IPMAT Average Questions PDF 2027: Concepts, Tricks, Solved Examples & Practice Set

An IPMAT average question is usually a 2–3 step problem: convert the average to a total, apply the change (add/remove/replace), then divide by the new count. In this guide, you’ll learn the exact formulas, the fastest shortcuts, and practice sets with solutions for IPMAT 2027.

Download Free Study Materials for IPMAT 2027

IPMAT average questions are one such topic.

Questions based on averages are commonly used to test how quickly you can understand numbers, apply a formula, and reach the answer without wasting time.

With regular practice, IPMAT Average Questions can become one of the more manageable parts of your Quantitative Ability preparation.

This guide covers the important average concepts, formulas, solved examples, shortcuts, and practice questions you should know before the exam.

Download Free IPMAT Time, Speed and Distance Questions PDF

Practice Questions on Averages for IPMAT 2027

Try these questions without looking at the answers first.

Question 1 The average of 7 numbers is 18. What is their sum?

A) 108
B) 116
C) 126
D) 136

Question 2 The average of 5 numbers is 32. If the number 40 is added, what will be the new average?

A) 32
B) 33⅓
C) 34
D) 35

Question 3 The average age of 12 students is 15 years. If a teacher aged 36 years joins them, what is the new average age?

A) 16
B) 16.5
C) 16⅗
D) 17

Question 4 The average of 8 numbers is 24. One number, 31, is replaced by 15. Find the new average.

A) 20
B) 21
C) 22
D) 23

Question 5: The average marks of 15 students is 48, and the average marks of another 25 students is 60. Find the average marks of all the students.

A) 54
B) 55.5
C) 56
D) 57

Question 6: The average of three consecutive integers is 25. What is the largest integer?

A) 24
B) 25
C) 26
D) 27

Question 7: The average of 9 numbers is 40. If each number is increased by 5, what will be the new average?

A) 40
B) 42
C) 45
D) 50

Question 8: The average weight of 6 people is 55 kg. If a person weighing 65 kg leaves the group, what is the average weight of the remaining people?

A) 52 kg
B) 53 kg
C) 54 kg
D) 55 kg

Question 9: The average of 10 numbers is 25. If one number is excluded, the average becomes 24. Find the excluded number.

A) 30
B) 32
C) 34
D) 35

Question 10: The average of the first five positive odd numbers is:

A) 4
B) 5
C) 6
D) 7

Answers to the Practice Questions

Question	Answer
1	C) 126
2	B) 33⅓
3	C) 16⅗
4	C) 22
5	B) 55.5
6	C) 26
7	C) 45
8	A) 53 kg
9	D) 35
10	B) 5

Why Are IPMAT Average Questions 2027 Important?

The Quantitative Ability section of IPMAT requires both accuracy and speed. Averages is useful because the basic calculations are usually straightforward once you identify the right approach.

The topic can also be connected with other arithmetic concepts such as:

• Percentages
• Ratios
• Profit and loss
• Time and work
• Mixtures
• Ages
• Data interpretation
• Weighted averages

A strong understanding of averages can therefore help beyond questions that directly mention the word "average."

For students preparing for the exam, the goal should not be to learn dozens of tricks. Instead, understand the basic relationship:

Total = Average × Number of observations

This one relationship can solve a surprisingly large number of questions.

Important Average Formulas for IPMAT 2027

Before solving averages questions for IPMAT, make sure these formulas are familiar.

1. Basic Average Formula

Average = Sum of observations ÷ Number of observations

Therefore:

Sum = Average × Number of observations

And: Number of observations = Sum ÷ Average

2. Average After Adding a New Number

Suppose the average of n numbers is A.

The original total is: nA

If a new number x is added, the new average becomes: New Average = (nA + x) ÷ (n + 1)

3. Average After Removing a Number

If the average of n numbers is A and a number x is removed: New Average = (nA − x) ÷ (n − 1)

4. Average After Replacing a Number

Suppose one number x is replaced by another number y.

The change in the total is: y − x

Therefore: Change in Average = (y − x) ÷ Number of observations. This is one of the most useful shortcuts for IPMAT.

