CAT Ratio and Proportion Questions for CAT Exam 2024 with Solutions

Overview: If you are a CAT aspirant, you must know that the CAT exam Maths questions are generally tricky and might confuse you with its conceptual questions. CAT Ratio and Proportion questions have been regularly used for the past five years.

• The QA section of the CAT exam is generally time-consuming and on the higher side of the difficulty level.
• In Ratio and Proportion CAT Questions, around 3-4 questions are directly or indirectly related to the basic concepts of this topic.
• Various shortcut formulas and tricks are used to solve these questions.

This article will answer many questions about CAT Ratio and Proportion Questions . These questions have been carefully selected based on an analysis of past year's trends in the CAT exam.

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CAT Ratio and Proportion Questions for Practice

Que 1. A tin contains a mixture of Dew and Sprite in the ratio of 7 : 3, and another tin contains Dew and Sprite in the ratio of 5 : 4. In what proportion should the solution of two tins be mixed to achieve a perfect proportion of 2 : 1 (in which Dew is 2 times that of sprite).

(a) 10: 3 
(b) 4 : 1 
(c) 3 :10 
(d) 3 : 1

Que 2. There are two containers A and B filled with mentha oil with different prices and their volumes are 140 litres and 6 mangoes for a rupee. What is the ratio of profit to the cost price? 60 litres respectively. Equal quantities are drawn from both A and B so that the oil drawn from A is poured into B, and the oil drawn from B is poured into A. The price per litre becomes equal in both A and B. How much oil is drawn from each of A and B :

(a) 40 litre
(b) 21 litre
(c) 42 litre
(d) can’t be determined

Que 3. A three digit number is such that this number itself is divisible by the sum of its digits. The sum of hundreds and unit digits is 6, while the sum of the tens and unit digits is 5. What is the ratio of unit and tens digit :

(a) 1 : 2
(b) 2 : 3
(c) 3 : 4
(d) 2 : 7

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Que 4. Sachin bought 1.5 kg fresh grapes. The ratio of water is to pulp was 4 : 1. When his naughty child crushed these grapes, then some water get wasted. Now the ratio of water to the pulp is 3 : 2. What is the total amount of crushed grapes?

(a) 0.5 kg
(b) 1 kg
(c) 0.75 kg
(d) none of these

Que 5. A man bought 9 mangoes for a rupee and sold them at 6 mangoes for a rupee. What is the ratio of profit to the cost price?

(a) 3/10
(b) 3/2
(c) 1/2
(d) none of these

Que 6. Half of the volume of Petrol and kerosene mixture of ratio 7 : 5 is converted into a mixture of ratio 3 : 1 by the substitution (or replacement) method. Meanwhile, the mixture of ratio 7 : 5 was formed from the mix of 7 : 3 by adding the Kerosene in it. If 240 litres of petrol is required for the replacement method, what is the total amount of Kerosene added to prepare the mixture of 7 : 5?

(a) 100 litres
(b) 400 litres
(c) 50 litres
(d) 200 litres

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Que 7. Sometimes, in a cinema hall, a blockbuster movie was shown. Due to the excessive demand for the show, the manager of the cinema hall increased the prices of tickets in all three categories. 25% in first class, 12.5% in special class and 40% in balcony. If the collection of one show was ₹ 218925, then find the collection from the balcony only given that the ratio of the price of a ticket (increased price) for first class, special class and balcony is 5 : 9 : 14.

(a) 109462.5
(b) 58800
(c) 14400
(d) data insufficient

Que 8. In a mixture of petrol and Kerosene petrol is only 99 litres. if this same quantity of petrol would be presented in another mixture of petrol and Kerosene where total volume would be 198 litres less than the actual mixture then the concentration of petrol in the actual mixture would have been 13.33% point less than that of the new mixture. What is the concentration of petrol in actual mixture?

(a) 20%
(b) 16.66%
(c) 26.66%
(d) 8.33%

Que 9. A drum of 20 litres is filled with milk. A milkman has only two measuring vessels of 3 litres and 5 litres without any calibration. He has to measure four litres of milk for a customer without using any other vessel. Minimum how many operations are required for this work, where an operation is counted if the milk is transferred from one vessel to another vessel?

