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

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 2024:

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)?

• 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.

2. 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

3. 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

SA: SB = x/(x-45)

car B beats car C by 50 km

SB: SC = x/(x-50)

car A beats car C by 90 km

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

• Ratio, Proportions and Variations
• HCF and 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

• Quantitative Aptitude for the CAT – Sarvesh Verma.
• 2IIM (YouTube, (Link: https://www.youtube.com/watch?v=7DUDv6hdMSA )
• CAT Sample Papers and previous years questions

Part 2: CAT 2024 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

CAT 2024 Syllabus Topic: Previous Year CAT questions for Venn Diagram” (Part-1) and Venn Diagram Questions

CAT Exam 2024: 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.

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

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

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.

CAT syllabus 2024: 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 2024: 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 2024:

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)

• How to Prepare for Verbal Ability and Reading Comprehension for the CAT by Arun Sharma and Meenakshi Upadhyay
• Wren and Martin
• https://www.youtube.com/watch?v=_WH6WQrtTJw

CAT exam: References to Study (Practice)

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

Free PDFs for CAT Preparation 2024

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

Thank you! All the Best!