Introduction by Rahul Sir
Hello Aspirants,
I am Rahul Sir, and over the years I have trained thousands of banking aspirants preparing for IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, RRB, and other competitive examinations. Among the most frequently asked topics in the Quantitative Aptitude section is Average. Many students consider it an easy chapter, yet they often lose marks because of calculation mistakes, incorrect assumptions, or lack of shortcut techniques.
Average forms the foundation for several advanced topics such as Partnership, Profit and Loss, Mixture and Alligation, Data Interpretation, and Time & Work. Therefore, mastering averages not only helps you solve direct questions but also improves your overall quantitative aptitude.
In this article, I will share practical tips, shortcut methods, exam-oriented tricks, and solved examples that can significantly improve your speed and accuracy in banking examinations. If practiced regularly, these techniques can help you solve average-based questions within seconds during the examination.
Let us begin by understanding the concept and then move toward advanced tricks used by banking toppers.
1. Understanding the Basic Concept of Average
Average represents a central value that reflects the overall performance of a group of numbers. The basic formula is:
Average = Sum of Observations ÷ Number of Observations
For example:
The marks obtained by five students are:
40, 50, 60, 70, 80
Sum = 300
Average = 300 ÷ 5 = 60
In banking exams, questions are rarely this straightforward. Examiners test your understanding by introducing changes, replacements, additions, or exclusions in the dataset.
Averages help simplify large amounts of data into one representative value. Instead of remembering every individual observation, you can understand the general trend through a single figure.
Important points:
- Average can be an integer or decimal.
- The average always lies between the smallest and largest values.
- If all values increase by a fixed number, the average also increases by the same number.
- If all values decrease by a fixed number, the average decreases accordingly.
Example:
Average of 8 numbers is 25.
Total sum = 25 × 8 = 200
This simple relationship between average and total sum forms the basis of most exam questions.
Students should memorize this relationship because many questions can be solved without actually calculating individual values.
The quicker you convert averages into totals, the faster you can solve banking aptitude questions.
2. The Golden Formula: Total = Average × Number
One of the most important tricks in average problems is converting average into total.
Formula:
Total Sum = Average × Number of Terms
Example:
Average salary of 20 employees is ₹25,000.
Total salary = 20 × 25,000
= ₹5,00,000
This approach saves significant time.
Example:
Average age of 15 students is 18 years.
Total age = 15 × 18 = 270 years.
If one student leaves and another joins, we compare the totals instead of calculating individual ages.
Banking examinations frequently use this concept.
Shortcut:
Whenever you see average, immediately think about total sum.
Questions involving additions, replacements, increases, decreases, and missing values become much easier when solved using total values.
Example:
Average of 10 numbers is 30.
Total = 300
One number is replaced by 50 and average becomes 32.
New Total = 320
Difference = 20
Thus replaced number = 50 − 20 = 30
Such tricks save several calculation steps.
Practice converting every average question into total sum form before attempting detailed calculations.
This habit alone can improve your speed dramatically.
3. Finding Missing Numbers Using Average
Questions involving missing values are extremely common in IBPS examinations.
Example:
Average of five numbers is 24.
Four numbers are 20, 22, 25, and 28.
Find the fifth number.
Solution:
Total sum = 24 × 5 = 120
Sum of known numbers:
20 + 22 + 25 + 28 = 95
Missing number = 120 − 95
= 25
Shortcut Approach:
Calculate total first.
Subtract known values.
The remainder is the missing value.
Another Example:
Average of seven numbers is 40.
Six numbers total 220.
Total required = 40 × 7 = 280
Missing number = 280 − 220
= 60
Such questions become extremely easy once you focus on total sums rather than averages directly.
Exam Tip:
Never calculate averages repeatedly.
Convert to total, solve, and then reconvert if necessary.
This technique reduces mistakes and improves accuracy.
4. Addition and Removal of Members
Many banking exam questions involve adding or removing people from a group.
Example:
Average age of 10 students is 15 years.
A new student joins.
Average becomes 16 years.
Find the age of the new student.
Solution:
Original total = 10 × 15 = 150
New total = 11 × 16 = 176
New student’s age = 176 − 150
= 26 years
Example of Removal:
Average age of 12 employees is 30 years.
