CAT Exam Focus on Ratio, Proportion, Selection-based Puzzle Questions and Strategies for RC & PYQs- Day 26

CAT 2024 QA Preparation Tips (Ratio and proportions CAT questions)

Ratio and Proportion is an important topic in the CAT 2025 QA section, often used to test your conceptual clarity and calculation speed. It forms the base for many arithmetic questions, including time, work, and mixtures. A clear understanding of ratios helps in comparing quantities, solving real-life word problems, and interpreting data effectively. Before diving into advanced questions, make sure your basics are strong and well-practiced.

1. Comparing the quantities (a : b)

2. Dividing in the ratio by parts method

3. Learn the concept of the compounded ratio

4. Duplicate ratio of a : b is a2 : b2

5. Triplicate ratio of a b is a3: b3

6. Sub-duplicate ratio of a: b is a1/2: b1/2

7. Sub-triplicate ratio of a: b is a1/3: b1/3

8. Practice complex problems

AT Exam Focus on Ratio, Proportion, Selection-based Puzzle Questions and Strategies for RC & PYQs- Day 26

Ratio and Proportion Definition:

Ratio and Proportion are fundamental concepts used to compare quantities and establish relationships between them. They are extensively used in various fields, including arithmetic, algebra, geometry, and real-life problem-solving. We have to learn the ratio and proportion formula, the difference between ratio and proportion, and practice various ratio and proportion problems on the ratio and proportion worksheet to have more grasp on this topic.

Examples of Ratio:

1. Fruit Basket : In a fruit basket, there are 4 apples and 6 oranges. The ratio of apples to oranges is 4 : 6, which can be simplified as 2 : 3.

2. Students in a Classroom: In a classroom, there are 30 boys and 20 girls. The ratio of boys to girls is 30 : 20, which can be simplified as 3 : 2.

Examples of Proportion:

• Mixing Juice: To make a fruit juice mixture, you need to mix 2 cups of apple juice with 3 cups of orange juice. The proportion of apple juice to orange juice is 2 : 3.

• Speed and Time: A car travels 300 miles in 5 hours. To find the proportion of speed to time, we divide the distance by time, which gives us 300 miles / 5 hours = 60 miles per hour.

Previous Year Ratio And Proportion Questions

Q1. The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157 : 3, then the sum of the two numbers is:

[CAT Exam: 2019]

1. 58

2. 95

3. 85

4. 50

Answer: (D)

Let the numbers be x and y.

So, xy = 616

Also, (x³ – y³)/ (x-y)³ = 157/3

⇒ [(x - y) (x²+ y²+ xy)]/ (x-y)³ = 157/3

⇒ (x²+ y²+ xy)/ (x² + y² - 2xy) = 157/3

⇒ 3(x² + y²) + 3xy = 157(x² + y²) - 314xy

⇒ 154(x² + y²) = 317xy

⇒ 154(x² + y²) = 317 × 616

⇒ (x² + y²) = 1268

We know that, (x + y)² = x² + y² + 2xy

⇒ (x + y)² = 1268 + 2 × 616

⇒ (x + y)² = 2500

⇒ x + y = 50

Hence, the correct answer is 50.

Q2. Raju and Lalitha originally had marbles in the ratio 4 : 9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5 : 6. What fraction of her original number of marbles was given by Lalitha to Raju? [CAT exam: 2018]

1. 1/5

2. ¼

3. 7/33

4. 6/19

Solution: (C)

Let Raju and Lalitha initially have 4x and 9x marbles with them.

Lalitha gave y marbles to Raju, then

(4x+ y)/ (9x – y) = ⅚

⇒ 24x + 6y = 45x – 5y

⇒ 11y = 21x

⇒ y = 21x/11

she gave a fraction of Lalitha’s original number of marbles to Raju = (21x/11)/ 9x =7/33

Q3. If the evaluation of company A and company B are in the ratio of 3 : 4 while that of B and C are in the ratio 2 : 1, then which one of the following is a possible value of evaluation of company A if the difference of evaluation of company B and company C is multiple of 14?

1. 323 crores

2. 268 crores

3. 423 crores

4. 420 crores

Solution: (D)

A : B : C = 3 : 4 : 2 (since A : B = 3 : 4 and B : C = 2: 1)

Then the evaluation of companies A, B, and C are 3y, 4y, and 2y respectively where y is a positive integer.

