CAT QA TIME SPEED DISTANCE QUESTIONS

A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less, it would have needed 6 hours more. The distance, in km, travelled by the train is

A bus starts at 9 am and follows a fixed route every day. One day, it travelled at a constant speed of 60 km per hour and reached its destination 3.5 hours later than its scheduled arrival time. Next day, it travelled two-thirds of its route in one-third of its total scheduled travel time, and the remaining part of the route at 40 km per hour to reach just on time. The scheduled arrival time of the bus is

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

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?

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

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

Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is

A boat takes 2 hours to travel downstream a river from port A to port B, and 3 hours to return to port A. Another boat takes a total of 6 hours to travel from port B to port A and return to port B. If the speeds of the boats and the river are constant, then the time, in hours, taken by the slower boat to travel from port A to port B is

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

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

The minor angle between the hours hand and minutes hand of a clock was observed at 8:48am

. The minimum duration, in minutes, after 8.48 am when this angle increases by 50%

 is

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

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

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]

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

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

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

Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8kmph, and at 9:40 am if he travels at 15kmph. Leaving home at 9:10 am, at what speed, in kmph, must he travel so as to reach office exactly at 10:00 am?

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

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

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

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?

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

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

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)

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

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

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

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

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

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

A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another train leaves B at 10:30 am, heading towards A at a speed of 20 km/hr. The trains meet each other at

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

In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is

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

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

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?

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]

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)

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]

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]

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]

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:

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: (TITA)

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:

Vikas and Nitish start running from two points A and B respectively and run towards each other (Nitish is faster than Vikas). At the first time they meet 100 meters away from A on the track. They continue to move in this manner and meet again 80 meters away from B on the track. Find the distance between A and B (in meter).

In a 2km race, Alexei beats Braiden by 200 m and Dev by 200 seconds. After the race has started , at any point of time in the race till Alexei finishes the race, the position of one of the three was exactly midway between the position of the other two. If K is the product of all possible speeds of Braiden then, find the value of 152K.

Three athletes Prem, Rahul and Deepak are running on a circular track in a race, in which the person who completes ‘a’ round first wins the race. In the given race, Prem beats Rahul by 139 meters and Deepak by 293 meters. Similarly, in the same race Rahul beats Deepak by 155 meters. If the length of the circular track is 695 m, then the value of a is

Jan Shatabdi express starts from Delhi for Pune at 6 AM in the morning. After travelling for 2 hours, it reaches a place x. At this moment driver reduces his speed by 20% because of which the train reaches Pune 90 minutes late of the scheduled time. If the decrease in speed was made after travelling a distance of 100 Km from x, the train would have reached Hyderabad 60 minutes late of its scheduled time. What is the distance between Delhi and Pune(in Km)?

There are two cities P and Q, such that the road to travel between them is partially uphill, partly on level ground and partly downhill. It took 3 hrs. for a bus to go from P to Q, whereas it took 40 minutes more for the same bus to come back from Q to P. Find the distance (in Km ) from P to Q, if the speed of the bus at the uphill , downhill and that on the level ground are 40km/hr. ,60km/hr. and 48km/hr. respectively.

Aman takes 210 steps to climb up an escalator moving downwards and it takes him only 70 steps to climb down the same escalator. If the escalator is stationary, how many steps would Aman take to climb up the escalator from the bottom?

Two athletes, X and Y , start running around a circular track simultaneously in the same direction. They meet for the first time after 42 minutes , During which, Athlete Y completes exactly 4 laps. If they had run in opposite directions, after how many minutes from the start would their 18th meeting have taken place? (speed of X is more than speed of Y)

Two guns are fired from a point A at an interval of 70 seconds. A man is traveling in a train towards A. He hears the second gunshot 56 seconds after he hears the first. Find the speed of the train (in m/s). [speed of sound = 330 m/sec]

Akash, Amen, and Ajay start a race from the same point in the same direction at speeds of 30 km/hour, 40 km/hour, and x km/hour, respectively. Amen starts the race 3 hours after Akash, and Ajay starts the race 4 hours after Akash. If Amen and Ajay overtake Akash at the same time, find the value of x.

