30+ Averages CAT Questions with Solutions Free PDF Download

Overview: Boost your CAT exam preparation with 30+ most important Averages CAT Questions with solutions. Continue reading to know more!

In the CAT exam, questions on averages consistently form a significant portion of the quantitative aptitude section, with nearly 30% of arithmetic questions involving average calculations.

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These questions not only test fundamental arithmetic skills but also your ability to interpret and analyze data swiftly and accurately. Whether it is dealing with simple averages, weighted averages, or changes in averages as new data points are added or removed, mastering this topic can significantly impact your overall CAT score.  

Practising these Averages CAT questions, including CAT previous year questions, you can significantly boost your score. Read on to know more To perform well, it's essential to understand both the basic and advanced types of CAT Averages Questions. 

What Are Averages in CAT 2026?

The averages CAT questions are also known as the arithmetic mean, which is defined as the sum of all observations divided by the number of observations. It forms the basis of many quantitative problems involving data analysis, speed, age, income, and more.

Formula:

Average=Sum of all items/Number of items

The concept often appears in variations like weighted averages and mixtures, making it essential to grasp all forms thoroughly.

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30+ Most Important Averages CAT Questions 2026 to Practice Now 

1. A class of 40 students has an average weight of 55 kg. If the weight of the teacher is included, the average increases by 0.5 kg. What is the weight of the teacher?
a) 75 kg
b) 73 kg
c) 77 kg
d) 79 kg
Correct Answer: c) 77 kg

2. The average marks of 30 students in a test is 45. Later, it was found that one student’s marks were misread as 40 instead of 50. What is the correct average?
a) 45.33
b) 46
c) 46.33
d) 44.5
Correct Answer: a) 45.33

3. The average age of 25 people in a room is 30 years. A 50-year-old person enters the room. What is the new average?
a) 31
b) 32
c) 30.8
d) 30.5
Correct Answer: c) 30.8

Read More: How to Prepare for Data Interpretation for CAT Exam

4. The average monthly salary of 10 employees is ₹40,000. If the manager’s salary is added, the average increases by ₹4,000. What is the manager’s salary?
a) ₹90,000
b) ₹88,000
c) ₹84,000
d) ₹80,000
Correct Answer: d) ₹80,000

5. The average age of three friends A, B, and C is 26 years. After 4 years, the age of A will be 30 years. What is the present average age of B and C? 
a) 27
b) 25
c) 26
d) 28
Correct Answer: a) 27

6. The average of 7 consecutive numbers is 27. What is the largest of these numbers?
a) 31
b) 32
c) 33
d) 34
Correct Answer: a) 31

7. A cricketer has a batting average of 50 after playing 20 innings. If in the next inning he scores 70 runs, what will be his new average?
a) 50.5
b) 51
c) 51.5
d) 52
Correct Answer: a) 51

8. The average of 8 numbers is 20. If one number is removed, the average becomes 19. What was the removed number?
a) 26
b) 27
c) 28
d) 29
Correct Answer: c) 28

Check: How to prepare for Quantitative Aptitude for CAT exam

9. A passenger covers 3 equal distances at speeds of 30 km/hr, 40 km/hr, and 60 km/hr. What is the average speed of the entire journey?
a) 40
b) 42
c) 45
d) 46
Correct Answer: b) 42

10. The average of the first 10 natural numbers is:
a) 5
b) 5.5
c) 6
d) 6.5
Correct Answer: b) 5.5

Moderate-Level Averages CAT Questions 2026

11. The average salary of 21 employees of a company is ₹20,000. If the manager’s salary is included, the average increases by ₹1,000. Find the manager’s salary.
a) ₹30,000
b) ₹40,000
c) ₹42,000
d) ₹35,000
Correct Answer: b) ₹42,000

12. The average age of 5 members of a family is 21 years. If the age of the father is included, the average increases by 7 years. What is the father’s age?
a) 42
b) 48
c) 50
d) 52
Correct Answer: b) 48

Check: Venn Diagram Practice Questions for CAT 2026

13. The average marks of a class of 50 students is 72. On verification, it was found that one student’s marks were entered as 27 instead of 72. Find the correct average.
a) 71
b) 71.8
c) 72.5
d) 73
Correct Answer: b) 71.8

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14. A batsman in 12 innings has an average score of 28 runs. What minimum score must he make in his 13th inning to raise his average to 30?
a) 65
b) 66
c) 68
d) 70
Correct Answer: a) 65

15. The average of 5 consecutive odd numbers is 61. What is the smallest number?
a) 57
b) 59
c) 61
d) 63
Correct Answer: a) 57

16. The average age of a group of 8 men is increased by 2 years when one of them whose age is 24 years is replaced by a new person. What is the age of the new person?
a) 38
b) 40
c) 42
d) 44
Correct Answer: b) 40

Read more: CAT Ratio and Proportion Questions

17. A man spends 1/3 of his journey at 30 km/hr, 1/3 at 60 km/hr, and 1/3 at 90 km/hr. Find the average speed of the entire journey.
a) 52.5
b) 60
c) 58.5
d) 55
Correct Answer: a) 52.5

18. The average marks of 100 students in a subject is 40. The average of the top 50 is 60. What is the average of the remaining 50 students?
a) 20
b) 22
c) 25
d) 30
Correct Answer: a) 20

19.The average age of 15 students is 15 years. One student leaves, and the average reduces by 1. What is the age of the student who left?
a) 30
b) 31
c) 32
d) 33
Correct Answer: a) 30

20. The average weight of 10 people is 50 kg. If each person is replaced by another person whose weight is 2 kg higher than the replaced one, what will be the new average?
a) 52
b) 51
c) 50
d) 54
Correct Answer: b) 52

