Average Tricks: Formulas, Weighted Average and Questions with Solutions for SSC CGL, CHSL
Rahul Kumar
SSC Exam Expert & Content Editor
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PDF Notes: Average Tricks: Formulas, Weighted Average and Questions with Solutions for SSC CGL, CHSL
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Average is one of the easiest chapters of SSC maths, but only if you know the 5 standard question types. The questions are about the average of numbers, a number removed or added, a person who joins or leaves a group, a batsman’s average and the average of two groups. These average tricks for SSC give the formulas, the method for each type and solved questions.
Basic Formulas
| Item | Formula |
|---|---|
| Average | Sum of the observations / Number of observations |
| Sum | Average × Number of observations |
| Average of first n natural numbers | (n + 1) / 2 |
| Average of first n even numbers | n + 1 |
| Average of first n odd numbers | n |
| Average of consecutive numbers | The middle number (for an odd count) |
| Weighted average | (n1 × a1 + n2 × a2) / (n1 + n2) |
| Average speed for equal distances | 2xy / (x + y) |
Five Question Types
| Type | Method |
|---|---|
| Number removed or added | Find the total sum first, then add or subtract the number, then divide by the new count |
| One number replaced | Change in the average = (new number − old number) / count |
| New person joins a group | New person = new average × new count − old sum |
| Two groups together | Use the weighted average |
| Batsman’s average | New score = new average × innings − old total |
Solved Examples
Example 1. The average of 5 numbers is 20. One number, 30, is removed. Find the average of the remaining numbers.
Total = 100. After removing 30: 70. The new average = 70 ÷ 4 = 17.5.
Example 2. The average of 10 numbers is 15. If a number 12 is replaced by 22, what is the new average?
The change = (22 − 12)/10 = 1. The new average = 16.
Example 3. 20 students have an average of 60 marks and 30 students have an average of 70 marks. Find the average of all.
(20 × 60 + 30 × 70)/50 = 3300/50 = 66.
Example 4. The average age of 5 persons is 30 years. A new person joins and the average becomes 32. Find the age of the new person.
Old sum = 150. New sum = 6 × 32 = 192. The new person = 42 years.
Example 5 (cricket). A batsman has an average of 40 in 10 innings. How many runs must he score in the 11th innings to make the average 42?
New total = 11 × 42 = 462. Old total = 400. Runs = 62.
Example 6. The average of 5 consecutive numbers is 30. Find the largest number.
The numbers are 28, 29, 30, 31, 32. The largest is 32.
Example 7. The average of 3 numbers is 20. The average of the first two is 18. Find the third number.
Total = 60. First two = 36. The third = 24.
Tips
- Always find the total (sum) first. It makes every average question easy.
- If every number is increased by x, the average also increases by x.
- If every number is multiplied by x, the average is also multiplied by x.
- Do not add two averages and divide by 2, unless the groups are equal in size.
Quick Tips
- Find the sum first.
- Use the weighted average for two groups.
- Use the change method when one number is replaced.
- Remember the averages of natural, even and odd numbers.
Quick Revision Points
- Average = Sum / Number.
- The average of the first n natural numbers is (n + 1)/2.
- The average of the first n odd numbers is n.
- Weighted average = (n1a1 + n2a2)/(n1 + n2).
- If every number is increased by x, the average increases by x.
Practice Questions With Answers
- Find the average of 4, 8, 12 and 16.
Answer: 10 - Find the average of the first 20 natural numbers.
Answer: 10.5 - The average of 6 numbers is 25. One number, 35, is removed. Find the new average.
Answer: 23 - 10 boys have an average of 50 marks and 20 girls have an average of 80 marks. Find the average of all.
Answer: 70 - The average age of 5 persons is 30. A new person joins and the average becomes 32. Find his age.
Answer: 42 years - The average of 5 consecutive even numbers is 40. Find the largest number.
Answer: 44 - A batsman has an average of 40 in 10 innings. He scores 62 in the 11th innings. Find the new average.
Answer: 42 - Find the average speed for equal distances at 40 km/h and 60 km/h.
Answer: 48 km/h - Find the average of the first 5 odd numbers.
Answer: 5 - The average of 8 numbers is 12. Find their sum.
Answer: 96
How to Practise This Chapter
Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Mathematics notes page, read the previous topic Simple and Compound Interest and the next topic Ratio, Proportion and Alligation. Formulas are in the Formula Guide and more practice is in the Quantitative Aptitude notes.
Frequently Asked Questions
What is the formula for average?
Average = Sum of the observations / Number of observations.
What is the average of the first n natural numbers?
It is (n + 1)/2.
What is the average of the first n odd numbers?
It is n.
What is a weighted average?
It is the average of two or more groups of different sizes, found with (n1a1 + n2a2)/(n1 + n2).
What happens to the average if each number is increased by 5?
The average also increases by 5.
How do I find a new member’s age?
New member = new average × new count − old sum.
How do I find the runs needed in the next innings?
Runs = new average × innings − old total.
What is the average of consecutive numbers?
It is the middle number if the count is odd.
Is average asked in SSC exams?
Yes. Average questions are asked in every SSC maths paper.
What are the common mistakes?
Adding two averages and dividing by 2 when the groups are not equal.
How much time should I take?
About 30 seconds.
What is the average speed for equal distances?
2xy / (x + y).
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Simple Interest and Compound Interest Tricks: Formulas, Difference and Questions for SSC CGL, CHSL
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Ratio and Proportion Tricks: Partnership, Mixture and Alligation Questions for SSC CGL, CHSL
Rahul Kumar
SSC Exam Expert & Content Editor
Rahul is a senior SSC exam strategist with 8+ years of experience helping aspirants crack CGL, CHSL and MTS exams. He writes in-depth notification breakdowns, exam pattern guides and preparation strategies.