Pariksha SaathiAverage Questions with Solutions
Average questions are mostly about handling the formula backwards — getting from an average back to a sum is more often the actual skill being tested than the plain average itself. Here’s the concept, four fully worked examples, and a few to try yourself.
The concept, quickly
- Average = Sum of all values / Number of values.
- Reversed, this gives Sum = Average × Number of values — this reversal is the key to most average questions, which usually give you an average and ask for something about the sum (or vice versa).
- When a new value joins a group, work out the new total sum first (old sum + new value), then divide by the new count — never average the old average directly with the new value.
- Useful shortcut: if adding one new value to n existing values changes the average from A to A′, the new value itself = A′ + n(A′ − A).
Worked examples
1. Find the average of 12, 15, 18, 21, and 24.
Solution
- Sum = 12 + 15 + 18 + 21 + 24 = 90
- Average = Sum / Count = 90 / 5
- = 18
Answer: 18
2. The average of 5 numbers is 27. If one number is excluded, the average of the remaining 4 numbers becomes 25. Find the excluded number.
Solution
- Sum of all 5 numbers = 5 × 27 = 135
- Sum of the remaining 4 numbers = 4 × 25 = 100
- Excluded number = 135 − 100 = 35
Answer: 35
3. The average weight of 30 students in a class is 42 kg. When the teacher’s weight is included, the average rises by 1 kg. Find the teacher’s weight.
Solution
- Old sum (30 students) = 30 × 42 = 1,260 kg
- New average (31 people) = 42 + 1 = 43 kg, so new sum = 31 × 43 = 1,333 kg
- Teacher’s weight = new sum − old sum = 1,333 − 1,260 = 73 kg
Answer: 73 kg
4. In a class of 40 students, the average marks are 60. There are 20 boys and 20 girls in the class. If the boys’ average marks are 50, find the girls’ average marks.
Solution
- Total marks (40 students) = 40 × 60 = 2,400
- Boys’ total marks (20 boys) = 20 × 50 = 1,000
- Girls’ total marks = 2,400 − 1,000 = 1,400, so girls’ average = 1,400 / 20 = 70
Answer: 70
Try these yourself
Work through these the same way, then check against the answer.
1. Find the average of 8, 12, 16, 20, and 24.
Answer: 16
2. The average age of 6 people in a room is 30 years. A seventh person enters and the average becomes 32 years. Find the age of the seventh person.
Answer: 44 years
3. A cricketer has an average of 40 runs over 10 innings. How many runs must he score in the 11th innings to raise his average to 42?
Answer: 62 runs
Where this comes up
Average is tested directly in the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — and the same reversed-formula skill carries over into data-interpretation questions.
Practice more Average questions
This page covers the concept and a handful of worked examples. Pariksha Saathi has full topic-wise practice sets for Average (and every other Quant/Reasoning/English topic) with instant scoring and explanations — free, no account required.
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