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Time Speed Distance Race Questions & Solutions For CAT Exam | Day 33

Time Speed Distance Race Questions & Solutions For CAT Exam | Day 33

Edited By Irshad Anwar | Updated on Oct 09, 2023 02:36 PM IST | #CAT

Hello CAT 2023 candidates, On November 26, the CAT exam 2023 for MBA admissions 2024–2026 will take place. In this CAT 2023 60-day preparation guide series of Careers360, we will discuss the strategies for day 33 that can help you prepare well and crack the CAT entrance test 2023.

This article includes time, speed, distance race questions, linear races questions for CAT exam, Introduction to Venn diagrams and Verbal analogies questions. Time, speed, distance race questions are tricky and students should do a thorough revision for the same. CAT Preparation 2023 in 60 days

Part-1: Quantitative Aptitude for CAT exam

CAT Exam Important Topic: Strategy to Prepare “Time, speed and Distance (Linear Races and Circular Races) and time speed distance race questions.

Students can also download time speed and distance questions for cat pdf

Important Concept/Formula Used/Tricks in Linear and Circular Races Concept for CAT exam & Time speed distance race questions


  1. Linear Races for CAT entrance exam:

  • A gives B a head start of x metre: it means at the start of the race B is x metre ahead of A.
  • A gives B a start of t seconds: It means A start the race after t second of B.
  • A beats B by x metres: A finishes the race before x metres than B.
  • A beats B t seconds: A finishes race t seconds before B.
  • Dead heat: All finish the race at the same time and at the same point.

2. Circular Races for CAT 2023:

Circular Track formulas-

The questions asked in this concept are as follows:

  1. When do the two participants (speeds x and y) meet first anywhere on the track (length of the track is L)?

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  • Races problems shortcuts Trick: L/(x-y), when both are moving in the same direction.
  • L/(x+y), when both are moving in the opposite direction.
  1. How many times do the participants meet?

    • Races problems shortcuts Trick: (x-y), when both are moving in the same direction.
    • (x+y), when both are moving in the opposite direction.
    • Here, x: y should be in its simplest form
  2. When do they first time meet at the starting point or ending point?
    Circular Race questions shortcuts Trick: LCM (L/x, L/y)

3. Practice Sample papers and CAT Previous year questions.

Previous Year CAT Questions On Time, Speed Distance (Linear and Circular Races):

Q1. 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 in exactly after 3 minutes. The number of rounds Mira walks in one hour is [TITA, CAT 2021, Slot 3]

Linear Races Questions for CAT Exam With Solution: Answer is 8.

Let Amal complete 1 round in x minutes and Mira complete the same in y minutes.

Since, Amal completes exactly 3 more rounds than Mira

So, 45/x – 45/y = 3

1/x−1/y = 1/15— (1)

If they walk in opposite directions, then they meet for the first time exactly after 3 minutes. It means, in 3 minutes, Amal and Mira together complete one round.

Therefore,

3/x+ 3/y= 1 — (2)

On solving both equations, we get y = 15/2

So, Meera requires 15/2 minutes to complete 1 round and hence will complete 8 rounds in an hour.

Circular Race Questions and Linear Races Questions for CAT Exam

Q2. 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 [CAT 2020, slot 2]

  1. 550
  2. 475
  3. 500
  4. 450

Time speed distance race questions with Solution: [4]

car A beats car B by 45 km

1696841508819

SA: SB = x/(x-45)

car B beats car C by 50 km

1696841509068

SB: SC = x/(x-50)

car A beats car C by 90 km

1696841508936

SA: SC = x/(x-90)

Also,

SA/ SC = (SA/ SB) x (SB/ SC)

So, x/(x-90) = [x/(x-45)] [ x/(x-50)]

On solving, we get x = 450 Kms.

