metres long, five heavy stones are placed two metres apart beginning at the end X. A worker, starting at X, has to transport all the stones to Y, by carrying only one stone at a time. The minimum distance he has to travel (in metres) is

CAT/2002(Quantitative Ability)

### Question. 94

Only a single rail track exists between station A and B on a railway line. One hour after the north bound super fast train N leaves station A for station B, a south bound passenger train S reaches station A from station B. The speed of the super fast train is twice that of a normal express train E, while the speed of a passenger train S is half that of E. On a particular day N leaves for station B from Station A, 20 minutes behind the normal schedule. In order to maintain the schedule both N and S increased their speed. If the super fast train doubles its speed, what should be the ratio (approximately) of the speed of passenger train to that of the super fast train so that passenger train S reaches exactly at the scheduled time at station A on that day

CAT/2002(Quantitative Ability)

### Question. 95

On a 20 km tunnel connecting two cities A and B there are three gutters. The distance between gutter 1 and 2 is half the distance between gutter 2 and 3. The distance from City A to its nearest gutter, gutter 1 is equal to the distance of city B from gutter 3. On a particular day the hospital in city A receives information that an accident has happened at the third gutter. The victim can be saved only if an operation is started within 40 minutes. An ambulance started from city A at 30 km/hr and crossed the first gutter after 5 minutes. If the driver had doubled the speed after that, what is the maximum amount of time the doctor would get to attend the patient at the hospital? Assume 1 minute is elapsed for taking the patient into and out of the ambulance

CAT/2002(Quantitative Ability)

### Question. 96

A car rental agency has following terms. If a car is rented for 5 hours or less the charge is Rs 60 per hour or Rs 12 per kilometre whichever is more. On the other hand, if the car is rented for more than 5 hours, the charge is Rs 50 per hour or Rs 7.50 per kilometre whichever is more. Akil rented a car from this agency, drove it for 30 kilometers and ended up paying Rs 300. For how many hours did he rented the Car?

CAT/2002(Quantitative Ability)

### Question. 97

A train approaches a tunnel AB. Inside the tunnel is a cat located at a point that is 3/8 of the distance AB measured from the entrance A. When the train whistles the cat runs. If the cat moves to the entrance of the tunnel, A, the train catches the cat exactly at the entrance. If the cat moves to the exit, B, the train catches the cat at exactly the exit. The speed of the train is greater than the speed of the cat by what order?

CAT/2001(Quantitative Ability)

### Question. 98

A can complete a piece of work in 4 days. B takes double the times taken by A, C takes double that of B, and D takes double that of C to complete the same task. They are paired in groups of two each. One pair takes two- third the time needed by the second pair to complete the work. Which is the first pair?

CAT/2001(Quantitative Ability)

### Question. 100

At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in six hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour?

CAT/2001(Quantitative Ability)

### Question. 101

Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom’s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?

CAT/2001(Quantitative Ability)

### Question. 102

There’s a lot of work in preparing a birthday dinner. Even after the turkey is in the oven, there’s still the potatoes and gravy, yams, salad, and cranberries, not to mention setting the table. Three friends, Asit, Arnold, and Afzal, work together to get all of these chores done. The time it takes them to do the work together is six hours less than Asit would have taken working alone, one hour less than Arnold would have taken alone, and half the time Afzal would have taken working alone. How long did it take them to do these chores working together?

CAT/2001(Quantitative Ability)

### Question. 103

A train X departs from station A at 11.00 am for station B, which is 180 km away. Another train Y departs from station B at 11.00 am for station A. Train X travels at an average speed of 70 kms/hr and does not stop any where until it arrives at station B. Train Y travels at an average speed of 50 kms/hr, but has to stop for 15 minutes at station C, which is 60 kms away from station B enroute to station A. Ignoring the lengths the train , what is the distance , to the nearest km, from station A to the point where the trains cross each other?

CAT/2001(Quantitative Ability)

### Question. 104

Three runners A, B and C run a race, with runner A finishing 12 metres ahead of runner B and 18 metres ahead of runner C, while runner B finishes 8 metres ahead of C. Each runner travels the entire distance at constant speed. What was the length of the race?

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

The petrol consumption rate of a new model car ‘Palto’ depends on its speed and may be described by the graph below.

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

The petrol consumption rate of a new model car ‘Palto’ depends on its speed and may be described by the graph below.