According to the question:

4y- 2y = 2y is multiple of 14

Evaluation of company A = 3y is a multiple of 7 and 3.

420 satisfies this condition.

Hence, the correct answer is 420 crores.

Q4. In a bag there are coins of three denominations of Re. 1, Rs. 2 and Rs. 5. The first two are in the ratio of 2 : 3 and the last two in the ratio of 4 : 5. If the total number of coins in the bag is less than 100, the total value of coins in the bag can be Rs. _____________. Fill in the blank.

1. 107

2. 214

3. 321

4. Cannot be determined

Solution: D

In terms of number of coins, Re. 1 : Rs. 2 = 2 : 3 and Rs. 2 : Rs. 5 = 4 : 5.

∴ Re. 1 : Rs. 2 : Rs. 5 = 8 : 12 : 15

Total number of coins = 8 + 12 + 15 = 35 units

Thus the only integral possibilities below 100 coins in total are 35 coins or 70 coins.

If the total is 35, then Re. 1 = 8 coins, Rs.2 = 12 coins and Rs. 5 = 15 coins.

∴ Total Value = 8 + 24 + 75 = Rs. 107

If the total is 70, then Re.1 = 16 coins, Rs. 2 = 24 coins and Rs. 5 = 30 coins.

∴ Total Value = 16 + 48 + 150 = Rs. 214

Both the values are there in the options.

So, the content of the blank cannot be determined.

Hence, the correct answer is " Cannot be determined ".

CAT 2024: Prerequisite:

1. Fraction and comparison

2. Basics of calculations

CAT syllabus: References to Study (Theory):

1. How to Prepare for Quantitative Aptitude for CAT by Arun Sharma (7th Edition: Page No 281- 285)

2. https://www.youtube.com/watch?v=jfoJBivWlnQ (CareerRide YouTube Channel)

CAT syllabus References to Study (Practice):

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

2. CAT Previous year Papers.

3. CAT Sample Papers.

CAT 2025 DILR Preparation Tips for Logical Reasoning and Data Interpretation

Master CAT 2025 DILR by practising puzzles, caselets, and data sets daily. Focus on logical clarity, visual representation, and time management to boost accuracy and speed in complex reasoning problems. However, you should prepare all the topics prescribed in the CAT 2025 Syllabus.

CAT Previous Year Questions on Selection-based Puzzles:

Comprehension:

Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence as their performance of their first items. [CAT exam: 2019]

The following additional facts are known.

1. No composer who assigned the item to the Princess assigned any item to the Queen.

2. No composer who assigned the item to Rani assigned any item to Samragni.

3. The first performance was by Princess; this item was assigned by Badal.

4. The last performance was by Rani; this item was assigned by Gagan.

5. The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.

Q1. Which of the following is true?

1. The second performance was composed by Dyu.

2. The third performance was composed by Ashman.

3. The second performance was composed by Gagan.

4. The third performance was composed by Dyu.

Q2. Which of the following is FALSE?

1. Samragni did not perform in any item composed by Ashman.

2. Princess did not perform in any item composed by Dyu.

3. Queen did not perform in any item composed by Gagan.

4. Rani did not perform in any item composed by Badal.

Q3. The sixth performance was composed of

1. Badal

2. Ashman

3. Dyu

4. Gagan

Q4. Which pair of performances were composed by the same composer?

1. The second and the sixth

2. The first and the seventh

3. The third and the seventh

4. The first and the sixth

Solution:

Trick 1: Look for concrete information first

P, Q, R, S (Four finalists)

A, B, G, D (Four Composers)

Each dancer performed on items by two different composers.

P and Q have no composer in common.

R and S have no composer in common.

First four performances on items by four different composers and so the last four.

Items by A for two consecutive performances i.e., Dance 4 and Dance 5.

P performed 1st (Item by B) and 5th.

R Performed 4th and 8th (Item by G).

Trick 2: Using the above information, draw a table for the selection.

D (2nd or 3rd item and 6th or 7th item)

G (2nd or 3rd)

B (6th or 7th)

Trick 3: Elimination of Possibilities

Clue:

The number of performances between items assigned by each of the remaining composers was the same.

Case 1: If item 2 is composed of G which is performed by Q (From table) then item 3 will be composed of D which is to be performed by S. Then item 6 is performed by Q and must be composed by D. Item 7 is performed by S and must be composed by B.

