Ratio & Proportion questWhich are the most repeating Ratioions on the CAT exam are crucial component of the Arithmetic section. These questions ask candidates about fundamental concepts of ratios and proportions. The difficulty of these questions typically ranges from easy to moderate, making them essential for aspirants to master.

**Properties of Ratio & Proportion for CAT?**

**Unchanged Ratio:** If the numerator and denominator of a ratio are divided by the same number, the ratio remains the same.

**Comparison: **Two ratios can be compared by equating their denominators and then comparing the values of their numerators.

**Fraction Ratio: **The ratio of two fractions can be Known as ratio of two integers.

**Ratio & Proportion Tricks for the CAT Exam**

**Simplify and Identify:**Identify the given ratio in the problem and simplify it by dividing both parts by their highest common factor to solve the calculation easily.**Problem Understanding**: Carefully read the problem to understand what information is provided and what is being asked give extra attention to words like Not, Other, Except etc.**Don't forget the basics**: Revise your understanding of basic concepts and formulas related to ratios and proportions.

**Types of Ratio & Proportions for the CAT Exam**

- Compounded Ratio
- Duplicate Ratio
- Reciprocal Ratio
- Ratio of equalities
- Ratio of Inequalities

**Best Ratio and Proportion questions for the CAT exam**

**Q 1.** In the PMO Office, the number of people aged 57 years and above is 30 and there are at most 39 people whose ages are below 57 years. The average age of all the people in the office is 44 years. What is the largest possible average age, in years, of the people whose ages are below 57 years?

A. 35

B. 36

C. 37

D. 34

**Level: Easy**

**Answer:** Option D

**Q 2**. In the PMO Office, the number of people aged 57 years and above is 30 and there are at most 39 people whose ages are below 57 years. The average age of all the people in the office is 44 years. What is the largest possible average age, in years, of the people whose ages are below 57 years?

A. 35

B. 36

C. 37

D. 34

**Level: Difficult**

**Answer:** Option D

**Q 3**. In January of a certain year, the average age of a Husband and Wife was 20 Years . After their first male child in January of 2020, the family’s average age decreased to 16. After their twin children were born, the family’s average age decreased to 12. What is the year and the average age of the family 5 years after the twin children were born?

A. 2029, 17 Years

B. 2030, 16 Years

C. 2028, 15 Years

D. 2029, 13 Years

**Level: Moderate**

**Answer:** Option A

**Q 4**. Indian Batting Legend, Virat Kohli played a certain number of test matches in the year 2022. The average runs scored by him increases by 1 if his first 10 matches are not considered, and decreases by 1 if his last 10 matches are not considered. If the average runs scored by him for the first 10 and the last 10 matches are 20 and 30, respectively, then the total number of matches Kohli played in 2022 is

**Level: Difficult**

**Answer:** 60

**What are the must-do Ratio and Proportion questions for the CAT exam?**

**Q 5.** Three consecutive positive integers are raised to the first, second and third powers respectively and then added. The sum so obtained is a perfect square whose square root equals the total of the three original integers. Which of the following best describes the minimum, say m, of these three integers?

[1] 1 ≤ m ≤ 3

[2] 4 ≤ m ≤ 6

[3] 7 ≤ m ≤ 9

[4] 10 ≤ m ≤ 12

**Level: Easy**

**Answer:** Option A

**Q 6 **Two sides of a triangle have lengths 10 and 20. How many integers can take the value of the third side length:

[1] 18

[2] 19

[3] 20

[4] 21

**Level: Difficult**

**Answer:** Option B

**Q 7.** At a science lab, a student was given 4 liters of a mixture of HCL and NaOH containing 20% NaOH. Out of curiosity, he added 1L of similar mixture containing 30% NaOH. He further added 1 liter of NaOH to the new mixture. What is the percentage of HCl in the resulting concoction?

A. 35%

B. 65%

C. 25%

D. 45%

**Level: Moderate**

**Answer:** Option A

**Q 8. **The average weight of a class of 10 students increased by 2 kg when Ravi left and Suri joined. After a few months, Suri left and Raghu joined. The weight of Ravi was 30 Kgs and Raghu weighed 10 Kg less than Suri. What is the difference in the final average weight of the class and the initial average weight of the class?

**Level: Easy**

**Answer: ** 1

**Q 9**. A batsman played n + 2 innings and got out on all occasions. His average score in these n+2 innings was 29 runs and he scored 38 and 15 runs in the last two innings. The batsman scored less than 38 runs in each of the first innings. In these n innings, his average score was 30 runs and lowest score was x runs. The smallest possible value of x is

A. 4

B. 3

C. 2

D. 1

**Level: Moderate**

**Answer:** Option C

**Which are the most repeating Ratio & Proportion questions in the CAT Exam**

** Q 10: **In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by

A. 2

B. 4

C. 3

D. 6

**Level: Easy**

**Answer:** Option B

** Q 11. **In a company there are three departments A,B,C. The average age of employees in A,,B and C are 48 years, 50 years, 52 years respectively.The average age of employees in A and C together is 50.5 years. The average age of employees in B and C together is 51(1/9)years.

What is the average age of employees of A,B,C taken together?