CAT/2000(Quantitative Ability)

### Question. 107

A and B are two cities 10 km apart. A load of 80 kg has to be transported form A to B. The courier service charges @ 10Rs per hour. The optimal speed that one can go without load is 10 km/hr, the speed reduces to 5 km/hr with a weight of 10 Kg. Further with 20 kg (which is the maximum weight that can be carried), the speed is 2 km/hr. what is the minimum cost?

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

There are five machines A, B, C, D and E – situated on a straight line at distances of 10 m, 20 m, 30 m, 40 m and 50 m respectively from the origin of the line. A robot is stationed at the origin of the line. The robot serves the machines with raw material whenever a machine becomes idle. All the raw materials are located at the origin. The robot is in an idle state at the origin at the beginning of a day. As soon as one or more machines become idle, they send messages to the robot-station and the robot starts and serves all the machines from which it received messages. If a message is received at the station while the robot is away from it, the robot takes notice of the message only when it returns to the station. While moving, it serves the machines in the sequence in which they are encountered, and then returns to the origin. If any messages are pending at the station when it returns, it repeats the process again. Otherwise, it remains idle at the origin till the next message(s) is/are received.

CAT/2000(Quantitative Ability)

### Question. 108

Suppose on a certain day, machines A and D have sent the first two messages to the origin at the beginning of the 1st second, C has sent a message at the beginning of the 5th second, B at the beginning of the 6th second and E at the beginning of the 10th second. How much distance has the robot travelled since the beginning of the day, when it notices the message of E? Assume that the speed of movement of the robot is 10 m/s.

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

There are five machines A, B, C, D and E – situated on a straight line at distances of 10 m, 20 m, 30 m, 40 m and 50 m respectively from the origin of the line. A robot is stationed at the origin of the line. The robot serves the machines with raw material whenever a machine becomes idle. All the raw materials are located at the origin. The robot is in an idle state at the origin at the beginning of a day. As soon as one or more machines become idle, they send messages to the robot-station and the robot starts and serves all the machines from which it received messages. If a message is received at the station while the robot is away from it, the robot takes notice of the message only when it returns to the station. While moving, it serves the machines in the sequence in which they are encountered, and then returns to the origin. If any messages are pending at the station when it returns, it repeats the process again. Otherwise, it remains idle at the origin till the next message(s) is/are received.

CAT/2000(Quantitative Ability)

### Question. 109

Suppose there is a second station with raw material for the robot at the other extreme of the line which is 60 m from the origin, i.e., 10 m from E. After finishing the services in a trip, the robot returns to the nearest station. If both stations are equidistant, it chooses the origin as the station to return to. Assuming that both stations receive the message sent by the machines and that all the other data remains the same, what would be the answer to the above question?

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

Rajiv travels to B from A in 4 hrs. travelling at 35 kmph for two hrs and at 45 kmph for the next two hrs. Aditi travels on the same route at speeds of 30, 40 and 50 kmph, covering equal distances at each of these speeds. The relation between fuel consuption and speed is given in the following graph.

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

Rajiv travels to B from A in 4 hrs. travelling at 35 kmph for two hrs and at 45 kmph for the next two hrs. Aditi travels on the same route at speeds of 30, 40 and 50 kmph, covering equal distances at each of these speeds. The relation between fuel consuption and speed is given in the following graph.

CAT/1999(Quantitative Ability)

### Question. 113

Navjeeven exp., which goes form Ahmedabad to Chennai leaves Ahmedabad at 6:30 am and travels at a constant speed of 50 kmph towards Baroda, which is 100 kms away. At 7:00, the How -Ambd exp. leaves for Ahmedabad from Baroda at a constant speed of 40 kmph. At 7:30 Mr. Shah, the control officer, realises that both the trains are on the same track. How much time does Mr. Shah have to avert the accident?

CAT/1999(Quantitative Ability)

### Question. 114

A railway engine moves with the speed of 42 kmph. The reduction in speed varies as the square root of the number of compartments attached to it. The speed is 24 kmph when 9 compartments are attached. What is the maximum number of compartments that the engine can pull?

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

There is a network of routes as shown in the figure given below. D is the mid point of AC, AB is perpendicular to BC and AB = 100km. The persons, X & Y, go from A to C, starting at the same time and reaching at the same time. X follows the path A-B-C with an average speed of 61.875 kmph, and Y follows the straight path A-C, covering part AD at 45 kmph and part DC at 55 Kmph.

