# CAT Averages, Ratio and Proportion Questions With Solutions

Averages, Ratios and Proportions are the parts of Arithmetic. The questions from these topics have been asked frequently in the Quantitative section of the CAT exam. Averages, Ratios and Proportions are the topics which deal with real-life scenarios. Having a firm grasp of Basics & Formulas is imperative to solve the questions from these topics. If we look at the Previous year's papers of CAT Ratio, Proportions and Averages have made a recurrent appearance in the CAT Quant Section. It is a very important topic and hence must not be avoided by the aspirants. Take 3 Free CAT Mock Tests which will help you know where you currently stand, and will help you in analysing your strengths and weaknesses.

To help the aspirants ace this topic, we provide you with all the questions from CAT previous papers with detailed video solutions, which are given below, separated year-wise. One can also download all the CAT previous Questions from Averages, Ratios and Proportions in a PDF format, along with the video solution for every question.

## Averages, Ratios & Proportions Questions Weigthage Over Past 5 Years

 Year Weightage 2023 7 2022 13 2021 14 2020 5 2019 10 2018 12

CAT Ratio & Proportions - Tip 1: Questions based on this concept appear in the CAT and other MBA entrance exams every year. If you're starting the prep, firstly understand the CAT Quants Syllabus; Based on our analysis of Ratio Proportion and Variation questions in CAT Previous Years this was the CAT Ratios, Averages, and Mixtures weightage: 4-5 questions were asked from these topics (in CAT 2021).

CAT Ratio & Proportions - Tip 2: The CAT Ratio and proportion questions are Not very tough to solve. A strong foundation in this topic will help you in answering these questions with ease. Getting yourself acquainted with the basics of these concepts will help you solve the problems. Download this ratio proportion and variation questions with solutions PDF (which also includes the ratio and proportion concept PDF). Learn all the major formulae from these concepts (You can learn all the Important CAT Ratios & Proportions Formulas here). Also, do check out the ratio and proportion questions from CAT Mock tests.

## CAT Averages, Ratio and Proportion Formulas PDF

One of the important topics is Ratio and Proportion, which is essential for solving many mathematical problems. Understanding the formulas and concepts related to Ratio and Proportion can significantly improve the chances of scoring high in the CAT exam. The CAT Averages, Ratio and Proportion Formulas PDF is a valuable resource that provides a comprehensive overview of the formulas and concepts related to Ratio and Proportion. Click on the below link to download CAT Averages, Ratio and proportion formulas PDF.

1. Mixture of mixtures Formula

In a mixture of mixtures, two quantities of some mixtures are mixed to get a mixture of mixtures.

Let Mixture 1 have ingredients A and B in ratio a: b, and Mixture 2 have ingredients A and B in ratio x : y.

Now, the M unit of mixture 1 and N unit of mixture 2 are mixed to form a resultant mixture. Then, in the resultant mixture, the ratio of A and B is

$$\dfrac{Q_a}{Q_b}=\ \dfrac{M\left(\frac{a}{a+b}\right)+N\left(\frac{x}{x+y}\right)\ }{M\left(\frac{b}{a+b}\right)+N\left(\frac{x}{x+y}\right)}$$

2. Replacement of solution Formula

If a container has 'a' liters of liquid A and if 'b' liters of solution is withdrawn and is replaced with an equal volume of another liquid B and the operation is repeated for 'n' times, then after nth operation,

The final quantity of Liquid A in the container = $$\left(\ \frac{\ a-b}{a}\right)^{^n}\times\ a$$

3. Alligation Formula

Alligation Rule: This is used to find the ratio of individual components in a mixture. If two components A and B, costing Rs. X and Rs. Y individually, are mixed and the resultant mixture has an average price of Rs. Z, then the ratio of A and B in the mixture is $$\frac{Z-Y}{X-Z}$$

4. Weighted Average Formula

The weighted average of n terms equals $$\frac{w_1*x_1+ w_2*x_2+. . .+ w_n*x_n}{ w_1+ w_2+ . . . w_n}$$

## CAT 2023 Averages, Ratio and Proportion questions

#### Question 1

A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture P and replaced with same amount of cocoa powder to form a new mixture Q. If the ratio of coffee and cocoa in the mixture Q is 16 : 9, then the ratio of cocoa in mixture P to that in mixture Q is

#### Question 2

Anil mixes cocoa with sugar in the ratio 3 : 2 to prepare mixture A, and coffee with sugar in the ratio 7 : 3 to prepare mixture B. He combines mixtures A and B in the ratio 2 : 3 to make a new mixture C. If he mixes C with an equal amount of milk to make a drink, then the percentage of sugar in this drink will be

#### Question 3

The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is

#### Question 4

There are three persons A, B and C in a room. If a person D joins the room, the average weight of the persons in the room reduces by x kg. Instead of D, if person E joins the room, the average weight of the persons in the room increases by 2x kg. If the weight of E is 12 kg more than that of D, then the value of x is

#### Question 5

In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the nonmanufacturing employees is

#### Question 6

The salaries of three friends Sita, Gita and Mita are initially in the ratio 5 : 6 : 7, respectively. In the first year, they get salary hikes of 20%, 25% and 20%, respectively. In the second year, Sita and Mita get salary hikes of 40% and 25%, respectively, and the salary of Gita becomes equal to the mean salary of the three friends. The salary hike of Gita in the second year is

#### Question 7

A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is

## CAT 2022 Averages, Ratio and Proportion questions

#### Question 1

In a village, the ratio of number of males to females is 5 : 4. The ratio of number of literate males to literate females is 2 : 3. The ratio of the number of illiterate males to illiterate females is 4 : 3. If 3600 males in the village are literate, then the total number of females in the village is

#### Question 2

The average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is

#### Question 3

Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months, his monthly expense was ₹3500, and he foresees that, tenth month onward, his monthly expense will increase to ₹3700. In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be

#### Question 4

Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of ₹1752. She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744. Then the amount, in rupees, that she had spent in buying almonds is

#### Question 5

A glass contains 500 cc of milk and a cup contains 500 cc of water. From the glass, 150 cc of milk is transferred to the cup and mixed thoroughly. Next, 150 cc of this mixture is transferred from the cup to the glass. Now, the amount of water in the glass and the amount of milk in the cup are in the ratio

#### Question 6

In an election, there were four candidates and 80% of the registered voters casted their votes. One of the candidates received 30% of the casted votes while the other three candidates received the remaining casted votes in the proportion 1 : 2 : 3. If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was

#### Question 7

In an examination, the average marks of students in sections A and B are 32 and 60, respectively. The number of students in section A is 10 less than that in section B. If the average marks of all the students across both the sections combined is an integer, then the difference between the maximum and minimum possible number of students in section A is

#### Question 8

The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is

#### Question 9

A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of lemon juice and sugar syrup in the new mixture is

#### Question 10

There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then the half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container is

#### Question 11

If a and b are non-negative real numbers such that a+ 2b = 6, then the average of the maximum and minimum possible values of (a+ b) is

#### Question 12

Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is

#### Question 13

Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3 : 5. If the total number of persons in the queue is less than 300, then the maximum possible number of persons standing ahead of Pinky is