Time Speed & Distance is one of the most important and most repeated topics in Arithmetic for CAT 2026, appearing in both standalone and data-driven Quant formats. This page provides comprehensive CAT arithmetic important questions covering relative speed, trains, boats & streams, and circular motion — all based on repeated CAT patterns and high-difficulty problem types. The focus is on building strong conceptual speed and logical accuracy for the CAT Quant section.
Q90. City A and city B are 270 km away from each other. Private cars run from city A to city B at 60 kmph and a car leaves city A for city B every 30 minutes. Red buses run from city B to city A at 45 kmph and a red bus leaves city B for city A every 45 minutes. The first car starts from city A at 8 am and the first red bus starts from city B at 9 am. How many cars will cross the first red bus till the first car reaches city B?
Q91. Two trains A and B were moving in opposite directions. The two trains completely cross each other in 2 minutes. The front end of train A crossed the rear end of train B in 40 seconds after the front ends of the trains had crossed each other. If the length of train A is 574 m, then the length of train B, in metres, is:
Q92. Namita completes exactly 2 more rounds than Namrata in 24 minutes if they start walking along a circular track starting from the same point at the same time in the same direction. They meet for the first time exactly after 4 minutes if they walk in opposite directions. If the length of the circular track is 800 meters, then the walking speed of Namrata, in km/hr, is:
Q93. Hari and Hemant start running on two different circular tracks from their respective starting points simultaneously. The radii of the two tracks are 35 meters and 105 meters respectively. Speed of Hari is 10 kmph and that of Hemant is 15 kmph. The number of full rounds made by Hari in the time in which he completes 5 rounds more than that of Hemant is:
Q94. A stretch of a straight road is parallel to a rail track. A train running on that track at a constant speed crosses two bikers from behind on the road, whose speeds are 36 kmph and 54 kmph, in 40 seconds and 50 seconds respectively. The length of the train, in meters, is:
Q95. A and B simultaneously start running from X to Y at the speeds of 9 m/s and 6 m/s respectively. A reaches Y, immediately turns back and starts running towards X. As A crosses B, at the same instant, C starts running from X towards Y at 4 m/s. B reaches Y and then turns back and starts running towards X. If the distance between X and Y is 150 meters, then the distance (from Y), in meters, of the point at which B will meet C for the first time will be:
Q96. Three friends A, B and C simultaneously start running from the same point in the same direction on a circular track of length 5 km. The speeds of A, B and C are 5 kmph, 9 kmph and 12 kmph respectively. When B and C meet for the first time at the starting point, the minimum distance along the track between the starting point and A, in km, is:
Q97. Two cars start moving from two ends of a straight path towards each other simultaneously and meet after some time. After meeting each other, the first car takes 54 minutes and the second car takes 24 minutes, respectively, to reach the opposite ends. The speeds of the two cars do not change during the entire journey. The ratio of the speed of the first car to that of the second car is:
Q98. A train travelled at two-thirds of its usual speed, and hence reached the destination 46 minutes after the scheduled time. If the train had travelled half the distance at its usual speed and the rest of the distance at double of its usual speed, the total time of travel, in minutes, would have been:
Q99. A motorcycle moving with a speed of 70 kmph is chasing a train moving with a speed of 60 kmph in the same direction. Initially the rear end of the train is at a distance of 200 km from the motorcycle. If the motorcycle chases down the train within 20 hours and 6 minutes, find the time taken (in seconds) by the same train moving at 18 kmph to cross a pole.
Q100. Two trains A and B were running in opposite directions with speeds in the ratio 6: 5 respectively. Ram was running at a speed of 10.8 km/h parallel to the railway track in the same direction as that of train B. Train A and train B took equal time to cross Ram. Also, train A and train B crossed each other in 15 seconds. If the length of train B is 180 m, then the length, in meter, of train A is:
Q101. Two runners Ram and Ravi simultaneously start running around a circular track. They run in the same direction. Ram runs at 9 m/s and Ravi runs at ‘s’ m/s. If they cross each other at exactly two points on the circular track and ‘s’ is a natural number, how many values can ‘s’ take?