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

There is a network of routes as shown in the figure given below. D is the mid point of AC, AB is perpendicular to BC and AB = 100km. The persons, X & Y, go from A to C, starting at the same time and reaching at the same time. X follows the path A-B-C with an average speed of 61.875 kmph, and Y follows the straight path A-C, covering part AD at 45 kmph and part DC at 55 Kmph.

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

There is a network of routes as shown in the figure given below. D is the mid point of AC, AB is perpendicular to BC and AB = 100km. The persons, X & Y, go from A to C, starting at the same time and reaching at the same time. X follows the path A-B-C with an average speed of 61.875 kmph, and Y follows the straight path A-C, covering part AD at 45 kmph and part DC at 55 Kmph.

CAT/1998(Quantitative Ability)

### Question. 118

A company has a job to prepare certain no. of cans and there are three machines A, B & C for this job. A can complete the job in 3 days, B can complete the job in 4 days and C can complete the job in 6 days. How many days the company will take to complete job if all the machines are used simultaneously?

CAT/1998(Quantitative Ability)

### Question. 119

Distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed 4 kmph. While the other man travelled with varying speeds as follows : In first hour his speed was 2 kmph, in the second hour it was 2.5 kmph, in the third hour it was 3 kmph, and so on. When will they meet each other?

CAT/1998(Quantitative Ability)

### Question. 120

I started climbing up the hill at 6 am and reached the temple at the top at 6 pm Next day I started coming down at 6 am and reached the foothill at 6 pm. I walked on the same road. The road is so short that only one person can walk on it. Although I varied my pace on my way, I never stopped on my way. Then which of the following must be true

CAT/1997(Quantitative Ability)

### Question. 122

Boston is 4 hours ahead of Frankfurt and two hours behind India. X leaves Frankfurt at 06:00 pm on Friday and reaches Boston the next day. After waiting there for two hours, he leaves exactly at noon and reaches India at 01:00 am. On his return journey, he takes the same route as before, but halts at Boston for one hour less than his previous halt there. He then proceeds to Frankfurt.

If his journey, including stoppages, was covered at an average speed of 180 miles per hour, what was the distance between Frankfurt and India?

CAT/1997(Quantitative Ability)

### Question. 123

Boston is 4 hours ahead of Frankfurt and two hours behind India. X leaves Frankfurt at 06:00 pm on Friday and reaches Boston the next day. After waiting there for two hours, he leaves exactly at noon and reaches India at 01:00 am. On his return journey, he takes the same route as before, but halts at Boston for one hour less than his previous halt there. He then proceeds to Frankfurt.

If X had started his return journey from India at 02:55 am on the same day that he reached there, after how much time would he reach Frankfurt?

CAT/1997(Quantitative Ability)

### Question. 124

Boston is 4 hours ahead of Frankfurt and two hours behind India. X leaves Frankfurt at 06:00 pm on Friday and reaches Boston the next day. After waiting there for two hours, he leaves exactly at noon and reaches India at 01:00 am. On his return journey, he takes the same route as before, but halts at Boston for one hour less than his previous halt there. He then proceeds to Frankfurt.

What was X’s average speed for the entire journey?

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

A thief, after committing the burglary, started fleeing at 12:00 noon, at the speed of 60 kmph. He was then chased by a policeman X. X started the chase 15 minutes after the thief had started, at a speed of 65 kmph.

### Comprehension

**Directions for questions: Read the information given below and answer the questions that follow :**

A thief, after committing the burglary, started fleeing at 12:00 noon, at the speed of 60 kmph. He was then chased by a policeman X. X started the chase 15 minutes after the thief had started, at a speed of 65 kmph.

CAT/1996(Quantitative Ability)

### Question. 127

Persons X, Y and Z wish to go from place A to place B, which are separated by a distance of 70 km. All the three persons start off together from A, with X and Y going by Luna at a speed of 20 kmph. X drops Y somewhere along the way and returns to pick up Z, who has already started walking towards B at a speed of 5 kmph. Y, after being dropped by X, starts walking towards B at a speed of 5 kmph. In this manner, all three of them reach B at the same time.

How much distance is covered by Z on foot?

