# Time, Speed and Distance

Time, speed, and distance, often considered the formula for motion, hold the key to your CAT exam success. Our goal at Quantifiers is to make the universe of time, speed, and distance understandable so that preparing for the CAT test may be a fun adventure. Come along as we examine the powerful trio of ideas and see how they may help you ace the CAT exam!

## Understanding Time, Speed and Distance

Before we get into the intricacies of time, speed, and distance in the CAT exam, let’s go on a trip to understand how these ideas work. Time, speed, and distance are like the language of motion, allowing us to measure and understand how objects move. They’re the tools for solving real-world problems involving travel, speed, and the passage of time.

Let’s connect the dots between time, speed, and distance and the CAT exam. Here’s why these concepts are essential to master:

• Problem Solving: Many CAT questions, especially those involving travel scenarios, require a solid understanding of time, speed, and distance.

• Data Interpretation: Time, speed, and distance concepts can pop up in data interpretation problems, where you’ll need to analyze travel data and make calculations.

• Logical Reasoning: These mathematical tools are essential for solving logical reasoning questions, where you’ll assess the speed, time, and distance implications of given situations and make logical conclusions.

At Quantifiers, we’re all about making these concepts not just comprehensible but also enjoyable. Mastering time, speed, and distance isn’t just about taking the CAT exam; it’s about enhancing your problem-solving skills, and critical thinking, and making informed decisions in various aspects of life, from planning your daily commute to interpreting data efficiently.

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## Practice Questions for CAT with Solutions

#### 1. CAT - Time, Speed & Distance

A, B and C run a race on a linear track (All 3 starting at same time). If A beats B by 20 seconds or 180 meters, B beats C by 40 seconds or 240 meters, what is the ratio of speeds of A and C ?

2 : 1

#### 2. CAT - Time, Speed & Distance

Two friends, Ram and Shyam, start at the same point, at the same time. Ram travels straight north at a speed of 10km/hr, while Shyam travels straight east at twice the speed of Ram. After 15 minutes, Shyam messages Ram that he is just passing by a large telephone tower and after another 15 minutes Ram messages Shyam that he is just passing by an old banyan tree. After some more time has elapsed, Ram and Shyam stop. They stop at the same point of time. If the straight-line distance between Ram and Shyam now is 50 km, how far is Shyam from the banyan tree (in km)? (Assume that Ram and Shyam travel on a flat surface.)

45

#### 3. CAT - Time, Speed & Distance

Everyday 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?

60

#### 4. CAT - Time, Speed & Distance

A boy starts from his home at a certain time with a certain speed to pick up his girlfriend from office at 5.00pm. One day his girlfriend left the office at 3.00 pm and start walking to home at the speed of 40 km/hr and meet the boy in the way who left his home at his usual time .They reached home 40 min earlier than their usual time. Find the speed of the boy.

200 Km/hr

#### 5. CAT - Time, Speed & Distance

After travelling 180km, driver of a train thinks if he will go by same speed then he will be late. Then he increases the speed of train by 6.5 kmph and reaches at the scheduled time. Had he covered whole of the distance at the increased speed, he would have reached early by 40 minutes. If he had travelled whole of the distance at the original speed then he would be late by 14 minutes. Find the total distance

243 Km

#### 6. CAT - Time, Speed & Distance

A and B start swimming from two ends of a 70 meter long swimming pool simultaneously at uniform speeds, The moment they reach the opposite ends , they turn back and keep on swimming. Speed of A and B is 7m/s and 3m/s respectively. How far will B be from his starting point when he meets A for the 4th time while swimming?

35 m

#### 7. CAT - Time, Speed & Distance

The reduction in the speed of an engine is directly proportional to the square of the number of bogies attached to it. The speed of the train is 100 km/hr when there are 4 bogies and 55 kmph when there are 5 bogies. What is the maximum number of bogies that can be attached to the train so that it can move?

5

#### 8. CAT - Time, Speed & Distance

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

1. 190

2. 184

3. 192

4. 180

1. 190

#### 9. CAT - Time, Speed & Distance

Two trains A and B were moving in opposite DIRECTIONSs, 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)

1. 3 : 2

2. 2 : 1

3. 5 : 3

4. 2 : 3

1. 3 : 2

#### 10. CAT - Time, Speed & Distance

Mira and Amal walk along a circular track, starting from the same point at the sometime. 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)

8

#### 11. CAT - Time, Speed & Distance

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)

1. 5.2

2. 4.6

3. 4.8

4. 4.2

3. 4.8

#### 12. CAT - Time, Speed & Distance

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: (CAT 2020)

1. 11 : 45 am

2. 10 : 45 am

3. 11 : 00 am

4. 11 : 20 am

3. 11 : 00 am

#### 13. CAT - Time, Speed & Distance

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 2020)

1. 27

2. 28

3. 26

4. 29

2. 28

#### 14. CAT - Time, Speed & Distance

Navin takes 60 mins to reach Manoj’s house. Navin leaves his house for Manoj’s house with his dog. The speed of the dog is thrice that of Navin’s. The dog reaches Manoj’s house and comes back to meet Navin and again runs towards Manoj’s house and returns to Navin and so on. When will the dog meet Navin for the third time?

52.5 mins

#### 15. CAT - Time, Speed & Distance

Train T leaves station X for station Y at 3 pm. Train S, traveling at (6/7)th of the speed of T, leaves Y for X at 5 pm. The two trains pass each other at a station Z, where the distance between X and Z is (5/8) of that between X and Y. How many hours does train T take for its journey from X to Y?

10 Hours 40 Min

#### 16. CAT - Time, Speed & Distance

Alok started one hour after Bimol from city P towards city Q and crossed Bimol at a distance of 10 km from P. After reaching city Q, Alok immediately started moving back to city P along the same route. On the way back, he again met Bimol, who still needed 1 hour and 12 minutes to reach city Q. What is the distance between city P and city Q if Alok and Bimol travelled at a constant speed throughout the journey and Alok’s speed was 5 km/hr?

30 Km

### 17. CAT - Time, Speed & Distance

Sounak, Niraj and SK need to reach the lecture hall on time which is 15 km away from their current location. They had only one bike which can accommodate maximum 2 persons at a time. Sounak came up with an idea where all of them can reach at the same time. He took SK with him on bike and asked Niraj to walk until he picks him up. Sounak dropped SK at a point and moved back to pick Niraj, SK walked the remaining distance. If both SK and Niraj walks at a speed of 10 kmph and Sounak drove at a constant speed of 30 kmph then find how much time (in minute) they took to reach the Lecture Hall.

50 mins

### 18. CAT - Time, Speed & Distance

On an upward moving escalator Amit, Sanjeev and Vicky take 10 steps, 8 steps and 5 steps respectively to reach the top. On the same upward moving escalator Amit takes 30 steps to come down from the top. Find the ratio of the time taken by Sanjeev and Vicky to reach the top.

7 : 10

### 19. CAT - Time, Speed & Distance

You travel by Delhi Metro every day from Botanical Garden, Noida to Hauz Khas, Delhi. At Hauz Khas metro station, you use an escalator to get out of the station. The escalator takes 80 seconds. One day, the escalator was not working and you walk up the escalator in 50 seconds. How many minutes does it approximately take you to walk down the working escalator?