Q102. Three cars – A, B and C travel at the speed of 90, 60 and 50 km/h respectively. These cars start from the same point and in the same direction. Car A and Car C started at 9 AM and 6 AM respectively. If all the three cars meet at the same place at the same time, then at what time did Car B start?
Q103. P and Q are running around a circular stadium that has three concentric running tracks of lengths 500 m, 600 m and 700 m. They run in opposite directions with initial speeds of 5 m/s and 20 m/s, respectively. Whenever they meet, they move to the next outer track and P doubles his speed whereas Q runs at half the speed in the previous track. After what time (in seconds) from the start will they meet for the third time?
Q104. Three friends A, B and C start simultaneously from city P to city Q. A rides the bike. The speed of the bike is 32 km/h and the walking speed of both B and C is 8 km/h. The distance between P and Q was 140 km. First A and B go together on the bike, A drops B on the way, goes back to pick up C who was walking towards Q and reach Q on the bike. After getting dropped, B walked towards Q and reached Q at the same time as A, C. Find the total distance (in km) covered by the bike.
Q105. Tajpur and Rajpur are 2 stations. A single track runs between them. Train A leaves every day from Tajpur at 8:00 AM and reaches Rajpur. Another train B starts from Rajpur as soon as A reaches there. B reaches Tajpur at 10:00 AM. The speed of B is four times that of A. One day, A started from Tajpur 20 minutes late as per the schedule. In order to maintain B’s right arrival time at Tajpur, both trains travel at an increased speed. If B doubles its speed, find the ratio of the new speeds of A and B.
Q106. Due to a technical snag, the speed of a train was reduced by 20%. As a result, it reached its destination 30 minutes later than its scheduled time. Instead, if the speed of the train was reduced by 25%, by how many minutes would the train have reached its destination late?
Q107. A truck leaves Delhi at 10 am and moves towards Agra at a uniform speed. A Bus leaves Agra at 12 noon and moves towards Delhi at a uniform speed which is 40% more than that of the truck. They meet at 1:12 pm at a point which is 160 km away from Delhi. What is the distance, in km, between Delhi and Agra?
Q108. Sruti and Smriti start simultaneously from the same point on a circular track. If they travel in opposite directions, they meet at 9 distinct points on the track whereas if they travel in the same direction, then they meet at ‘n’ distinct points on it where ‘n’ is a prime number. If Smriti’s speed is S% less than that of Sruti, then which of the following can be a value of S?
Q109. A boat travels 60 km upstream and 100 km downstream in 8 hours and then travels 75 km upstream and 175 km downstream in 12 hours. What is the speed (in km/h) of the boat in still water?
Q110. Binu takes 210 strides to cross a slowly moving metro train while moving in the same direction as the train. If he was moving in the opposite direction it takes him only 70 strides. If the train was stationary on the platform, how many strides would he take to stride from the front to the back of the train?
Q111. Rohan had to pick his wife from home since they had planned to go for a movie. He planned to reach home from office and leave immediately to the movie hall. The movie hall and their home were in opposite directions from Rohan’s office. Since he got delayed by 20 minutes, he asked his wife to pick an auto and come towards his office. His home was a 50-minute drive from his office. He asked her to start from her home at the moment he left his office towards his home. He picked her on the way and they managed to reach the venue just in time for the movie. If Rohan drives at an average speed of 80 km/h, find the speed (in km/h) of the auto-rickshaw.
Q112. Ajay left Hyderabad for Bengaluru at 6 AM. at 9:30 AM, Bhaskar left Hyderabad for Bengaluru at a speed that was 12 km/h more than the speed of Ajay. At 4:30 PM on the same day, the two were 91 km apart. If their cars had travelled with no halts, find the speed (in km/h) of car in which Ajay is travelling.
