We have covered Average in detail, derived the Average formula and concepts, and solved questions to understand how the formula is applied. We then covered different types of Average questions and practiced them through 55 questions, including MCQs, True/False, Fill in the Blanks and Word Problems.
Now, we are moving to Average Previous Year Questions (PYQs) from SSC, RRB, Banking and Defence Exams.
The questions in this section are based on questions asked in previous year examinations. To make them more engaging, relatable and suitable for MathsByNITian, we may modify the context, names and numbers while retaining the underlying concepts and question patterns of the original exam questions.
Try to solve each question yourself first. Check the answer or detailed solution only after you have made a genuine attempt. Avoid looking at the solution before solving the question, as the purpose of this section is to test and strengthen your understanding of Average.
For complete and free competitive-exam Maths preparation, explore our Competitive Exams Maths Notes, Formula, Practice and PYQ sections. Together, these resources are designed to make your preparation structured, easier and completely free.
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Question 1: In a MathsByNITian Average mock test, the scores of six aspirants are 30, 72, 53, 68, x and 87, where x is unknown. If the average score of the six aspirants is 60 marks, what is the score of the aspirant who scored x marks? (Bank PO)
Solution
Given:
Six values are 30, 72, 53, 68, x and 87.
Average = 60
Number of times present = 6
Formula Used:
Average = Total ÷ Number of times present
Solution:
60 = (30 + 72 + 53 + 68 + x + 87) ÷ 6
60 × 6 = 310 + x
360 = 310 + x
x = 360 − 310
x = 50
Answer: 50
Question 2: A new coaching centre conducts an assessment for five newly enrolled students. Their scores are represented by A, B, C, D and E, which are five consecutive integers. If the average score is 62 marks, what is the product of the scores represented by A and E? (CPO)
Solution
Given:
Five consecutive integers are A, B, C, D and E.
Average = 62 marks
Number of times present = 5
Formula Used:
Average = Total ÷ Number of times present
Solution:
Since the five numbers are consecutive and their average is 62, the middle number is C = 62.
Therefore:
A = 60
B = 61
C = 62
D = 63
E = 64
Now,
A × E = 60 × 64
A × E = 3840
Answer: 3840
Question 3: In a MathsByNITian mock-test batch, there are 50 students. Their average weight is 45 kg. When one student leaves the batch, the average weight decreases by 100 g. Find the weight of the student who left the batch. (RRB NTPC)
Solution
Given:
- Number of students = 50
- Average weight = 45 kg
- Decrease in average weight = 100 g = 0.1 kg
- Students remaining = 50 − 1 = 49
Formula Used:
Average = Total ÷ Number of times present
Solution:
Original total weight:
45 × 50 = 2,250 kg
New average weight:
45 − 0.1 = 44.9 kg
Total weight of the remaining 49 students:
44.9 × 49 = 2,200.1 kg
Therefore, the weight of the student who left:
2,250 − 2,200.1 = 49.9 kg
Answer: 49.9 kg
Question 4: In a cricket tournament among SSC CGL-selected candidates, a team scored an average of 50 runs per innings over 40 innings. The difference between the team’s highest and lowest scores was 172 runs. If the innings with the highest and lowest scores are excluded, the average score of the remaining 38 innings is 48 runs. Find the team’s highest score in an innings. (SSC CGL)
Solution
Given:
- Number of innings = 40
- Average score = 50 runs
- Difference between highest and lowest scores = 172 runs
- Number of remaining innings = 38
- Average score of remaining innings = 48 runs
Formula Used:
Average = Total ÷ Number of times present
Solution:
Total score in 40 innings:
50 × 40 = 2,000 runs
Total score in the remaining 38 innings:
48 × 38 = 1,824 runs
Therefore, the sum of the highest and lowest scores:
2,000 − 1,824 = 176 runs
Let the highest score be H and the lowest score be L.
H + L = 176
H − L = 172
Adding both equations:
2H = 348
H = 174
Answer:
The team’s highest score was 174 runs.
Question 5: In a MathsByNITian mock test, the average score of two aspirants is 10 marks, and the square root of the product of their scores is 6. What are the scores of the two aspirants? (SSC CGL)
Solution
Given:
- Average score of two aspirants = 10 marks
- Square root of the product of their scores = 6
Formula Used:
Average = Total ÷ Number of times present
Solution:
Let the two scores be x and y.
10 = (x + y) ÷ 2
x + y = 20
Also,
√(xy) = 6
Squaring both sides:
xy = 36
We need two numbers whose sum is 20 and product is 36.
The two numbers are 2 and 18.
Check:
2 + 18 = 20
2 × 18 = 36
Answer: The two scores are 2 marks and 18 marks.