Difficult-Level Averages CAT Questions 2026

21. The average of 11 numbers is 50. If the average of the first six is 49 and the average of the last six is 52, find the 6th number.
a) 48
b) 50
c) 52
d) 54
Correct Answer: b) 50

22. In a college, the average marks of 120 students in a subject is 35. Later, on re-examining, it is found that for 10 students, marks were taken as 45 instead of 54. Find the correct average.
a) 35.75
b) 36
c) 34.75
d) 36.25
Correct Answer: d) 36.25

23. A person covers a journey by train at 60 km/hr, by bus at 30 km/hr, and by car at 10 km/hr, each part covering an equal distance. What is his average speed for the full journey?
a) 18
b) 20
c) 22
d) 24
Correct Answer: b) 20

Click Here: Download CAT Arithmetic questions PDF with Solutions

24. The average monthly income of A, B, and C is ₹12,000, and their incomes are in the ratio 2:3:5. What is the income of C?
a) 15,000
b) 18,000
c) 19,500
d) 20,000
Correct Answer: b) 20,000

25. The average marks of A, B, and C in a test is 60. A scored 15 more than the average, B scored 10 less than A, and C scored 5 more than B. What is C’s score?
a) 60
b) 62
c) 63
d) 65
Correct Answer: c) 63

26. The average run rate of a cricket team in 8 matches is 250 runs. The average in the first four matches is 220. Find the average for the last four matches.
a) 270
b) 280
c) 290
d) 300
Correct Answer: d) 280

27. The average weight of 20 students is 45 kg. By the admission of one more student, the average weight increases by 1 kg. Find the weight of the new student.
a) 65
b) 66
c) 67
d) 68
Correct Answer: b) 66

28. The average marks of a class of 50 students is 40. If the average marks of the boys are 35 and that of the girls is 45, how many boys are there in the class?
a) 25
b) 30
c) 35
d) 20
Correct Answer: b) 30

29. The average height of 30 students is 160 cm. If the average height of 20 students is 165 cm, what is the average height of the remaining 10 students?
a) 150
b) 145
c) 140
d) 135
Correct Answer: a) 145

30. The average of 5 numbers is 30. The average of the first 3 is 27, while the 4th number is 6 more than the 5th. Find the 5th number.
a) 29
b) 30
c) 31
d) 32
Correct Answer: b) 30

31. The average of 20 numbers is 45. If two numbers, 50 and 60, are removed, what is the new average?
a) 44.5
b) 44
c) 43.5
d) 45
Correct Answer: a) 44.5

32. A man covers half his journey at 40 km/hr and the other half at 60 km/hr. Find the average speed of the total journey.
a) 48
b) 49
c) 50
d) 52
Correct Answer: c) 48

33. A group of 60 students has an average score of 75. The top 10% have an average of 90, while the remaining students have an average of 73. What is the average of the full group?
a) 75
b) 76
c) 77
d) 74
Correct Answer: a) 75

34. The average temperature of the first 10 days of June is 28°C, while that of the last 20 days is 32°C. What is the average temperature of the entire month?
a) 31°C
b) 30°C
c) 29°C
d) 28.5°C
Correct Answer: b) 30°C

35. The average age of a committee of 10 members is 40 years. A new member replaces an older one, reducing the average to 39 years. If the replaced member is 60 years old, what is the age of the newcomer?
a) 50
b) 49
c) 48
d) 47
Correct Answer: d) 49

CAT Averages Questions Weightage Over Past 3 Years

Year	Weightage
2024	7
2023	8
2022	7
2021	6

Key Concepts in Averages CAT Questions 2026

Before tackling past Averages CAT Questions, it is good to review a few key ideas about averages.

• Average Formula: The average is the sum of all numbers divided by the count of those numbers.
• Deviation Method: This method helps when adding or removing items from a group. It looks at how each new item's value differs from the original average. This difference then impacts the overall average.
• Weighted Average: Use this when different groups have different counts or importance. It involves summing the products of each value and its weight (or count), then dividing by the total weight.
• Non-Decreasing Sequence: In such a sequence, each number is either greater than or equal to the number before it. The numbers never go down.

Read More: 

Types of CAT Averages Questions to Expect in 2026

• Calculating simple averages of a data set
• Weighted averages involving different groups or quantities
• Changes in average when new data points are added or removed
• Problems involving average speed, age, income, or marks
• Missing values in sets based on average data

Why Focus on CAT Averages Questions 2026?

Over the years, CAT Averages Questions have consistently appeared in the exam often in cleverly disguised formats. Since averages are also the foundation for other arithmetic topics like mixtures, ratio, and percentages, mastering CAT Averages Questions also helps improve your performance across multiple quant areas.

Conclusion

Working through these past averages CAT questions shows that while some problems are simple, others can be quite tricky. The key to doing well is to practice a lot of different question types. Focus on understanding the core concepts and different methods like deviation and allegation.

Remember these key takeaways for your CAT preparation:

• Practice PYQs: Solving questions from CAT Previous Year (2017-23) DILR Sets with Solutions and CAT Quant PYQs (2017-23) Solution helps you recognize patterns and apply the right strategy quickly.
• Time Management: Some questions, like the non-decreasing sequence or complex quadratic problems, can take too much time. Learn to spot these and move on, saving them for later if time allows.
• Understand Different Approaches: Knowing methods like deviation and allegation can make hard questions simple.
• Review Your Basics: Make sure your understanding of ratios, percentages, and basic algebra is solid.

Keep practicing Averages CAT Questions consistently. This helps you build speed and accuracy for the CAT exam. If you are preparing for CAT 2026, consider checking out the CAT 2024 Comprehensive Batch for more detailed guidance. For CAT 2026, you can explore the Target CAT & OMETs 2026 program. With consistent effort, you can master the Quant section and achieve a high percentile.