Q113. A swimming pool is 120 feet long. John and Terry start from the opposite ends of the pool at speeds of 5 feet/s and 4 feet/s respectively and swim for 15 minutes. How many times do they cross each other?
Q114. Vishal went from A to B at a certain speed and came back to A from B at a speed that was twice the speed at which he went from A to B. The entire journey took 5 hours. Had Vishal returned at a speed that was 25% more than the speed at which he actually returned, how long would it have taken him for the entire journey?
Q115. Ravi made an upstream journey of 15 km in a certain time. If his speed in still water was 2 km/h less and the speed of the stream was 2 km/h more, he would have taken five hours more for that journey. Find his upstream speed (in km/h).
Q116. Two motorboats, A and B are travelling to and fro in a moving river. In still water, the speed of motorboat A is 50% more than that of motorboat B. To cover ‘d’ km to and fro, motorboat A takes 20 minutes less than motorboat B. Instead, if motorboat A covers 2d km to and fro, motorboat A takes 16 minutes more than the time taken by motorboat B to cover ‘d’ km to and fro. How much time will the motorboat A takes to cover ‘d’ km to and fro?
Q117. Two friends named Ajay and Vijay simultaneously start swimming from points A and B respectively towards points B and A respectively with constant speed. On reaching points B and A respectively, they immediately turn back and swim towards their starting points with the same speed. They continue swimming this way. If their first meeting point is at a point 180 m away from A, where will be their second meeting point, if the distance between A and B is 300 m?
Q118. If Priya starts at 10 AM from her home and walks at 3 km/hr, she reaches the school 5 minutes after the first bell. If she starts at the same time but instead of walking, if she cycles at 6 km/hr, she reaches the school 5 minutes before the first bell. What must be the distance between Priya’s house and the school?
Q119. An escalator in a mall moves up from the ground floor to the first floor. If Suresh walks up the escalator while the escalator is moving, he reaches the first floor in 9 seconds. On the other hand, if he walks down the escalator while the escalator is moving up, he reaches the ground floor from the first floor in 36 seconds. If he just stands on the escalator without moving, how many seconds would he take to reach the first floor from the ground floor?
Q120. Rakesh and Rajesh simultaneously start walking around a circular garden of circumference 720 m from the same point in opposite directions. Rakesh’s speed is 8 m/s and Rajesh’s speed is 4 m/s. After they meet, they change their directions as well as speeds and walk back to the starting point. Which of the following is true?
Q121. Varun drove from his home to his office at 40 kmph in the morning. While returning he took a different path to avoid the evening traffic. This path is 10 km more than his onward journey. He drove half of the path at a speed of 30 kmph and rest at a speed of 50 kmph. His return journey took 19 minutes more than his onward journey. How much did he travel while returning from office?
Q122. In a 720 feet race, C beats B by 120 feet and B beats A by 360 feet. By what distance will C beat A?
Q123. A motorbike leaves City-1 at 11 am and moves towards City-2 at a uniform speed. A car leaves City-2 at 1 pm same day and moves towards City-1 at same uniform speed as that of the motorbike. They meet each other at 4 pm. What would be meeting time if the motor biker had driven at 20% higher speed and the car driver had driven at 20% lower speed (assume that their starting time remains unchanged)?
Q124. Ram and Shyam simultaneously start running from the same point in opposite directions along the perimeter of a circular garden of circumference 600 m. If their first point of meeting is at a distance of 240 m in a counterclockwise direction from the starting point, what would be the distance of their third meeting point from the starting point in the clockwise direction?
Q125. Arman made a journey of 80 km at a constant speed from Chandigarh to Patiala in the morning. While returning in the evening he increased his speed and took 5 hours less. In fact, he covered half of the total distance in the morning in 3 hours less time than the time taken to complete the return journey. What was his speed in the morning?