Pre-requisite for time speed distance race questions

  • Ratios, Proportion and variations
  • HCF/LCM
  • Basics of Time, speed and distance

CAT study material: References to Study (Theory)

  • How to Prepare for Quantitative Aptitude for CAT by Arun Sharma (7th Edition; Pg No 335 to 339)
  • CAT Funda (YouTube, Link: https://www.youtube.com/watch?v=DgrnxHUDAqo)

References to Practice time speed distance race questions

Part-2: CAT 2023 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

CAT 2023 Syllabus Topic: Previous Year CAT questions for Venn Diagram” (Part-1) and Venn Diagram Questions

CAT Exam 2023: Important Venn Diagram Concepts

Start with Universal (A rectangle), Then a circle represents each set of values in the problem.

Where the circles overlap, the value belongs to more than one set.

1696841509275

CAT Exam:

CAT Past Year Venn Diagram Questions:

Q1. Each of the 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H is [CAT 2018]

Venn Diagram Questions for CAT:

According to information given in the question

1696841509168

According to given information:

a+ b+ c+ d+ 10 + 20 = 72

⇒ a+ b+ c+ d= 42

Also, a+ c+ 20 + 10 = b+ d+ 10+ 20

⇒ a+ c = b+ d

From above two equations;

2 (a+ c) = 42

⇒ a+ c = 21

Therefore, number of students studying H = a+ c+ 20 + 10 = 21+ 20+ 10 = 51.

CAT entrance exam: Prerequisite to Venn Diagram CAT Questions

  • Set Theory
  • Solving Linear Equations
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Tips and Tricks for CAT

  • A thorough study of the basics of Venn diagram.
  • Understand representations and Venn diagram formulas for 2-set, 3-set or 4- set Venn diagrams.
  • Practice CAT questions on Set theory and the Venn diagram.
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CAT syllabus 2023: References to Study (Theory) Venn Diagram Concepts

  • Verbal and Non-Verbal Reasoning by B S Sijwali
  • CAT LRDI by Arun Sharma
  • Mission CAT (YouTube link: https://www.youtube.com/watch?v=HF2sY7ZBDcs)
  • CAT Exam

References to Study (Practice) Venn Diagram Questions

  • Verbal and Non-Verbal Reasoning by R S Agrawal.
  • CAT Previous year Papers and Sample Papers.
  • (YouTube; Link: https://www.youtube.com/watch?v=knClqCBHTsA)

Part-3: CAT Exam Preparation 2023: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)

CAT Exam Important Topic: Strategy to Prepare “Verbal Analogies”.

CAT Important Concepts

These pairs of words share some kind of relationship that must be deciphered.

Amongst four pairs, a pair of words share the same relationship with its pair as the pair given in the question.

CAT Previous Years' Questions on Verbal Analogies

Comprehension:

During the frigid season... it's often necessary to nestle under a blanket to try to stay warm. The temperature difference between the blanket and the air outside is so palpable that we often have trouble leaving our warm refuge. Many plants and animals similarly hunker down, relying on snow cover for safety from winter's harsh conditions. The small area between the snowpack and the ground called the subnivium... might be the most important ecosystem that you have never heard of.

The subnivium is so well-insulated and stable than its temperature holds steady at around 32 degrees Fahrenheit (0 degree Celsius). Although that might still sound cold, a constant temperature of 32 degrees Fahrenheit can often be 30 to 40 degrees warmer than the air temperature during the peak of winter. Because of this large temperature difference, a wide variety of species...depend on the subnivium for winter protection.

For many organisms living in temperate and Arctic regions, the difference between being under the snow or outside is a matter of life and death. Consequently, disruptions to the subnivium brought about by climate change will affect everything from population dynamics to nutrient cycling through the ecosystem.

The formation and stability of the subnivium require more than a few flurries. Winter ecologists have suggested that eight inches of snow are necessary to develop a stable layer of insulation. Depth is not the only factor, however. More accurately, the stability of the subnivium depends on the interaction between snow depth and snow density. Imagine being under a stack of blankets that are all flattened and pressed together. When compressed, the blankets essentially form one compacted layer. In contrast, when they are lightly placed on top of one another, their insulative capacity increases because the air pockets between them trap heat. Greater depths of low-density snow are therefore better at insulating the ground.

