# CAT Averages Questions With Video Solutions & Formulas

Averages is one of the important topics of Arithmetic. The questions from this topic keep repeating every year in the CAT. The funda of Average are also present in other important Quant topics such as Progressions of Algebra. Practice diverse quality questions which will strengthen your fundamentals in Averages. Averages basically incude core concepts of Averages, Weighted Averages and Alligations. The average questions in CAT are a little tricky and not very difficult to solve. So ensure that you practice more questions from the concept of the averages to ace these questions in the quant section of CAT.

Practicing questions from CAT Previous Papers will help you understand the trends, change in pattern of the exam across years. 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 ace the quantitative aptitude section in the CAT exam, one must focus on key concepts such as Arithmetic, Geometry, Mensuration, Algebra, etc. Among these topics, Arithmetic has the maximum weightage in the quant section of CAT. The questions from Averages, Percentages, Ratios and Proportions, Mixtures and Allegations, Time Speed & Distance, and Time & Work come under the Arithmetic concept. Almost 30% of the question might be asked based on averages from the Arithmetic concepts.

## CAT Averages Weightage Over Past 3 Years

 Year Weightage 2023 4 2022 2 2021 2

## CAT Averages Formulas PDF

Averages are some of the essential topics in the quantitative aptitude section, and it is vital to have a clear understanding of the formulas related to them. To help the aspirants to ace this topic, we have made a PDF containing a comprehensive list of formulas, tips, and tricks that you can use to solve Profit, loss and interest questions with ease and speed. Click on the below link to download the CAT Averages formulas PDF

1. Average of n terms Formula

The average of n terms equals $$\frac{x_1+x_2+. . .+x_n}{n}$$

2. 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 questions

#### Question 1

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 2

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

## CAT 2022 Averages questions

#### Question 1

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 2

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 3

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 4

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 5

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 6

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

## CAT 2021 Averages questions

#### Question 1

Onion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg, respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, in rupees per kg, for the family over these 5 months is closest to

#### Question 2

The arithmetic mean of scores of 25 students in an examination is 50. Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being 30, then the maximum possible score of the toppers is

#### Question 3

In a football tournament, a player has played a certain number of matches and 10 more matches are to be played. If he scores a total of one goal over the next 10 matches, his overall average will be 0.15 goals per match. On the other hand, if he scores a total of two goals over the next 10 matches, his overall average will be 0.2 goals per match. The number of matches he has played is

## CAT 2020 Averages questions

#### Question 1

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 n innings. In these n innings, his average score was 30 runs and lowest score was x runs. The smallest possible value of x is

## CAT 2019 Averages questions

#### Question 1

The average of 30 integers is 5. Among these 30 integers, there are exactly 20 which do not exceed 5. What is the highest possible value of the average of these 20 integers?

#### Question 2

Ramesh and Gautam are among 22 students who write an examination. Ramesh scores 82.5. The average score of the 21 students other than Gautam is 62. The average score of all the 22 students is one more than the average score of the 21 students other than Ramesh. The score of Gautam is

## CAT 2018 Averages questions

#### Question 1

In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years?

#### Question 2

A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him is

## CAT 2017 Averages questions

#### Question 1

An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg. What is the maximum possible number of people in the group?

#### Question 2

The average height of 22 toddlers increases by 2 inches when two of them leave this group. If the average height of these two toddlers is one-third the average height of the original 22, then the average height, in inches, of the remaining 20 toddlers is

#### Question 3

A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is

## CAT 2007 Averages questions

#### Question 1

Consider the set S = {2, 3, 4, ...., 2n+1}, where n is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X - Y ?