CAT/1996(Quantitative Ability)

### Question. 128

Persons X, Y and Z wish to go from place A to place B, which are separated by a distance of 70 km. All the three persons start off together from A, with X and Y going by Luna at a speed of 20 kmph. X drops Y somewhere along the way and returns to pick up Z, who has already started walking towards B at a speed of 5 kmph. Y, after being dropped by X, starts walking towards B at a speed of 5 kmph. In this manner, all three of them reach B at the same time.

What is the total distance travelled by x?

CAT/1996(Quantitative Ability)

### Question. 129

Persons X, Y and Z wish to go from place A to place B, which are separated by a distance of 70 km. All the three persons start off together from A, with X and Y going by Luna at a speed of 20 kmph. X drops Y somewhere along the way and returns to pick up Z, who has already started walking towards B at a speed of 5 kmph. Y, after being dropped by X, starts walking towards B at a speed of 5 kmph. In this manner, all three of them reach B at the same time.

How long does it take them to go from A to B?

CAT/1996(Quantitative Ability)

### Question. 131

A man travels from A to B at a speed of x kmph. He then rests at B for x hours. He then travels from B to C at a speed of 2x kmph and rests at C for 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hours. If distances A-B, B-C, C-D are all equal to 12 km, the time for which he rested at B could be

CAT/1996(Quantitative Ability)

### Question. 133

In a mile race, Akshay can be given a start of 128 metres by Bhairav. If Bhairav can give Chinmay a start of 4 metres in a 100 metres dash, then who out of Akshay and Chinmay will win a race of one and a half mile, and what will be the final lead given by the winner to the loser? (one mile is 1600 metres)

CAT/1995(Quantitative Ability)

### Question. 135

A and B are running along a circular course of radius 7 km in opposite directions such that when they meet they reverse their directions and when they meet A will run at the speed of B and vice-versa. Initially, the speed of A is thrice the speed of B. Assume that they start from M0 and they first meet at M_{1} , then at M_{2} , next at M_{3} , and finally at M_{4}

What is the shortest distance between M_{1} and M2 ?

CAT/1995(Quantitative Ability)

### Question. 136

A and B are running along a circular course of radius 7 km in opposite directions such that when they meet they reverse their directions and when they meet A will run at the speed of B and vice-versa. Initially, the speed of A is thrice the speed of B. Assume that they start from M0 and they first meet at M_{1} , then at M_{2} , next at M_{3} , and finally at M_{4}

What is the shortest distance between M_{1} and M_{3} along the course?

CAT/1994(Quantitative Ability)

### Question. 137

Two towns A and B are 100 km apart. A school is to be built for 100 students of town B and 30 students of town A. Expenditure on transport is Rs 1.20 per km per student. If the total expenditure on transport by all 130 students is to be as small as possible, then the school should be built at

CAT/1994(Quantitative Ability)

### Question. 138

One man can do as much work in one day as a woman can do in 2 days. A child does one third the work in a day as a woman. If an estate-owner hires 39 pairs of hands, men, women and children in the ratio 6 : 5 : 2 and pays them in all Rs 1113 at the end of the days work. What must be the daily wage of a child, if the wages are proportional to the amount of work done?

CAT/1994(Quantitative Ability)

### Question. 139

A water tank has three taps A, B and C. A fills four buckets in 24 minutes, B fills 8 buckets in 1 hour and C fills 2 buckets in 20 minutes. If all the taps are opened together a full tank is emptied in 2 hours. If a bucket can hold 5 litres of water, what is the capacity of the tank?

CAT/1994(Quantitative Ability)

### Question. 140

Shyam went from Delhi to Simla via Chandigarh by car. The distance from Delhi to Chandigarh is 3/4 times the distance from Chandigarh to Simla. The average speed from Delhi to Chandigarh was half as much again as that from Chandigarh to Simla. If the average speed for the entire journey was 49 kmph. What was the average speed from Chandigarh to Simla?

CAT/1994(Quantitative Ability)

### Question. 142

Four friends start from four towns, which are at the four corners of an imaginary rectangle. They meet at a point which falls inside the rectangle, after travelling distances of 40, 50, and 60 metres. The maximum distance that the fourth could have travelled is (approximately)

CAT/1994(Quantitative Ability)

### Question. 145

The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 15 kmph, 16 kmph, 17 kmph, and 18 kmph respectively. What is the ratio of the time taken by B to time taken by D?