A and B ran a 1200 m race. A won by 200 m. Subsequently, B challenged A to another race. This time, A started 60 m behind the starting point, while B started 50 m ahead of the starting point. By what distance will the winner win?

In a race, A beats B and C by 24 and 18 m, respectively. As soon as A finishes the race, B doubles his speed and beats C by 3 m. Find the length of the race track.

A man is stepping down a downward moving escalator. He takes 10 steps to reach the bottom. As soon as he comes down, he realizes that he had left his wallet, so he runs back with 6 times the earlier speed. Now he takes 60 steps to reach the top of the escalator. Find the number of steps on the stationary escalator.

In a race, A beats B by 300 m and B beats C by 210 m. If A beats C by 450 m, then find out by what distance (in m) A will beat D who is 33.33% faster than C.

In a race, Arhan beats Bunny by 74 m and Corey by 80 m. If it is known that Bunny's speed is 60 % higher than that of Corey, then find the distance over which the race was run (in meters)?

Every day, Sahil rides a bicycle on a road from point A to point B at a constant speed of 15 kmph. A bus travels to and fro between points A and B. Every day, he meets the bus going from B to A at a roadside restaurant. Today, Sahil started 30 minutes later than his usual time. As a result, he met the bus at a point 6 km before the restaurant. What is the speed of the bus in kmph?

Trump and Putin start running from opposite ends of a linear track. Trump's speed is thrice the speed of Putin. If Trump takes 2 seconds to reach the opposite end after meeting Putin. How much time does Putin take to reach the opposite end from the instant he started running?

A swimmer swims at 6 km/hr in still water. He swims 12 km downstream and then returns upstream in a total time of 5 hours 20 minutes. What is the speed of the current (in km/hr)?

A motorboat covers a certain distance upstream and the same distance downstream in a total of  7 hours. If the upstream speed of the boat is 75% of its downstream speed, and the speed of the stream is 1.5 km/h, what is the total distance covered by the boat?

A boat takes 42 minutes 40 seconds less to cover 96 km downstream than it takes to cover the same distance upstream. If the speed of the boat in still water is 72 km/hr, what is the speed of the stream(in meter/sec)?

A fisherman rows to an island 60 km away and returns in 5 hours. He observes that he can row 6 km with the current in the same time as it takes him to row 4 km against the current. What is the speed of the current (in km/h)?

Raman was travelling upstream in a boat when his hat accidentally fell into the river. The hat started drifting downstream with the current. After 55 minutes, Raman realized that his hat was missing and immediately turned the boat around to retrieve it. Assuming he rows at a constant speed in still water and the speed of the stream remains uniform, in how many minutes after the moment when his hat was lost, will he be able to catch up with it?

Two cyclists, Ravi and Sohan, start riding on a circular track at the same time and in the same direction. Ravi rides at a speed of 10 m/s, and Sohan rides at a speed of s m/s, where s is a natural number. If they meet at exactly two distinct points on the circular track, what is the sum of all possible values of s?

Two runners, Rani and Simran, start from different points on a circular track of length 150 meters and run in the opposite direction. Rani runs at r m/s and Simran at s m/s. They meet for the first time after 10 seconds, and for the second time after 25 seconds from the start. If Simran had started in the opposite direction, they would have met for the first time after 12.5 seconds. If Simran is faster than Rani, find Simran's speed in m/s.

Ravi and Pooja are jogging on a circular park trail, starting from the same point at the same time. When jogging in the same direction, Ravi completes exactly 4 more rounds than Pooja in 36 minutes. If they jog in opposite directions starting from the same point, they meet for the first time after 4 minutes. In how many distinct points will they meet, if both start in the same direction from the same starting point and run infinitely?

X and Y are running on a circular track of length 500 meters. Their speeds are 12.5 m/s and 10 m/s, respectively. After how many seconds will they meet again for the first time at the starting point if they are running continuously?

Aman jogs on track A at 7 km/h, and Riya jogs on track B at 6 km/h. The sum of the lengths of tracks A and B is 700 meters. While Aman completes 14 rounds of track A, Riya completes 9 rounds of track B. In how many seconds can Riya complete one round of track A?