Now Sequence of items should be B G D A A D B G which is a violation of the above condition.

Case 2: If item 3 is composed of G which is performed by Q (From table) then item 2 will be composed of D which is to be performed by S. Then item 7 is performed by Q and must be composed by D. Item 6 is performed by S and must be composed by B.

Now Sequence of items should be B D G A A B D G which is a violation of the above condition.

The number of items between B and B is 4.

The number of items between D and D is 4.

The number of items between G and G is 4.

All conditions are satisfied.

Trick 4: Draw Final Table.

Answers:

Q1. (1)

Q2. (3)

Q3. (1)

Q4. (4)

CAT preparation: Prerequisite:

• Ranking, Blood Relations, Directions

• Puzzles on Selection (Basics)

CAT syllabus 2024: References to Study (Theory):

• LRDI for CAT by Nishit K. Sinha

• https://online.2iim.com › blogs › cat-preparation-strategy

• Cat preparation-iQuanta (YouTube Channel)

CAT exam: References to Study (Practice):

• Verbal and Non-Verbal Reasoning by R S Agrawal

• CAT Previous year Papers.

• CAT Sample Papers.

CAT Exam Preparation 2024: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)

Strengthen CAT 2025 VARC by reading diverse articles daily, improving vocabulary, and practising RC passages. Focus on inference-based questions, grammar accuracy, and time-bound practice to enhance comprehension and precision. Know about the previous year's questions on Reading Comprehension for CAT 2025.

Read the passage and answer the question based on it.

Understanding where you are in the world is a basic survival skill, which is why we, like most species, come hard-wired with specialized brain areas to create cognitive maps of our surroundings. Where humans are unique, though, with the possible exception of honeybees, is that we try to communicate this understanding of the world with others. We have a long history of doing this by drawing maps – the earliest version yet discovered was scrawled on cave walls 14,000 years ago. Human cultures have been drawing them on stone tablets, papyrus, paper and now computer screens ever since.

Given such a long history of human map-making, it is perhaps surprising that is only within the last few hundred years that North has been consistently considered to be at the top. In fact, for much of human history, the north almost never appeared at the top,

according to Jerry Brotton, a map historian… “North was rarely put at the top for the simple fact that north is where the darkness comes from,” he says. “West is also very unlikely to be put at the top because the west is where the sun disappears.”

Confusingly, early Chinese maps seem to buck this trend. But, Brotton, says, even though they did have compasses at the time, that isn’t the reason that they placed north at the top. Early Chinese compasses were actually oriented to point south, which

was considered to be more desirable than the deepest darkest north. But in Chinese maps, the emperor, who lived in the north of the country was always put at the top of the map, with everyone else, his loyal subjects, looking up towards him. “In Chinese culture, the emperor looks south because it’s where the winds come from, it’s a good direction. North is not very good but you are in a position of subjection to the emperor, so you look up to him,” says Brotton.

Given that each culture has a very different idea of who, or what, they should look up to it’s perhaps not surprising that there is very little consistency in which way early maps pointed. In ancient Egyptian times, the top of the world was east, the position of

sunrise. Early Islamic maps favoured south at the top because most of the early Muslim cultures were north of Mecca, so they imagined looking up (south) towards it Christian maps from the same era (called Mappa Mundi) put east at the top, towards the Garden of Eden and with Jerusalem in the centre.

So, when did everyone get together and decide that the north was the top? It’s tempting to put it down to European explorers like Christopher Columbus and Ferdinand Magellan who were navigating by the North Star. But Brotton argues that these early explorers didn’t think of the world like that at all. “When Columbus describes the world, it is in accordance with the east being at the top,” he says “Columbus says he is going towards paradise, so his mentality is from a medieval Mappa Mundi.” We’ve got to remember, adds Brotton, that at the time, “no one knows what they are doing and where they are going.”

Q1. Which one of the following best describes what the passage is trying to do?

1. It questions an explanation of how maps are designed.

2. It corrects a misconception about the way maps are designed.

3. It critiques a methodology used to create maps

4. It explores some myths about maps

Answer: B

Trick: See the first 2-3 lines of the first paragraph and the last 2-3 lines of the last paragraph to get an idea of the passage.

Q2. Early maps did NOT put the north at the top for all the following reasons EXCEPT

1. the North was the source of darkness

2. the South was favoured by some emperors.