5. Average of Two Groups

Suppose Group A contains n₁ observations with average A₁, while Group B contains n₂ observations with average A₂.

The combined average is: Combined Average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂)

Do not simply take the average of A₁ and A₂ unless both groups contain the same number of observations.

Prepare with Online Lectures for IPMAT 2027

How to Solve IPMAT Average Questions 2027?

A good way to approach average questions is to follow three simple steps.

Step 1: Find the information given

Look for:

• Number of observations
• Average
• Total
• A number being added
• A number being removed
• A number being replaced

Step 2: Convert the average into a total when required

Remember:

Total = Average × Number of observations

This often makes the question much easier.

Step 3: Apply the change

If something is added, add it to the total.

If something is removed, subtract it.

If something is replaced, calculate the difference between the old and new values.

Then divide by the new number of observations if necessary.

Solved IPMAT Average Questions 2027

Question 1: The average of five numbers is 24. What is their total?

Solution:

We know: Total = Average × Number of observations

Therefore: 24 × 5 = 120 Answer: 120

This is one of the easiest types of IPMAT Average Questions, but it forms the foundation for more difficult problems.

Question 2: The average of six numbers is 18. Five of the numbers are 12, 15, 20, 17 and 21. Find the sixth number.

Solution: 

Total of all six numbers: 18 × 6 = 108

Sum of the five given numbers: 12 + 15 + 20 + 17 + 21 = 85

Therefore: Sixth number = 108 − 85 = Answer: 23

Question 3: The average age of 8 students is 16 years. When a teacher joins the group, the average becomes 19 years. What is the age of the teacher?

Solution: 

Total age of the 8 students: 8 × 16 = 128

Total age after the teacher joins: 9 × 19 = 171

Teacher's age: 171 − 128 = Answer: 43 years

Notice that we did not need any complicated calculation. We simply converted both averages into totals.

Question 4: The average of 10 numbers is 25. If one number, 43, is removed, what will be the new average?

Solution: 

Original total: 10 × 25 = 250

After removing 43: 250 − 43 = 207

There are now 9 numbers. New average: 207 ÷ 9 = Answer: 23

Question 5: The average of 7 numbers is 30. One of the numbers, 24, is replaced by 38. Find the new average.

Solution:

 Increase in total: 38 − 24 = 14

Since there are 7 numbers, the increase in the average is:

14 ÷ 7 = 2 Therefore: New average = 30 + 2: Answer: 32

Shortcut

You do not always need to calculate the entire total.

When one value is replaced:

New Average = Old Average + (New Value − Old Value) ÷ Number of observations

This shortcut can save valuable time during an exam.

Question 6:  The average marks of 20 students is 60, while the average marks of 30 students is 70. Find the average marks of all 50 students.

Solution:

Total marks of the first group:

20 × 60 = 1200

Total marks of the second group:

30 × 70 = 2100

Combined total:

1200 + 2100 = 3300

Total students:

20 + 30 = 50

Combined average:

3300 ÷ 50 = 66

Answer: 66

A common mistake is to calculate:

(60 + 70) ÷ 2 = 65

That would be incorrect because the two groups have different numbers of students.

Question 7: Average of Consecutive Numbers: Find the average of the numbers from 11 to 21.

Solution:

The numbers are consecutive.

For a set of consecutive numbers, the average is the middle number.

The middle number between 11 and 21 is:

16

Therefore:

Answer: 16

You can also verify this using the formula:

(First number + Last number) ÷ 2

= (11 + 21) ÷ 2

= 32 ÷ 2

= 16

Question 8: Average of Consecutive Even Numbers

Find the average of the first 10 positive even numbers.

The numbers are:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Average:

(2 + 20) ÷ 2

= 11

Answer: 11

For consecutive numbers with equal differences, the average is generally the middle value or the average of the first and last values.

Click to Attempt Free Mock Test for IPMAT Prep

Question 9: Average and Percentage Change

The average salary of 10 employees is ₹40,000. If every employee receives a ₹5,000 increment, what will be the new average salary?

Solution:

If the same amount is added to every observation, the average also increases by that amount.

New average:

₹40,000 + ₹5,000

= ₹45,000

Answer: ₹45,000

There is no need to calculate the total salary in this question.

