Miscellaneous Topics for CAT Exam 2025 for DILR, Partnership Ratios, Practice Questions for RC & PYQs - Day 27

Part 1: Quantitative Aptitude For CAT 2025

Topic: Ratios in partnership

When two or more individuals formally agree to run a business or company and decide to share profits depending on the investment, it is called a Partnership.

Partnership depends on three main factors: Investment, time, and profit/loss

Important Concept/Formula Used in Ratio and Partnerships Problems
Problems on profit Sharing

• PA: PB: PC = IA x TA: IB x TB: IC x TC

• PA, PB, and PC are profit shares of A, B and C respectively.

• IA, IB, and IC are investments made by A, B and C respectively.

• TA, TB, and TC are the time of investment of A, B and C respectively.

CAT previous years' Questions on Ratio and Partnership

Q1. Peter started a business with 20, 000. John joined him 4 months later with 30, 000. After 2 more months, Peter withdrew 5,000 of his capital and 2 more months later, John brought in 20, 000 more. At the end of the year, what should be the ratio in which they should share the profits? [CAT exam]

Solutions:
Peter invested Rs 20000 and after 6 months (4 +2), he withdrew Rs 5000 and hence his investment remains Rs 15000.
John joins after 4 months i.e. for a total of 8 months with Rs 30, 000 for the initial 4 months and then invests Rs 20000 for the next 4 months.
Therefore, the share of profit of Peter and John will be in the ratio
P: J = (20000 x 6 + 15000 x 6): (30000 x 4 + 50000 x 4)
P: J = 21: 32

Q2. A profit of Rs 144000 has to be divided among three partners Akram, Bipin and Chintan if their investments are in the ratio 3:2:7. How much Rs. Chintan get [CAT exam]

1. 84000

2. 24000

3. 36000

4. 42000

Ans: [a]
Ratio of profit = ratio of investment = 3:2 :7 (Time of investment is equal)
Share of Chintan = 7 (144000)/12 = 84000

Prerequisite

• Ratios

• Percentage

• Average

CAT 2025 QA Preparation Tips for Ratio and Partnership

In the partnership math question, If the time of investment is the same for all the partners, then the profit ratio is equal to the ratio of their respective investments.
For Passive or sleeping partners, the share is only for their investment.
Share of Active (Working) partners is for both i.e. investment as well as work.

CAT study material: References to Study Theory

• Quantitative Aptitude by R S Agrawal

• Mission CAT (YouTube: https://www.youtube.com/watch?v=QPAf9lxnPGo)

CAT study material: References to Study (Practice)

• How to Prepare for Quantitative Aptitude for CAT by Arun Sharma (7th Edition: Page No 286- 300)

• CAT Previous years questions and CAT previous year papers

• (https://bodheeprep.com/cat-question-paper-previous-years-pdf)

Part 2: DILR (Logical Reasoning and Data Interpretation) For CAT 2025

CAT preparation: Concepts Used

1. Classification based Puzzle

2. Comparison based Puzzle

Topic: Strategy to prepare Problem Solving/Puzzle (Miscellaneous CAT Questions) Part 1

CAT's previous years' questions

Comprehension:

Fuel contamination levels at each of the 20 petrol pumps P1, P2, …, and P20 were recorded as either high, medium, or low.

Contamination levels at three pumps among P1 – P5 were recorded as high.

P6 was the only pump among P1 – P10 where the contamination level was recorded as low.

P7 and P8 were the only two consecutively numbered pumps where the same levels of contamination were recorded.

High contamination levels were not recorded at any of the pumps P16 – P20.

The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded. [CAT exam 2018]

Q1. Which of the following MUST be true?

1. The contamination level at P10 was recorded as high.

2. The contamination level at P13 was recorded as low.

3. The contamination level at P20 was recorded as a medium.

4. The contamination level at P12 was recorded as high.

Q2. What best can be said about the number of pumps at which the contamination levels were recorded as a medium?