Question 6: The average of A, B, C and D is 16. Half the sum of B, C and D is 23. What is the value of A? (RRB ALP)
Solution
Given:
- Average of A, B, C and D = 16
- Half the sum of B, C and D = 23
Formula Used:
Average = Total ÷ Number of times present
Solution:
Total of A, B, C and D:
16 × 4 = 64
From the second condition:
(B + C + D) ÷ 2 = 23
B + C + D = 46
Therefore:
A = 64 − 46
A = 18
Answer: 18
Question 7: At an RRB NTPC coaching centre, there are 32 male aspirants and 28 female aspirants. The average age of the male aspirants is 14 years, while the average age of the female aspirants is 13 years. What is the average age of all the aspirants, rounded to two decimal places? (NABARD)
Solution
Given:
- Male aspirants = 32
- Female aspirants = 28
- Average age of male aspirants = 14 years
- Average age of female aspirants = 13 years
Formula Used:
Average = Total ÷ Number of times present
Solution:
Total age of male aspirants:
32 × 14 = 448 years
Total age of female aspirants:
28 × 13 = 364 years
Total age of all aspirants:
448 + 364 = 812 years
Total number of aspirants:
32 + 28 = 60
Therefore,
Average age = 812 ÷ 60
= 13.5333… years
Rounded to two decimal places:
13.53 years
Answer: 13.53 years
Question 8: A food-stall vendor at Unnao Railway Station spends an average of ₹5,000 per month during the first 5 months of a year and ₹5,400 per month during the remaining 7 months. If his total savings for the year are ₹2,300, what is his average monthly income for the year? (Bank)
Solution
Given:
- Average monthly expenditure for the first 5 months = ₹5,000
- Average monthly expenditure for the remaining 7 months = ₹5,400
- Total annual savings = ₹2,300
- Total number of months = 12
Formula Used:
Average = Total ÷ Number of times present
Solution:
Expenditure during the first 5 months:
₹5,000 × 5 = ₹25,000
Expenditure during the remaining 7 months:
₹5,400 × 7 = ₹37,800
Total annual expenditure:
₹25,000 + ₹37,800 = ₹62,800
Total annual income:
₹62,800 + ₹2,300 = ₹65,100
Average monthly income:
₹65,100 ÷ 12 = ₹5,425
Answer: ₹5,425 per month
Question 9: At a coaching centre, the average score of female RRB aspirants in a mock examination is 76 marks, while the average score of male SSC aspirants is 72 marks. The overall average score of all the aspirants is 74.4 marks. Find the percentage of female RRB aspirants and male SSC aspirants among the students. (SSC)
Solution
Given:
- Average score of female RRB aspirants = 76 marks
- Average score of male SSC aspirants = 72 marks
- Overall average score = 74.4 marks
Formula Used:
Weighted Average = [(Number in Group 1 × Average of Group 1) + (Number in Group 2 × Average of Group 2)] ÷ (Number in Group 1 + Number in Group 2)
Solution:
Let the number of female RRB aspirants be G and male SSC aspirants be B.
Therefore,
74.4 = (76G + 72B) ÷ (G + B)
74.4G + 74.4B = 76G + 72B
74.4B − 72B = 76G − 74.4G
2.4B = 1.6G
B : G = 1.6 : 2.4
B : G = 2 : 3
Therefore,
Girls : Boys = 3 : 2
Total parts = 3 + 2 = 5
Percentage of female RRB aspirants:
(3 ÷ 5) × 100 = 60%
Percentage of male SSC aspirants:
(2 ÷ 5) × 100 = 40%
Answer: Female RRB aspirants = 60%; Male SSC aspirants = 40%.
Question 10: The average score of A aspirants in a mock test is B² marks, while the average score of B aspirants is A² marks. What is the average score of all (A + B) aspirants? (SSC)
Solution
Given:
- Number of A aspirants = A
- Average score of A aspirants = B² marks
- Number of B aspirants = B
- Average score of B aspirants = A² marks
Formula Used:
Average = Total ÷ Number of times present
Solution:
Total score of A aspirants:
A × B² = AB²
Total score of B aspirants:
B × A² = A²B
Total score of all (A + B) aspirants:
AB² + A²B
= AB(A + B)
Therefore,
Average score = AB(A + B) ÷ (A + B)
= AB
Answer: AB
Question 11: At a railway recruitment coaching centre, the average score of 8 aspirants in a mock test is 20 marks. The average score of the first 2 aspirants is 15.5 marks, while the average score of the next 3 aspirants is 21⅓ marks. If the sixth aspirant scored 4 marks less than the seventh aspirant and 7 marks less than the eighth aspirant, what was the score of the eighth aspirant? (SSC)
Solution
Given:
- Number of aspirants = 8
- Average score = 20 marks
- Average score of first 2 aspirants = 15.5 marks
- Average score of next 3 aspirants = 21⅓ marks
- Sixth score is 4 marks less than the seventh score and 7 marks less than the eighth score
Formula Used:
Average = Total ÷ Number of times present
Solution:
Total score of 8 aspirants:
20 × 8 = 160 marks
Total score of first 2 aspirants:
15.5 × 2 = 31 marks
Total score of the next 3 aspirants:
21⅓ × 3 = 64 marks
Therefore, the total score of the sixth, seventh and eighth aspirants:
160 − 31 − 64 = 65 marks
Let the sixth aspirant’s score be x.