Anita walks up an escalator. It takes her 60 seconds to reach the top when the escalator is moving upwards, and 90 seconds when the escalator is moving downwards. How much time (in seconds) would Anita take to walk up the escalator if it were not moving?

Meena and Rahul are climbing up a moving escalator that is going downwards. Meena takes 100 steps to reach the top, while Rahul takes 84 steps. Meena walks at a speed of 5 steps per second, and Rahul walks at 7 steps per second. What is the total number of steps in the escalator?

Aman is climbing up a moving escalator that is going upwards and takes 36 steps to reach the top. At the same time, Neha is coming down the same escalator. The ratio of Aman's speed to Neha's speed is 2:5. If both of them take the same amount of time to reach the opposite ends, calculate the total number of steps in the escalator.

At a mall, Neeraj and Kabir are going up on a moving escalator. Neeraj takes 60 steps to reach the top, while Kabir takes 45 steps. For every 6 steps that Neeraj takes, Kabir takes 4 steps. If the escalator is stationary, how many steps would each of them have to climb to reach the top?

Kunal and Deepak are climbing up an upward moving escalator. Kunal takes 90 steps to reach the top, while Deepak takes 140 steps. Kunal walks at a speed of 3 steps per second, and Deepak walks at 7 steps per second. If both of them were to stand still on the escalator, how much time (in seconds) would the escalator alone take to carry them to the top?

A car takes 55 minutes to travel between two cities. If its speed is reduced by 10 km/h, the journey takes 1 hour. What is the distance (in km) between the two cities?

Two delivery vans started from the same location at 9:00 AM — one drove east and the other drove south. By 10:30 AM, they were 156 km apart. If the faster van travelled 140% more distance per hour than the slower one, what was the positive difference in speed (in km/h) of both vans?

P is 31.25% faster than Q. If P gives Q a head start of 120 meters, how long should the race be so that the race ends in a dead heat?

In a 150-meter race, Rahul can beat Sohan by 30 meters, and Sohan can beat Aman by 10 meters. By how many meters can Rahul beat Aman in a 1500-meter race?

Ravi and Mohan participate in a 300-meter race. Ravi runs at a speed of 6 km/h and gives Mohan a head start of 20 meters. Despite that, Ravi finishes the race 12 seconds ahead of Mohan. How much distance(in km) Mohan will cover in 4 hours?

Two buses, Bus P and Bus Q, start at the same time from towns A and B respectively and travel toward each other. Bus P covers 20% of the total distance between A and B in 2 hours, while Bus Q covers 1/5 of the total distance in 3 hours. When Bus P has travelled 75 km, how much distance has Bus Q covered in the same time?

Three delivery drones take off from the same warehouse on the same route and deliver at the same location. Drone X takes off first. Drone Y takes off 1 minute later, and Drone Z takes off 1 minute after Drone Y. They fly at constant speeds of 6 m/s, 11 m/s, and 13.25 m/s respectively. Drone Y and Drone Z reach the delivery point at the same time. How many seconds after Drone Z reaches the delivery point does Drone X arrive?

A man travels to Jaipur, which is 840 km away from Delhi. He covers the first half of the journey by car, then spends 30 minutes reaching the metro station. He then travels one-third of the total distance by metro and finally takes an auto to cover the remaining distance. If the speeds of the car, metro, and auto are 70 km/h, 50 km/h, and y km/h respectively, what should be the minimum value of y so that he completes the entire journey in no more than 13.5 hours?

Neha usually takes 2 hours to cycle from her home to a nearby lake. One weekend, after covering 25% of the total distance, her bicycle’s chain started slipping, which reduced her speed by 20 km/h for the remaining part of the journey. As a result, she took 30 minutes longer than usual to reach the lake. What was her original speed in km/hr?

During a running race, Arjun finishes 15 meters ahead of Bharat and 90 meters ahead of Chirag. In the same race, Bharat finished 80 meters ahead of Chirag. What was the total length of the race in meters?