Average Questions with Step-by-Step Solutions and Formulas

Average questions are important in school maths, competitive exams, and daily life calculations because they show how to combine several values into a single representative number. These questions help students learn how to find the average of numbers, marks, ages, speeds, and more. Practicing average questions improves builds mental math speed and problem‑solving skills and confidence. In this article, you will learn the average formula, solved examples, and practice questions with answers.

Table of Contents

• Average Formula Explained
• Solved Questions on Average
• Practice Questions on Average
• Real-Life Use of Average Calculations
• Conclusion on Average Questions
• Frequently Asked Questions on Average Questions

Average Formula Explained

The basic average formula is:

Average = (Sum of Observations) / (Number of Observations)

There are also variations such as:

• Weighted Average = (Sum of weighted values) / (Sum of weights)

• Average Speed = Total distance / Total time

These formulas help solve a wide variety of average problems in different contexts.

  

Solved Examples on Average

Here are some solved average questions to help you understand the application:

Q1. Find the average of 12, 15, 17, 20, and 21.

Solution: (12 + 15 + 17 + 20 + 21) / 5 = 85 / 5 = 17

Q2. The average of five numbers is 36. If four of the numbers are 30, 34, 40, and 38, find the fifth number.

Solution: Total sum = 36 × 5 = 180

Sum of four = 30 + 34 + 40 + 38 = 142

Fifth number = 180 - 142 = 38

Q3. A car travels 60 km at 30 km/h and another 60 km at 60 km/h. What is the average speed?

Solution:

Time1 = 60 / 30 = 2 hrs, Time2 = 60 / 60 = 1 hr

Total time = 3 hrs, Total distance = 120 km

Average speed = 120 / 3 = 40 km/h

Q4. Find the average of the following set of numbers: 72, 88, 64, 96, and 120.

Solution: Given, the set of numbers is 72, 88, 64, 96, and 120.
Average = Sum of numbers / Total numbers
= (72 + 88 + 64 + 96 + 120) / 5
= 440 / 5
= 88

Q5. The sum of 8 numbers is 400. Find their average.

Solution: Given, the sum of 8 numbers = 400.
Average = Sum / Total numbers
= 400 / 8
= 50

Q6. What is the average of natural numbers from 1 to 51?

Solution: Given natural numbers 1 to 51.
Average of n natural numbers = (n + 1)/2
Here, n = 51
Average = (51 + 1) / 2 = 52 / 2 = 26

Q7. The average of 5 consecutive numbers is 31. What is the largest of these numbers?

Solution: Let the 5 consecutive numbers be x, x+1, x+2, x+3, x+4.
Average = (x + (x+1) + (x+2) + (x+3) + (x+4)) / 5 = 31
⇒ (5x + 10) / 5 = 31
⇒ 5x + 10 = 155
⇒ 5x = 145
⇒ x = 29
Largest number = x + 4 = 33

Q8. The average of 12 numbers is 18. If each number is increased by 6, what will the new average be?

Solution: Average of 12 numbers = 18
Sum = 18 × 12 = 216
Increase in total = 6 × 12 = 72
New sum = 216 + 72 = 288
New average = 288 / 12 = 24

Q9. The average of 40 numbers is 25. If two numbers 35 and 45 are discarded, find the average of the remaining numbers.

Solution: Average of 40 numbers = 25
Sum = 40 × 25 = 1000
Sum of discarded numbers = 35 + 45 = 80
Remaining sum = 1000 - 80 = 920
Remaining numbers = 40 - 2 = 38
Average = 920 / 38 ≈ 24.21

Q10. What is the average of the first six multiples of 7?

Solution: First six multiples of 7 are: 7, 14, 21, 28, 35, 42
Average = (7 + 14 + 21 + 28 + 35 + 42) / 6
= 147 / 6
= 24.5

Q11. The average age of three sisters is 18 years and their ages are in proportion 2:3:5. What is the age of the youngest sister?

Solution: Let the age of the youngest sister = 2x.
Then, ages = 2x, 3x, 5x.
Average = (2x + 3x + 5x)/3 = 18
10x / 3 = 18
10x = 54
x = 5.4
Youngest sister = 2x = 2(5.4) = 10.8 years

Q12. The average weight of a group of 8 students is 50 kg. The weights of 7 of them are 48, 55, 52, 49, 54, 47, and 56. Find the weight of the 8th student.