Then:
Seventh aspirant’s score = x + 4
Eighth aspirant’s score = x + 7
Therefore:
x + (x + 4) + (x + 7) = 65
3x + 11 = 65
3x = 54
x = 18
Therefore, the eighth aspirant’s score:
18 + 7 = 25 marks
Answer: 25 marks
Question 12: Seven bank employees are standing in a row facing North. Their average age is 28 years. If the average age of the first three employees is 21 years and the average age of the last three employees is 34 years, what is the age of the employee sitting in the middle of the row? (Bank PO)
Solution
Given:
- Number of bank employees = 7
- Average age of all employees = 28 years
- Average age of the first 3 employees = 21 years
- Average age of the last 3 employees = 34 years
Formula Used:
Average = Total ÷ Number of times present
Solution:
Total age of 7 employees:
28 × 7 = 196 years
Total age of the first 3 employees:
21 × 3 = 63 years
Total age of the last 3 employees:
34 × 3 = 102 years
The first 3 and last 3 employees together account for 6 employees. Therefore, the age of the middle employee is:
196 − 63 − 102 = 31 years
Answer: 31 years
Question 13: The average age of 11 players of the Railway North Zone cricket team decreases by 3 months when two players aged 18 years and 21 years are replaced by two new players. What is the average age of the two new players? (SSC)
Solution
Given:
- Number of players = 11
- Decrease in average age = 3 months
- Ages of the two replaced players = 18 years and 21 years
Formula Used:
Average = Total ÷ Number of times present
Solution:
Total age of the two players who left:
18 + 21 = 39 years
39 years = 39 × 12 = 468 months
Decrease in total age of the team:
3 × 11 = 33 months
Therefore, total age of the two new players:
468 − 33 = 435 months
Average age of the two new players:
435 ÷ 2 = 217.5 months
Convert into years and months:
217.5 months = 18 years 1.5 months
Answer: 18 years 1.5 months
Question 14: A railway canteen at Lucknow Railway Station remains closed on Monday. The average daily sales for the remaining six days of the week is ₹18,500, while the average daily sales from Tuesday to Saturday is ₹16,200. What were the sales on Sunday? (RRB)
Solution
Given:
- Average daily sales for the remaining 6 days = ₹18,500
- Average daily sales from Tuesday to Saturday = ₹16,200
- Monday = Closed
Formula Used:
Average = Total ÷ Number of times present
Solution:
Total sales from Tuesday to Sunday:
₹18,500 × 6 = ₹1,11,000
Total sales from Tuesday to Saturday:
₹16,200 × 5 = ₹81,000
Therefore, sales on Sunday:
₹1,11,000 − ₹81,000 = ₹30,000
Answer: ₹30,000
Question 15: At a bank branch, one employee retires and is replaced by a new employee aged 28 years. There are 12 employees in the branch, and as a result of the replacement, the average age of the employees decreases by 2 years. What is the age of the retired employee? (SSC)
Solution
Given:
- Number of bank employees = 12
- Age of the new employee = 28 years
- Decrease in average age = 2 years
Formula Used:
Average = Total ÷ Number of times present
Solution:
Since the average age of 12 employees decreases by 2 years, the total age of the employees decreases by:
2 × 12 = 24 years
Therefore, the retired employee was 24 years older than the new employee.
Age of the retired employee:
28 + 24 = 52 years
Answer: 52 years
Related Chapters
- Percentage
- Ratio and Proportion
- Age Problems
- Mixture and Alligation
- Data Interpretation
- Number System
Average PYQ Analysis
These 15 previous year questions cover the major Average concepts asked in SSC, RRB, Banking, Defence, and other competitive exams.
Difficulty Level
- Easy: 3 Questions
- Medium: 8 Questions
- Difficult: 4 Questions
Key Topics Covered
- Average Formula & Basic Concepts
- Missing Value in Average
- Average of Consecutive Numbers
- Change in Average
- Replacement of Members
- Weighted Average
- Reverse Weighted Average
- Average of Multiple Groups
- Average Based on Ages
- Average Based on Marks & Scores
- Average Based on Expenditure & Income
- Highest & Lowest Values
- Algebraic Average Problems
Exam Insight
Average questions often test total–average relationships, weighted averages, changes in average, and replacement of members. Identifying the question type quickly helps in choosing the right formula or shortcut.
What You Should Learn From These Average PYQs
After solving these questions, you should be able to:
- Apply the Average formula confidently.
- Find missing values and totals using averages.
- Solve weighted and reverse-weighted average problems.
- Handle changes in average, including addition, removal and replacement of members.
- Solve Average problems involving marks, ages, expenditure and other real-life situations.
- Use Average concepts and shortcuts to improve speed and accuracy.
If you can solve these 15 PYQs accurately, you will have covered the major Average question types commonly asked in competitive examinations.