Q126. Three runners Raja, Shan and Virat participate in a race and start running simultaneously from the starting point with respective constant speeds. Raja finishes the race 280 meters ahead of Shan and 560 meters ahead of Virat, whereas Shan finishes the race 360 meters ahead of Virat. What is the length of the race?
Q127. P and Q start from points X and Y to reach Y and X respectively. P starts at 8:00 AM and meets Q at point A at 10:30 AM. Point A is 150 km away from point Y, which is half the total distance between points X and Y. If Q travels with 75% of his original speed, he will have to start half an hour early to reach point A at 10:30 AM. After how much time will P and Q meet if Q travels with his original speed and both start at same time?
Q128. A, B and C, each running at uniform speed, participate in a 600 m race. If A beats B by 240 m and B beats C by 100 m, then by how many meters does A beat C?
Q129. In a 720 feet race, C beats B by 12 seconds and B beats A by 72 seconds. Instead, had both B and C agreed to give A a head-start of 240 feet, B would have beaten A by 24 seconds. In that case, by how many seconds would C have beaten A?
Q130. A boat is moving at a constant speed against the stream whose speed is constant, too. As the speed of the boat in still water is increased by 20%, the speed of the boat in upstream movement increased by 25%. What percentage more time will be required for the boat to cover same distance in upstream journey in comparison to downstream journey with its original speed?
Q131. A train covers a certain distance in 8 hours. However, the train left 1 hr 30 minutes later than its scheduled departure time due to a technical snag. If the train increased its speed by 15 kmph and managed to reach its destination on time, find the distance the train had to travel (in km).
Q132. Ajay and Vijay start running along a circular track from the same point in the same direction with speeds 11 kmph and 7 kmph respectively. How many times do they meet before meeting for the first time at their starting point?
Q133. Rajesh takes as much time to row 9 km downstream as he takes to row 5 km upstream. He takes a total of 11.2 hours to row from point A to B and return to point A (the distance between points A and B is 36 km). How many hours would he take to row 21 km in still water?
Q134. Karan and Arjun jog on track P and Q respectively. Track P is circular track while track Q is square track. When Karan finishes one third of the track, Arjun covers 25% of the track. If Arjun’s speed is less than that of Karan by 25% and Karan takes 6 minutes to complete one round of the track P, how much time will Arjun take to complete one round of both the tracks?
Q135. A train is going from Chandigarh to Jaipur. When the train reached Panipat, the engine developed a technical snag, because of which its speed dropped to 80% of its normal speed and it reached Jaipur late by 60 minutes. Had the technical snag occurred when the train had travelled additional 50 km past Panipat towards Jaipur, the train would have reached Jaipur late by only 45 minutes. What is the speed of the train (in kmph)?
Q136. Every day, a bus leaves Delhi for Ambala and at the same instant another bus leaves Ambala for Delhi. The two buses cross each other at Karnal. Yesterday the bus leaving Delhi started late by 30 minutes, as a result of which it met the bus going in the opposite direction 12 km short of the usual meeting point. Today, the bus leaving Ambala started late by 30 minutes, as a result of which the two buses met 12 minutes later than their usual meeting time. What is the speed of the bus going from Delhi to Ambala?
Q137. Sita and Geeta are running a 200 m race. They both start from the same point at the same time. Geeta beats Sita by 10 seconds. If Sita runs twice as fast as her normal running speed, Sita beats Geeta by 15 seconds. How much head-start should Geeta give Sita so that the race ends in a dead-heat, if both run at their usual speeds?
Q138. A river flows from Jaunpur to Bharatpur. Tarun starts swimming from Jaunpur to Bharatpur. On his way, he overtakes a wooden stick flowing with the current of water at point A. After overtaking the stick, he reached Bharatpur 30 minutes later after swimming for 12 km. He immediately reversed his direction and started swimming towards Jaunpur. After swimming for 30 minutes, he again crossed the same wooden stick at point B. The distance between point A and point B is 4 km. What is Tarun’s speed of swimming in still water?
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