1. At most 9

2. Exactly 8

3. More than 4

4. At least 8

Q3. If the contamination level at P11 was recorded as low, then which of the following MUST be true?

1. The contamination level at P12 was recorded as high.

2. The contamination level at P15 was recorded as a medium.

3. The contamination level at P18 was recorded as low.

4. The contamination level at P14 was recorded as a medium.

Q4. If the contamination level at P15 was recorded as a medium, then which of the following MUST be FALSE?

1. Contamination levels at P11 and P16 were recorded as the same.

2. Contamination level at P14 was recorded to be higher than that at P15.

3. Contamination levels at P13 and P17 were recorded as the same.

4. Contamination levels at P10 and P14 were recorded as the same.

Solution:

Tip 1: Write concrete information first

P6 was the only pump among P1 – P10 with a low contamination level.

Only P7 and P8 were the only two consecutively numbered pumps with the same levels of contamination.

Contamination levels at three pumps among P1– P5 were recorded as high i.e. P1, P3 and P5 have high Contamination levels whereas P2 and P4` will be with medium Contamination levels.

Tip 2: Draw all the possibilities

We get two possible cases for P1 to P10.

Tip 3: Eliminating the wrong possibilities

In Case I, Maximum number of H can be 8 (P1, P3, P5, P7, P8, P10, P12, P14) since high contamination cannot be in P16- P20

It is given that

H = 2L

8 = 2L

⇒ L = 4, therefore M must be 20- 8- 4 = 8

Thus H + L = 3L must be multiple of 3.

The possible arrangement will be

Also, 8 H can be at P1, P3, P5, P7, P88 P10, P13, P15, then

The possible arrangement will be

In case II, H can be 6 and L will be 3;

The number of pipes with medium contamination level = 11 which is not possible.

So, Case I is true with two possibilities.

Answers:

Q1. (1)

Q2. (2)

Q3. (4)

Q4. (1)

Prerequisite

• Ranking

• Selection and Arrangement-based Puzzles

Tips and Tricks

• Write Concrete information first

• Draw all possibilities by assigning the right value

• Eliminate the wrong possibilities

References to Study (Theory)

• Verbal and Non-Verbal Reasoning by R S Agrawal

• ADDA 247 (YouTube: https://www.youtube.com/watch?v=ONuoAGsIjDE)

References to Study (Practice)

• Data Interpretation & Logical Reasoning by Gautam Puri

• CAT Previous years Papers and Sample Papers.

Part 3: VARC (Verbal Ability & Reading Comprehension) For CAT 2024

Topic: Reading Comprehension Part-4 (Solving through CAT Previous Years Questions)

CAT Previous Years Question on RC:

Comprehension:

Read the passage and answer the question based on it.

Creativity is at once our most precious resource and our most inexhaustible one. As anyone who has ever spent any time with children knows, every single human being is born creative; every human being is innately endowed with the ability to combine

and recombine data, perceptions, materials and ideas, and devise new ways of thinking and doing. What fosters creativity? More than anything else: the presence of other creative people. The big myth is that creativity is the province of great individual

geniuses. In fact, creativity is a social process. Our biggest creative breakthroughs come when people learn from, compete with, and collaborate with other people.

Cities are the true fonts of creativity... With their diverse populations, dense social networks, and public spaces where people can meet spontaneously and serendipitously, they spark and catalyze new ideas. With their infrastructure for finance, organization and trade, they allow those ideas to be swiftly actualized.

As for what staunches creativity, that's easy, if ironic. It's the very institutions that we build to manage, exploit and perpetuate the fruits of creativity — our big bureaucracies, and sad to say, too many of our schools. Creativity is disruptive; schools and organizations are regimented, standardized and stultifying.

The education expert Sir Ken Robinson points to a 1968 study reporting on a group of 1,600 children who were tested overtime for their ability to think in out-of-the-box ways. When the children were between 3 and 5 years old, 98 percent achieved

positive scores. When they were 8 to 10, only 32 percent passed the same test, and only 10 percent at 13 to 15. When 280,00025-year-olds took the test, just 2 percent passed. By the time we are adults, our creativity has been wrung out of us.