Both the depth and density of snow are sensitive to temperature. Scientists are now beginning to explore how climate change will affect the subnivium, as well as the species that depend on it. At first glance, warmer winters seem beneficial for species that have difficulty surviving subzero temperatures; however, as with most ecological phenomena, the consequences are not so straightforward. Research has shown that the snow season (the period when snow is more likely than rain) has become shorter since l970. When rain falls on snow, it increases the density of the snow and reduces its insulative capacity. Therefore, even though winters are expected to become warmer overall from future climate change, the subnivium will tend to become colder and more variable with less protection from the above-ground temperatures.

The effects of a colder subnivium are complex... For example, shrubs such as crowberry and alpine azalea that grow along the forest floor tend to block the wind and so retain higher depths of snow around them. This captured snow helps to keep soils insulated and in turn, increases plant decomposition and nutrient release. In field experiments, researchers removed a portion. of the snow cover to investigate the importance of the subnivium's insulation. They found that soil frost in the snow-free area resulted in damage to plant roots and sometimes even the death of the plant. [CAT 2017]

Verbal Analogies questions with solution

Q1: In paragraph 1, the author uses blankets as a device to

  1. evoke the bitter cold of winter in the minds of readers.

  2. explain how blankets work to keep us warm.

  3. draw an analogy between blankets and the snowpack.

  4. alert readers to the fatal effects of excessive exposure to the cold

Ans: [C]

From the 3rd and 4th paragraphs,

draw an analogy between blankets and the snow peaks

CAT 2023:

Prerequisite

  • Synonyms/ Antonyms
  • Vocabulary

Tips and Tricks for CAT Exam

  • Analogies are simple and fall into neat, distinguishable patterns. Understand these patterns quickly.
  • Practice analogies to get familiar with the patterns. This will help to identify the relations.
  • While solving an analogy question, look for the precise relationship.
  • Analogies involve exactness and precision in their solving.
  • It is also important to substitute the pair of words into sentences in the same order as they are given in. For example, “painter creates a painting” is correct and “a painting created by a painter” is incorrect and vice-versa.

CAT exam: References to Study (Theory)

CAT exam: References to Study (Practice)

  1. Mastering the Verbal Ability for CAT by Ajay
  2. CAT Previous years Papers and Sample Papers.

Practice and remains focused; Day 34 will be posted tomorrow.

Thank you! All the Best!

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Questions related to CAT

Have a question related to CAT ?

Hello aspirant,

A bachelor's degree from an accredited university with a CGPA of at least 50% (or an aggregate of 45% for the SC, ST, and PwD/DA categories) is required in order to appear in the CAT exam in 2024. Duration and manner of degree: The course needs to last three years. The mode might be online, distant, or regular.

To know complete information you can visit our website by clicking on the link given below.

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Thank you

Hope this information helps you.

Hello student

As a self-employed individual with your own cafe, you'll need to provide documents that establish your business and work experience. Here are some documents you can prepare for your CAT application:


1. *Business Registration Documents*:

- Partnership Deed (already have)

- Business PAN Card (already have)

- FSSAI License (already have, though it's in your partner's name)

2. *Proof of Business Ownership*:

- Affidavit or declaration stating your ownership and role in the cafe

- Business registration certificate (if you have one)

3. *Proof of Work Experience*:

- A letter or certificate from your partner or co-owner confirming your work experience and role in the cafe

- A detailed resume highlighting your entrepreneurial journey and responsibilities

4. *Financial Documents*:

- Income Tax Returns (ITRs) for the last 2-3 years (if applicable)

- Balance Sheets and Profit & Loss statements for your cafe (if audited)

5. *Rental Agreement*:

- Already have, but ensure it's updated and signed


Additional tips:


- Ensure all documents are scanned and uploaded in the required format (usually PDF or JPEG)

- Keep your documents organized and easily accessible for the application process

- Be prepared to provide additional information or clarification if requested by the admission authorities


Remember to check the specific requirements for each B-school you're applying to, as they may vary. Good luck with your CAT application!

