CAT Time Distance Work Questions & Solutions

A sample of real CAT Time Distance Work past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 99 Time Distance Work questions in all — sign up free to practise them timed.

1. Q1.CAT 2025

   Shruti travels a distance of 224 km in four parts for a total travel time of 3 hours. Her speeds in these four parts follow an arithmetic progression, and the corresponding time taken to cover these four parts follow another arithmetic progression. If she travels at a speed of 960 meters per minute for 30 minutes to cover the first part, then the distance, in meters, she travels in the fourth part is

   • 76800

   • 112000

   • 96000

   • 86400

2. Q2.CAT 2023

   Brishti went on an 8-hour trip in a car. Before the trip, the car had travelled a total of $x$ km till then, where $x$ is a whole number and is palindromic, i.e., $x$ remains unchanged when its digits are reversed. At the end of the trip, the car had travelled a total of 26862 km till then, this number again being palindromic. If Brishti never drove at more than 110 km/h, then the greatest possible average speed at which she drove during the trip, in km/h, was

   • 110

   • 90

   • 100

   • 80

3. Q3.CAT 2022

   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

   • 4

   • 12

   • 8

   • 6

4. Q4.CAT 2020

   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 total 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

   • 29

   • 26

   • 28

   • 27

5. Q5.CAT 2019

   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?

   Answer: 48

6. Q6.CAT 2018

   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

   • 2 : 7

   • 2 : 9

   • 1 : 2

   • 1 : 4

7. Q7.CAT 2008

   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

   • 6 : 15 am

   • 6 : 30 am

   • 6 :45 am

   • 7 : 00 am

   • 7 : 15 am

8. Q8.CAT 2004

   A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is $\pi$ r during the first 30 seconds, $\pi$ r/2 during next one minute, $\pi$ r/4 during next 2 minutes, $\pi$ r/8 during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round?

   • 4

   • 8

   • 16

   • 32

9. Q9.CAT 2001

   At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hr less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 miles round trip, the downstream 12 miles would then take only 1 hr less than the upstream 12 miles. What is the speed of the current in miles per hour?

   • $\frac{7}{3}$

   • $\frac{4}{3}$

   • $\frac{5}{3}$

   • $\frac{8}{3}$

10. Q10.CAT 1999

    Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6:30 am and travels at 50km per hour towards Baroda situated 100 kms away. At 7:00 am Howrah - Ahmedabad express leaves Baroda towards Ahmedabad and travels at 40 km per hour. At 7:30 Mr. Shah, the traffic controller at Baroda realises that both the trains are running on the same track. How much time does he have to avert a head-on collision between the two trains?

    • 15 minutes

    • 20 minutes

    • 25 minutes

    • 30 minutes

11. Q11.CAT 1998

    I started climbing up the hill at 6 a.m. and reached the top of the temple at 6 p.m. Next day I started coming down at 6 a.m. and reached the foothill at 6 p.m. 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?

    • My average speed downhill was greater than that of uphill

    • At noon, I was at the same spot on both the days.

    • There must be a point where I reached at the same time on both the days.

    • There cannot be a spot where I reached at the same time on both the days.

12. Passage

    A thief, after committing the burglary, started fleeing at 12 noon, at a speed of 60 km/hr. He was then chased by a policeman X. X started the chase, 15 min after the thief had started, at a speed of 65 km/hr.
    Q12.CAT 1997

    At what time did X catch the thief?

    • 3.30 p.m.

    • 3 p.m.

    • 3.15 p.m.

    • None of these

CAT Time Distance Work previous year questions with solutions — AthenaPrep