(a) 5
(b) 6
(c) 8
(d) 11

Que 10. The ages of Vinay, Varsha, Veera and Vikram are in arithmetic progression but not in order. The ratio of ages of Vinay and Varsha is 6 : 5, and Veera to Vikram is 7 : 8. Two years later, the age of Varsha and Vikram will be 2 : 3. Find the ratio of ages of Vinay and Veera:

(a) 7 : 6
(b) 5 : 8
(c) 6 : 7
(d) 8 : 9

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Que 11. A container is filled with a mixture of milk and water. The ratio of milk and water is the same. Bobby and Sunny increase the concentration to 60%. Bobby adds the milk, and Sunny replaces the mixture with milk. What is the percentage of milk added by Bobby to that of milk replaced by Sunny :

(a) 100%
(b) 120%
(c) 133.33%
(d) None of these

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Que 12. There are two vessels, A and B, containing 25 litres each of pure milk and pure water, respectively. 5 litres of milk from A is taken and poured into B, then 6 litres of mixture from B is taken and poured into A. What is the ratio of water in A and B respectively:

(a) 4 : 5
(b) 1 : 4
(c) 5 : 4
(d) 2 : 3

Que 13. The ratio of age between A and B is 6 : 5, and the age of C and D is 9 times that of B. Age of F is less than A but greater than B. The ratio of ages between B and E is 2 : 3; also, the age of A is 3 years less than E. What is the ratio of ages of A and F if all the ages are in integers?

(a) 12 : 11
(b) 9 : 7
(c) 24 : 19
(d) 12 : 13

Que 14. The ratio of students in a coaching preparing for B.Tech and MBA is 4 : 5. The ratio of fees collected from each of B. Tech and MBA student is 25 : 16. If the total amount collected from all the students is 1.62 lakh, what is the total amount collected from only MBA aspirants?

(a) ₹ 62000
(b) ₹ 72000
(c) ₹ 80000
(d) none of these

Que 15. The cost of the marble varies directly with the square of its weight. Marble is broken into 3 parts whose weights are in the ratio 3 : 4 : 5. If marble had been broken into three equal parts by weight, then there would have been a further loss of ₹ 1800. What is the actual cost of the original (or unbroken) marble?

(a) ₹ 3600
(b) ₹ 10800
(c) ₹ 2160
(d) none of these

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Download CAT Ratio and Proportion Questions Solutions PDF

Tips for CAT Ratio and Proportion Questions

The CAT exam preparation requires a strategic approach, especially when tackling Ratio and Proportion CAT questions. These questions are a staple in the Quantitative Ability section and can be aced with the right techniques. Here are some crucial tips to follow before you start practising Ratio and Proportion questions for the CAT exam

1. The Basics of Ratio & Proportion

Before diving into profit and loss CAT questions for practice, ensure you have a solid understanding of the fundamental concepts:

• Ratio: A ratio is a way to compare two quantities by division. Understand how to simplify and interpret ratios.
• Proportion: Proportion refers to the equality of two ratios. Learn how to solve problems involving proportions.

2. Memorize Key Formulas

Familiarize yourself with key formulas and properties related to ratios and proportions:

• The ratio of A to B is expressed as A or A/B.
• If A= C, then A/B = C/D is a proportion.
• Cross multiplication: If A/B = C/D, then AD = BC.
• Compound ratios: Combine multiple ratios into a single ratio.

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3. Practice Simplification

Get comfortable with simplifying ratios:

• Reduce ratios to their simplest form.
• Convert complex fractions into simpler ratios.

5. Use Varied Practice Sources

Practice CAT Ratio and Proportion questions. questions from various CAT preparation books like Arun Sharma, Nishit Sinha, etc.

6. Analyze Previous Year Papers

Review CAT previous year papers to understand the type and difficulty level of Ratio and Proportion CAT questions appearing in the exam. This will give you a better idea of what to expect.

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Conclusion

To have a solid grasp onto CAT Ratio and Proportion questions for CAT exam requires a blend of conceptual understanding, strategic practice, and time management. By practising the right questions and following the best strategy, you'll be well-prepared to face any Ratio and Proportion questions that come your way.

Ratio and proportion CAT questions require conceptual understanding and practical application. By mastering these topics, you can enhance your problem-solving skills and perform better in the quantitative section of the CAT exam.

Practice diligently and apply the concepts to various problems to build confidence and proficiency. Remember, consistently working on CAT Ratio and Proportion Questions will improve your accuracy and boost your speed, giving you an edge over other test-takers.

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