One employee leaves.
Average becomes 29 years.
Original total = 360
New total = 11 × 29 = 319
Age of removed employee = 360 − 319
= 41 years
This concept appears frequently in IBPS PO and Clerk examinations.
Always compare old total and new total.
Never attempt long calculations.
5. Replacement Problems Made Easy
Replacement questions are among the most scoring questions in banking exams.
Example:
Average age of 20 students is 18 years.
One student is replaced.
Average increases by 1 year.
Find the age difference.
Solution:
Increase in total = 20 × 1
= 20 years
Thus new student is 20 years older than the student who left.
Shortcut Formula:
Difference in age = Change in Average × Number of Members
This direct formula eliminates lengthy calculations.
Example:
Average salary of 30 employees decreases by ₹500 after replacement.
Difference = 30 × 500
= ₹15,000
Thus replaced employee’s salary exceeded the new employee’s salary by ₹15,000.
Practice this formula extensively because it appears regularly in banking examinations.
6. Weighted Average Concept
Weighted average combines groups having different averages.
Formula:
Weighted Average = (Total Sum of Groups) ÷ (Total Members)
Example:
Average marks of 20 boys = 60
Average marks of 30 girls = 70
Total marks:
Boys = 20 × 60 = 1200
Girls = 30 × 70 = 2100
Combined average:
3300 ÷ 50
= 66
Many Data Interpretation questions use weighted averages.
Students should focus on totals first and then compute the final average.
This method is much faster than traditional calculations.
7. Average Speed Problems
Average speed questions are popular in banking and insurance exams.
Important Rule:
Average speed is NOT simply the arithmetic mean.
Example:
A car travels:
60 km at 30 km/hr
60 km at 60 km/hr
Total distance = 120 km
Total time = 2 + 1 = 3 hours
Average speed = 120 ÷ 3
= 40 km/hr
Many students incorrectly answer:
(30 + 60)/2 = 45
This is wrong.
Always use:
Average Speed = Total Distance ÷ Total Time
Remember this rule carefully.
8. Quick Approximation Tricks
Approximation saves precious exam time.
Example:
Average of
49, 51, 52, 48, 50
Since numbers are near 50,
Average ≈ 50
Exact average = 250 ÷ 5 = 50
In many DI questions, approximation can quickly eliminate options.
Useful when options are far apart.
Develop estimation skills to increase speed.
9. Common Mistakes Students Make
Students often:
- Forget to convert average into total.
- Use arithmetic mean in speed questions.
- Ignore additions and removals.
- Miscalculate total observations.
- Make multiplication errors.
To avoid mistakes:
- Write totals first.
- Double-check observations.
- Use shortcut formulas.
- Practice mental calculations.
Consistency and accuracy are more important than solving hundreds of questions blindly.
10. Exam-Oriented Practice Strategy
To master averages:
Week 1
Learn formulas and concepts.
Week 2
Solve basic problems.
Week 3
Practice addition, removal, and replacement questions.
Week 4
Attempt sectional tests.
Recommended Daily Routine:
- 15 Average questions.
- 10 Mixed Aptitude questions.
- 1 Mini Mock Test.
Within a month, average questions will become one of your strongest topics.
Banking toppers regularly practice averages because they frequently appear in prelims and mains examinations.
Focus on understanding totals rather than memorizing solutions.
With enough practice, most average questions can be solved in under 30 seconds.
How Teachers from OdTutor Can Help
At OdTutor, experienced banking faculty members guide students through shortcut techniques, exam-oriented strategies, and extensive practice sessions. Our teachers provide topic-wise classes on Quantitative Aptitude, including Average, Percentage, Ratio, Partnership, Profit & Loss, Data Interpretation, and Arithmetic. Students receive personalized doubt-solving support, mock tests, previous year question discussions, and performance analysis. Through live online classes and structured study plans, OdTutor helps aspirants improve speed, accuracy, and confidence. Whether you are preparing for IBPS PO, IBPS Clerk, SBI, RRB, or other competitive examinations, our expert mentors ensure that you learn the smartest methods to crack aptitude questions efficiently.
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