Question 10: Average Based on Ages

The average age of a group of 6 people is 25 years. If a person aged 30 years leaves the group, what is the new average age?

Solution:

Original total age:

6 × 25 = 150

Age remaining:

150 − 30 = 120

Number of people remaining: 5

New average: 120 ÷ 5 = 24 years

Answer: 24 years

Shortcuts for Solving IPMAT Average Questions Faster

Speed matters in IPMAT. Once you understand the basics, these shortcuts can help you save time.

Shortcut 1: Same Number Added to Every Value

If 5 is added to every number in a group, the average also increases by 5.

For example:

Old average = 30

Every value increases by 5.

New average = 35

Shortcut 2: Same Number Subtracted From Every Value

If 4 is subtracted from every observation, the average decreases by 4.

Old average = 25

New average = 21

Shortcut 3: Every Value Is Multiplied

If every number is multiplied by 3, the average is also multiplied by 3.

Old average = 12

New average = 36

Shortcut 4: Every Value Is Divided

If every observation is divided by 2, the average is also divided by 2.

Old average = 40

New average = 20

Shortcut 5: Replacement Method

When one number is replaced, focus only on the difference.

Suppose the average of 10 numbers is 35.

One number changes from 27 to 47.

Increase = 20

Increase in average:

20 ÷ 10 = 2

New average:

35 + 2 = 37

This method is considerably faster than calculating the original and new totals separately.

Common Mistakes Students Make in IPMAT Averages Questions 2027

Even simple questions can lead to mistakes if you rush.

1. Forgetting the number of observations

If the average of 8 numbers is 15, the total is:

15 × 8 = 120

Not 15 + 8.

2. Taking a simple average of two group averages

If two groups have different sizes, you cannot simply average their averages.

For example, if one group has 10 students and another has 40 students, their averages do not have equal weight.

Use:

Combined Average = Total of both groups ÷ Total number of observations

3. Using the wrong number of observations

When one observation is removed from a group of 10, there are 9, not 10, observations left.

Likewise, if one observation is added, the number increases to 11.

4. Spending too much time on easy questions

IPMAT is not only about getting questions right. It is also about managing time.

If a question can be solved in two or three steps, do not turn it into a long calculation.

5. Memorising shortcuts without understanding them

Shortcuts are useful only when you understand why they work.

If a question is slightly different from what you have practised, blindly applying a shortcut can lead to the wrong answer.

Free Demo Classes to Prepare for IPMAT 2027 Exam

How to Prepare Averages for IPMAT 2027?

You do not need to spend several days studying only averages. Instead, build the topic into your regular Quantitative Ability practice.

1. Start with the basics

First, make sure you can solve:

• Basic average questions
• Missing number questions
• Addition and removal questions
• Replacement questions
• Average of consecutive numbers

2. Move to mixed questions

Once the basics are comfortable, practise questions where averages are combined with:

• Percentages
• Ratios
• Ages
• Data interpretation
• Weighted averages

3. Practise with a timer

After learning the concepts, start solving questions under time pressure.

For example, take 10 average questions and give yourself 10–12 minutes initially. As your accuracy improves, try to reduce the time.

4. Analyse your mistakes

Do not simply check whether your answer is right or wrong.

Ask yourself:

• Did I misunderstand the question?
• Did I use the wrong number of observations?
• Did I make a calculation error?
• Was there a shorter method?
• Did I spend too much time on the question?

This analysis is often more useful than solving another 20 questions without reviewing your mistakes.

Conclsuion

IPMAT Average Questions may look simple at first, but the topic can become much more interesting when questions involve missing values, group averages, replacement, ages, or changes in the data.

The key ideas to remember are:

• Average = Total ÷ Number of observations
• Total = Average × Number of observations

And when one value is replaced:

Change in Average = Change in Value ÷ Number of observations

Once these concepts become familiar, most average questions become a matter of identifying the right approach and calculating carefully.

Do not try to master the topic by memorising every possible question. Understand the concept, practise different question types, review your mistakes, and gradually work on your speed.

With consistent practice, averages questions for IPMAT can become one of the easier areas to score from in your Quantitative Ability preparation.