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30+ Averages CAT Questions with Solutions Free PDF Download
March 19, 2026
Overview: Averages CAT questions are an essential component of the Quantitative Ability (QA) section in the CAT exam. These questions test your understanding of averages, from simple arithmetic mean to more complex weighted averages, and even variations where data points change.
Key Takeaways
- Gain a clear understanding of the average (arithmetic mean), weighted averages, and how averages change with new or removed data.
- Learn tested formulas and methods that simplify calculation and improve accuracy.
- Explore a range of exam‑level examples with detailed explanations to build confidence.
- Strengthen your problem‑solving speed with shortcut techniques and intelligent approaches.
What You Will Learn in This Blog: Key formulas, important Averages CAT questions with answers, and free formula PDFs to enhance your preparation. Expert tips, strategies, and shortcuts to solve Averages CAT questions quickly and accurately.
What Are Averages in CAT 2026?
The average of the CAT questions is 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.
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 teacher's weight 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
Quantitative Ability Individual Topics Formula Sheets
| Number System Formula PDF | |
| Arithmetic Formula PDF | |
| Number Theory Formula PDF | |
| Quadratic Equation Formula PDF | |
| Inequalities Formula PDF | |
| Logarithms, Surds & Indices Formula PDF | |
| Time, Speed & Distance Formula PDF | |
| Linear Equations Formula PDF | |
| Ratio, Proportion & Variations Formula PDF | |
| Simple Interest - Compound Interest Formula PDF | |
| Profit & Loss Formula PDF |
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
Types of CAT Averages Questions to Expect in 2026
You can expect the following types of average questions in the CAT 2026 examination:
|
Type of Question |
Description |
|
Simple Average (Arithmetic Mean) |
Questions based on calculating the average of a set of numbers. |
|
Weighted Average |
Involves calculating the average when different values have different weights (importance or frequency). |
|
Changes in Average |
Problems where the average changes due to the addition or removal of values. |
|
Average of Averages |
Questions where you are required to find the average of multiple averages. |
|
Mixtures and Alligation |
Problems involving the mixing of different quantities or values and calculating the resulting average. |
|
Group Average |
Involves calculating the average of a group of people/items, often with sub-groups involved. |
|
Successive Changes in Average |
Questions about successive changes in the average are often based on adding or removing elements from a dataset. |
|
Data Interpretation with Averages |
Includes interpretation of data presented in charts, tables, or graphs with a focus on calculating averages. |
Conclusion
Remember these key points for your CAT preparation:
- Practice PYQs: Solving questions from the CAT Previous Year (2017-25) helps you recognise patterns and apply the right strategy quickly.
- Time Management: Some questions, such as non-decreasing sequence problems 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.
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Frequently Asked Questions
What types of CAT Exam Quantitative Aptitude Questions are included in the CAT exam section?
How can I prepare for the CAT Exam Quantitative Aptitude Questions of the CAT exam?
Which arithmetic topics in CAT are closely related to averages?
How significant is the topic of averages in the CAT Quant section?
What are some common traps to watch for in CAT average questions?
Lalita Vishwakarma
Content Writer
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