CAT Time, Speed, Distance and Work is considered as one of the most important parts in the arithmetic section of Quantitative Aptitude. Out of 26 MCQ, 2 to 3 questions can be framed from this section. While preparing for this topic candidates are advised to solve based on concepts like relative speed, distance between two points, ratio of speed etc. Download CAT Question Papers

As per the analysis of previous year papers, the difficulty level of this topic has been rated easy to moderate by test takers. Candidates planning to appear for CAT 2021, can check the basic concepts of Time Speed & Distance, important formula, calculation shortcuts and much more. 

Basic Concepts of of Time, Speed, and Distance

• Time defines the duration of the activity of something or someone.
• Distance means the length of the space between two pints. 
• Work is the activity of someone or something.
• Speed means how fast something or someone is travelling. To find out the unit of any of them, one must know the value or unit of others. 

Calculation of Average Speed

• Average speed = Total Distance covered/ Total Time Taken
• If the distance is constant then
  • Average speed = 2xy/x+y
  • x and y are the two speeds at which the same distance has been covered

Calculation of Time and Distance

• Distance = Speed × Time
• If the distance is constant then
  • Speed will be inversely proportional to the time taken, therefore, when speed increases, time decreases and vice versa.

Calculation of Relative Speed

• Relative speed is the speed of a moving object with respect to another. 
• If 2 objects are moving in same direction then
  • Relative speed can be calculated as their difference. 

• If 2 objects are moving in opposite direction then
  • Relative speed can be calculated by adding the two speeds.

Sample Question on Relative and Increasing Speed:

Ques: Let us consider that Car X trails car Y by 50 meters and Car Y is traveling at a speed of 45km/hr. One more car i.e. Car is travelling from the opposite direction at the speed of 54km/hr. Car Z is at a distance of 220 meters from Car Y. If car A decides to overtake Car Y before cars Y and Z cross each other, what is the minimum speed at which car X must travel?

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

Correct Answer: ( 3)

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

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

Correct Answer: ( 2)

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CAT Time, Speed, and Distance Important Formulas

One can find an object's average speed if the total distance and the time is known. By following the same way, total time and distance can be found. In the below section, the primary formulas to solve questions of CAT Time, Speed, Distance are listed below. 

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CAT Sample Questions on Time, Speed, and Distance 

Some solved questions of Time, Speed, Distance and Work are given below.

Ques. A car with the length of 4m overtakes a trailer truck whose length is 20m travelling at 36km/hr within 10 seconds. What will be the speed that the car travels? 

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

Correct Answer: ( 3)

Ques. Rahul increases his speed from 20 Km/hr to 25 Km/hr and he takes 1 hour less than the time that he generally uses to cover a particular distance. Calculate the total distance covered by Rahul. 

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

Correct Answer: (2)

Ques. Two persons i.e A and B start moving from the point P towards Q. the distance of both the points are 1400 Km. Speed of A is 50 Km/hr whereas the speed of B is 20 Km/hr. Find out the distance between A and Q in the situation where Q meets B for the 22nd time. 

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

Correct Answer: (1)

Ques. In a circle, two ants i.e A and B start from a point P and the time of both of them are the same. Ant A moves clockwise whereas ant B moves anti-clockwise. Both the ants meet for the first time at 10:00 am in the situation where ant A has covered 60% of the circle. Find out the time of B after returning to the point P when A returns to P at 10:12 am?

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

Correct Answer: (1)

Ques. A boy travels by a motor boat down a river to his office and back. If The speed of the river remains unchanged and he doubles the speed of his motor boat, then the total time of his travel decreases by 75%. What will be the ratio of the original speed of the motor boat to the speed of the river?

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

Correct Answer: (2)

Ques. Vivek travels from A to B for a distance of 200 Km and at the speed of 40 Km/hr. At the same time, Ramesh starts the journey from point B at a speed of 20 Km/hr along a road which is perpendicular to AB. What is the time in which both Vivek and Ramesh will be closer to each other?

1. 4 hr
2. 3.33 hr
3. 5 hr
4. 8 hr

Correct Answer: (4)

Ques.The length of two trains A and B are 100 m and 150 m. Both are moving at one another at 54 Km/hr and 36 Km/hr respectively. Ashit is sitting on coach B1 of train A. Find out the total time taken by Ashit to completely cross train B.

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

Correct Answer: (2)

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

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

Correct Answer: (3)

Ques. There are two circular tracks i.e T1 and T2 of radii 100 m and 20 m, respectively. And both the trucks touch at a point A. Starting from A at the same time, both Umesh and Vicky are walking on track T1 and track T2 at the speed of 15 km/hr and 5 km/hr respectively. What is the total number of full rounds made by Umesh before meets Vicky again for the first time?

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

Correct Answer: ( 2)

Ques. On a straight line, there are two points i.e A and B. Hari runs from the point of A to B whereas Mohan runs from the point of B to A. After crossing each other, both Hari and Mohan reach their destinations in one and four minutes respectively. What is the ratio of Hari's speed to Mohan's speed when both of them start at the same time?

1. 2
2. 2√2
3. √2
4. 12

Correct Answer: (1)

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CAT Preparation Tips for Time, Speed, and Distance

In the below section, some tips for the preparation of CAT Time, Speed, and Distance are given below.

• Go through the basic concept and note down the important formula for each section.
• Before starting the calculation, understand carefully each question 
• Try to solve all the question form the previous year
• Give mock test daily