Hello aspirant,
The CAT exam syllabus is not officially prescribed, but it generally includes topics from the following sections:

1. Verbal Ability and Reading Comprehension (VARC)
2. Data interpretation and logical reasoning
3. Quantitative ability

  • Arithmetic

  • Algebra

  • Geometry and Mensuration

  • Number System

  • Modern Math

It seems unlikely that you would be able to get admission in the BTech CS branch at BIT Sindri or Mesra with a CML rank of 2058 and category rank of 433.

Key points:

1. The search results indicate that a CML (Common Merit List) rank of 2058 is quite low for admission to premier engineering colleges like BIT Sindri or NIT Mesra.

2. The cutoff ranks for BTech CS branch at these institutes are usually much higher, often in the range of 1000-2000 for the general category.

3. With a category rank of 433, you may have a better chance of getting admission in the reserved category quota, but the competition is still quite high.

4. The search results do not provide specific cutoff details for BIT Sindri or NIT Mesra, but the general trend suggests your current ranks may not be sufficient for the CS branch in these institutes.

My advice would be to:

1. Check the latest cutoff ranks and admission criteria on the official websites of BIT Sindri and NIT Mesra.

2. Explore other options like state-level engineering colleges or NITs where your current ranks may have a better chance of securing admission.

3. Consider improving your performance in the next attempt of the entrance exam to increase your chances of getting into your desired BTech program.



For VARC, read daily from diverse sources (newspapers, novels, journals) to improve comprehension and vocabulary. Practice RC passages and verbal ability questions regularly. For DILR (Data Interpretation and Logical Reasoning) and QA (Quantitative Aptitude), solve previous years' papers and take mock tests to identify weak areas. Join a coaching institute or online courses for guidance and stay consistent with your study schedule. Review and analyze your performance in mocks to understand mistakes and improve. Maintain a positive mindset and stay disciplined in your preparation.

View All

1-radian measures 600. (True/False)

Option: 1

True


Option: 2

False


$111111^2$ = 

Option: 1

123456654321


Option: 2

123454321


Option: 3

123454321


Option: 4

12345654321


1111112 =___________ 

Option: 1

 123456654321


Option: 2

1234554321


Option: 3

123454321


Option: 4

12345654321


159702 is divisible by

Option: 1

7


Option: 2

9


Option: 3

11


Option: 4

6


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What best can be said about the number of satellites serving C? 

Option: 1

Must be between 450 and 725 

 


Option: 2

Cannot be more than 800 
 


Option: 3

Must be between 400 and 800 

 


Option: 4

Must be at least 100 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What is the minimum possible number of satellites serving B exclusively? 

Option: 1

100


Option: 2

200


Option: 3

500


Option: 4

250


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S? 

Option: 1

At most 475 

 


Option: 2

Exactly 475 
 


Option: 3

At least 475 

 


Option: 4

No conclusion is possible based on the given information 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

 If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE? 

Option: 1

The number of satellites serving C cannot be uniquely determined 

 


Option: 2

The number of satellites serving B is more than 1000 
 


Option: 3

All 1600 satellites serve B or C or S 

 


Option: 4

The number of satellites serving B exclusively is exactly 250 


2839155 is divisible by

Option: 1

2


Option: 2

7


Option: 3

55


Option: 4

None of the above


'a' for which x^{2}-ax+9= 0 can be written as square of a linear factor is

Option: 1

6


Option: 2

-6,6


Option: 3

\left ( 6,\infty \right )


Option: 4

\left ( -\infty,-6 \right )


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