3. East and south were more important for religious reasons for some civilisations

4. East was considered by some civilisations to be a more positive direction

Answer: B

Trick: Search the given line in the paragraph

Option A: Given in the second paragraph (True)

Option C: From third paragraph (True)

Option D: From the third and fourth paragraph (True)

Q3. According to the passage, early Chinese maps placed north at the top because

1. the Chinese invented the compass and were aware of magnetic north

2. they wanted to show respect to the emperor.

3. the Chinese emperor appreciated the winds from the south.

4. north was considered the most desirable direction.

Answer: B

Trick: Search the question in the passage

See the third paragraph to find the answer.

CAT 2024: Prerequisite:

• Tenses and Parts of Speech

• Comprehension reading skills

CAT Tricks/Strategies to Solve the Comprehension:

• Read first then attempt

• After reading the questions, refer to the paragraph.

• Rationale (Eliminate wrong options generally with words like ‘never’, ‘always’, and ‘maybe’

CAT exam 2024: References to Study (Theory):

• How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)

CAT exam: References to Study (Practice):

• CAT Previous year Papers.

• 2iim (Web)

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Tips and Tricks to Solve Ratio and Proportion Questions in CAT 2025

Ratio and proportion questions are a staple in CAT’s Quantitative Aptitude section, and solving them quickly can significantly improve your score. The following tips with examples will help you approach these problems efficiently.

1. Simplify Ratios Before Solving

Always simplify ratios to their lowest terms before attempting to solve problems. Simplification reduces complexity and helps avoid errors during calculations. For example, if a problem gives the ratio 12:18, simplify it to 2:3. Working with 2:3 instead of 12:18 makes subsequent steps easier and faster.

2. Use Cross Multiplication for Missing Values

Cross multiplication is a powerful method to find unknown quantities in ratio equations. For instance, if ab=34\frac{a}{b} = \frac{3}{4}ba=43 and you know b=16b = 16b=16, cross multiplying gives a=34×16=12a = \frac{3}{4} \times 16 = 12a=43×16=12. This method is quicker than setting up equations or guessing values.

3. Convert Ratios into Fractions for Operations

Treat ratios as fractions when you need to add, subtract, or compare them. This simplifies calculations significantly. For example, to add ratios 2:3 and 1:4, convert them into fractions: 23+14=812+312=1112\frac{2}{3} + \frac{1}{4} = \frac{8}{12} + \frac{3}{12} = \frac{11}{12}32+41=128+123=1211. This technique is especially helpful in mixture or work problems.

4. Create Equivalent Ratios for Easier Calculations

Sometimes, scaling ratios by multiplying or dividing both terms by the same number can make calculations simpler. For example, the ratio 5:7 can be converted to 10:14 by multiplying both terms by 2. This helps when you need to compare or combine ratios with different bases.

5. Apply the Alligation Method for Mixtures

The alligation method is a quick way to solve mixture problems involving different concentrations or ratios. Suppose you mix two solutions with 20% and 50% concentrations in the ratio 3:2. Using alligation, the final concentration is calculated as

(20×3)+(50×2)3+2=60+1005=32%\frac{(20 \times 3) + (50 \times 2)}{3 + 2} = \frac{60 + 100}{5} = 32\%3+2(20×3)+(50×2)=560+100=32%

6. Break Down Complex Problems into Smaller Parts

Complex problems involving multiple ratios can be simplified by breaking them into parts. For example, if A:B = 2:3 and B:C = 4:5, find A:B:C by equalising the common term B. Scale A:B by 4:6 and B:C by 3:5, resulting in A:B:C = 8:12:15. This step-by-step approach reduces confusion and errors.

7. Practice Common Ratio-Based Word Problems

Regular practice with word problems involving ages, work, speed, and mixtures will solidify your understanding of ratios. For example, if A and B’s ages are in the ratio 3:5 and their combined age is 40 years, then A’s age is

33+5×40=15 years\frac{3}{3+5} \times 40 = 15 \text{ years}3+53×40=15 years

Study resources for CAT 2024

Top Ebooks for CAT 2025 Exam Preparation

Preparing for the CAT 2025 exam becomes easier with the right ebooks. These books cover all key areas like QA, VARC, and DILR. Easy to carry and read anywhere, ebooks help you study smartly and revise important topics at your own pace. Go through the table below to get download links for different topics.