A. 50(1/9)years

B. 50(1/3)years

C. 51(1/9)years

D. 51(1/3)years

**Level: Moderate**

**Answer:** Option B

** Q 12. **The prices per liter of petrol, diesel and CNG are in the ratio 1 : 1/2 : 1/3 while the mileage of three cars A, B, C (in km/liter) are in the ratio 2 : 1 : 3/2. If petrol, diesel and CNG that cost the same amount is filled in A, B, C respectively, the distance traveled by A, B, C is on those fuel are in the ratio of

A. 4:4:9

B. 4:6:9

C. 6:6:9

D. 9:9:4

**Level: Difficult**

**Answer:** Option A

** Q 13. **Two types of coffee, X and Y, are mixed and then sold at Rs. 40 per kg. The profit is 10% if X and Y are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of X and Y are in the ratio

A. 21:25

B. 19:24

C. 18:25

D. 17: 25

**Level: Easy**

**Answer:** Option B

** Q 14. **There are two villages P and Q. The adult population of P exceeds that of Q by 100. The ratio of the number of men and women in P is 5 : 7 while that in Q is 3 : 7. Each adult in P or Q is employed or unemployed or studying. The ratios of the number of employed, unemployed and studying in P and Q are 1 : 2 : 3 and 1 : 3 : 6 respectively. The number of adults who are studying in P and Q are equal. Find the total number of women in both villages.

A. 400

B. 500

C. 600

D. 700

**Level: Easy**

**Answer:** Option D

**Find some previous year Ratio and Proportion questions from the CAT 2023**

**Find some previous year Ratio and Proportion questions from the CAT 2023**

** Q 15. **An alloy is prepared by mixing three metals A, B and C in the proportion 3 : 4 : 7 by volume. Weights of the same volume of the metals A. B and C are in the ratio 5 : 2 : 6. In 130 kg of the alloy, the weight, in kg. of the metal C is

A. 48

B. 84

C. 70

D. 96

**Level:Difficult**

**Answer:** Option B

** Q 16. **Two alcohol solutions, A and B, are mixed in the proportion 1:3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B is

A. 90%

B. 94%

C. 92%

D. 89%

**Level: Easy**

**Answer:** Option C

** Q 17. **Ravi has three alloys A, B and C with copper percentages as 36%, 50% and 60% respectively in them. In which of the following ratios could he melt the three alloys and mix them so as to get a percentage of 45% in the mixture?

A. 3:2:1

B. 4:3:2

C. 5:3:2

D. 3:4:6

**Level: Moderate**

**Answer:** Option C

** Q 18. **The cost price of 6 apples is equal to the marked price of 5 mangoes. The cost price of 5 mangoes is equal to the marked price of 2 apples. If the shopkeeper gives 2 mangoes free on the selling of 6 apples and makes a profit of 87.5%, find the profit percentage on selling 1 mango at its marked price.

A. 50

B. 40

C. 30

D. 20

**Level: Difficult**

**Answer:** Option D

** Q 19. **In a company XYZ, there are three departments, P, Q and R. The number of employees in department P is half of the number of employees in department R. The total number of employees of Q and R is 280. If 20 employees of the department R are transferred to the department Q, then the ratio of the number of employees in department P to that of Q will be the same as the ratio of the number of employees in department Q to that of department R. Find the number of employees in department R.

**Level: Moderate**

**Answer:**180

** Q 20. **Three vessels P, Q and R contain a solution of water and alcohol. The ratio of water and alcohol in vessel P and vessel Q are 2:3 and 1:4. After combining Q and R in the ratio 1:2, the resulting mixture contains the water and alcohol in the ratio 4:11. Find the percentage of water in a mixture which has P, Q and R combined in a ratio 3:5:2.

**Level: Easy**

**Answer:**28

**Which are the most difficult Ratio and Proportion questions for the CAT exam?**

**Which are the most difficult Ratio and Proportion questions for the CAT exam?**

** Q 21. **An amount of 300 is divided into three numbers such that the first number is thrice of the second number. Find the maximum possible product of all the three numbers.

**Level: Moderate**

**Answer:**750000

** Q 22. **In a class of 90 students, 35 students drink orange juice, 46 students drink apple juice and 25 students drink lemon juice. A is the maximum number of students who drink exactly 2 of the 3 drinks and B is the maximum number of students who drink all the 3 drinks. What is the ratio of A : B? It is known that all the students drink atleast one drink.

A. 2:1

B. 3:1

C. 1:1

D. 3:2

**Level: Difficult**

**Answer:** Option A

** Q 23. **Three vessels P, Q, and R contain a solution of water and alcohol. The ratio of water and alcohol in vessel P and vessel Q are 2:3 and 1:4. After combining Q and R in the ratio 1:2, the resulting mixture contains the water and alcohol in the ratio 4:11. Find the percentage of water in a mixture which has P, Q and R combined in a ratio 3:5:2.

**Level: Easy**

**Answer:**28

** Q 24. **There are 2 jars A and B. Jar A contains water and alcohol in the ratio 3:2. Jar B contains alcohol-water mixture in some ratio. When 1 unit of the mixture from jar A is mixed with 2 units of mixture from jar B, the resultant mixture contains twice as much water as alcohol. The ratio of alcohol to water in jar B is

A. 3:10

B. 3:13

C. 3:7

D. 3:17

**Level: Difficult**

**Answer:** Option C

**What are some other important CAT Arithmetic Questions with Solutions?**

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