Solution: Average weight = 50 kg
Total weight = 50 × 8 = 400 kg
Sum of 7 students = 48 + 55 + 52 + 49 + 54 + 47 + 56 = 361 kg
Weight of 8th student = 400 - 361 = 39 kg

Q13. The mean of 20 numbers is 42. If the mean of the first 8 numbers is 38 and the mean of the last 8 numbers is 45, find the sum of the remaining 4 numbers.

Solution: Mean of 20 numbers = 42
Total sum = 42 × 20 = 840

Sum of first 8 numbers = 38 × 8 = 304
Sum of last 8 numbers = 45 × 8 = 360

Sum of 16 numbers = 304 + 360 = 664
Remaining sum = 840 - 664 = 176

Q14. The average of 6 numbers is 22. If five numbers are 18, 20, 24, 26, and 19, find the sixth number.

Solution: Given average of 6 numbers is 22

Total sum = 22 × 6 = 132
Sum of five = 18 + 20 + 24 + 26 + 19 = 107
Sixth number = 132 − 107 = 25

Q15. The average of 8 numbers is 15. If one number 27 is replaced by 9, what is the new average?

Solution: Original sum = 15 × 8 = 120
New sum = 120 − 27 + 9 = 102
New average = 102 ÷ 8 = 12.75

Q16. A teacher gives an average of 20 marks to 10 students and 30 marks to another 5 students. Find the overall average.

Solution: Total marks = (20 × 10) + (30 × 5) = 200 + 150 = 350
Total students = 15
Average = 350 ÷ 15 ≈ 23.33

Q17.  The average height of 6 students is 140 cm. If a new student joins and the average becomes 142 cm, find the height of the new student.

Solution: Given the average height of 6 students is 140 cm.
Old sum = 140 × 6 = 840
New sum = 142 × 7 = 994
New student height = 994 − 840 = 154 cm

Q18. A bus travels 100 km at 50 km/h and returns the same distance at 25 km/h. Find the average speed of the whole journey.

Solution:
Time = 100/50 = 2 hrs, 100/25 = 4 hrs
Total distance = 100 + 100 = 200 km
Total time = 6 hrs
Average speed = 200 ÷ 6 = 33.33 km/h

Q19. The average of 12 numbers is 50. One number 80 is incorrectly recorded as 30. Find the correct average.

Solution: Given average of 12 numbers = 50
Error = 80 − 30 = 50
Correct total = (50 × 12) + 50 = 650
Correct average = 650 ÷ 12 = 54.17

Q20. The average of 15 numbers is 40. If the average of first 10 numbers is 38 and last 10 numbers is 42, find the 6th and 10th number overlap contribution.

Solution:
Total sum = 600
First 10 sum = 380
Last 10 sum = 420
Sum of both = 800
First 10 + last 10 = 20 terms, but actual numbers = 15
⇒ Overlap = 5 numbers
So overlap sum = 800 − 600 = 200
Average overlap group 200 ÷ 5 = 40

Practice Questions on Average

1. Find the average of the numbers 18, 24, 30, 36, and 42.

2. The average of 6 numbers is 25. Find the total sum of the numbers.

3. The average marks of 8 students is 72. If the total marks of 7 students is 490, find the marks of the 8th student.

4. Find the average of the first 10 natural numbers.

5. A person travels 150 km in 3 hours and another 100 km in 2 hours. Find the average speed for the whole journey.

6. The average of 9 numbers is 40. If one number 56 is removed, what will be the average of the remaining numbers?

7. Find the average of the following numbers: 45, 55, 65, 75, and 85.

8. The average age of 5 friends is 16 years. If a new friend aged 21 joins the group, what will be the new average age?

9. The average of 7 consecutive odd numbers is 35. Find the smallest number.

10. A class has 20 students with an average weight of 48 kg. If the teacher’s weight of 72 kg is included, find the new average weight.

Real-Life Use of Average Calculations

• Household Budgeting: Estimating average monthly expenses

• Classroom Analysis: Understanding Class Performance Trends

• Business: Calculating average revenue or cost per unit

• Health: Monitoring average heart rate or calorie intake

• Travel: Estimating average speed or fuel consumption

Conclusion on Average Questions

Understanding the concept of average in maths is essential for both academic excellence and real-life utility. From calculating test scores to analyzing business profits, averages help simplify data and reveal trends. Practicing a wide range of average questions sharpens your speed, accuracy, and confidence in solving mathematical problems. With a grasp of the average formula, students are equipped to handle various math challenges with ease.

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