I once asked the great urbanist, Jane Jacobs, what makes some places more creative than others. She said, essentially, that the question was an easy one. All cities, she said, were filled with creative people; that's our default state as people. But some cities had more than their shares of leaders, people and institutions that blocked out that creativity. She called them "squelchers."

Creativity (or the lack of it) follows the same general contours of the great socio-economic divide - our rising inequality – that plagues us. According to my own estimates, roughly a third of us across the United States, and perhaps as much as half of us in our most creative cities - are able to do work which engages our creative faculties to some extent, whether as artists, musicians, writers, techies, innovators, entrepreneurs, doctors, lawyers, journalists or educators - those of us who work with our minds. That leaves a group that I term "the other 66 percent," who toil in low-wage rote and rotten jobs — if they have jobs at all — in which their creativity is subjugated, ignored or wasted.

Creativity itself is not in danger. Its flourishing is all around us - in science and technology, arts and culture, in our rapidly revitalizing cities. But we still have a long way to go if we want to build a truly creative society that supports and rewards the creativity of each and every one of us.

Q1. In the author's view, cities promote human creativity for all the following reasons EXCEPT that they

1. contain spaces that enable people to meet and share new ideas.

2. expose people to different and novel ideas, because they are home to varied groups of people.

3. provide the financial and institutional networks that enable ideas to become reality.

4. provide access to cultural activities that promote new and creative ways of thinking.

Ans: D

CAT Tips and Tricks: Search each statement individually in the passage.

(A), (B) and (C) are mentioned in the second paragraph

A, refers to new ideas

B, refers to a diverse population

C, refers to the infrastructure of finance

Q2. The author uses 'ironic' in the third paragraph to point out that

1. people need social contact rather than isolation to nurture their creativity

2. institutions created to promote creativity eventually stifle it

3. the larger the creative population in a city, the more likely it is to be stifled

4. large bureaucracies and institutions are the inevitable outcome of successful cities

Ans: B

CAT Tips and Tricks: See only third paragraph (Search keywords) or eliminate the irrelevant options

Option A: did not discuss in the third paragraph

Option C: Contrary statement

Option D: Irrelevant

Option B: Explicitly mentioned in the paragraph

Q3. The central idea of this passage is that

1. social interaction is necessary to nurture creativity

2. creativity and ideas are gradually declining in all societies

3. the creativity divide is widening in societies in line with socio-economic trends

4. more people should work in jobs that engage their creative faculties

Ans: A

CAT Tips and Tricks: Go through options and search in the passage

Neither B nor C is mentioned in the passage whereas D is a recommendation of the passage.

Q4. Jane Jacobs believed that cities that are more creative

1. have to struggle to retain their creativity

2. have to 'squelch' unproductive people and promote creative ones

3. have leaders and institutions that do not block creativity

4. typically, do not start off as creative hubs

Ans: C

CAT Tips and Tricks: Go through options and search in the passage

Key Words: Jane, Jacob, Creative

Q5. The 1968 study is used here to show that

1. as they get older, children usually learn to be more creative

2. schooling today does not encourage creative thinking in children

3. the more children learn, the less creative they become

4. technology today prevents children from being creative.

Ans: B

CAT Tips and Tricks: Go through options and search in the passage

Key Words: 1968 study

Prerequisite

• Good reading skills (speed)

• Understanding the comprehension

CAT 2024: References to Study (Theory)

• How to Prepare for Verbal Ability and Reading Comprehension for CAT’- by Arun Sharma & Meenakshi Upadhyay

CAT 2024: References to Study (Practice)

• Verbal Ability and Reading Comprehension for the CAT’ – by Nishit K Sinha

• CAT Previous Years Question Papers RCs

Free PDFs for CAT 2024 preparation

• Best Books for CAT Entrance Exam

• CAT 2022 Section Wise Preparation and Strategy