Quantitative Aptitude practice

Averages Questions with Answers

Average is the sum of a set of values divided by how many values there are. Averages questions in SSC CGL, CHSL and MTS, RRB NTPC and Group D, and bank prelims usually ask you to find a missing value, a new average after someone joins or leaves, or a combined average of two groups. They look easy, but the setup is where marks are lost. Tip: always work with totals (average × count). Most averages problems become one subtraction once you have the totals.

Formulas you need

Average = Sum of all values ÷ Number of values
Sum = Average × Number of values
Average of first n natural numbers = (n + 1) ÷ 2
Average of first n even numbers = n + 1; of first n odd numbers = n
Combined average of two groups = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂)
If a new member joins and the average rises by x, new member = old average + x × (new count)
If every value is increased by k, the average also increases by k
Average speed over equal distances = 2ab ÷ (a + b)
Average of consecutive numbers (or an arithmetic progression) = (first + last) ÷ 2

Worked examples

Q1. The average of five numbers is 18. If one of the numbers, 12, is removed, what is the average of the remaining four numbers?

Sum of five numbers = 18 × 5 = 90
Sum of remaining four = 90 − 12 = 78
New average = 78 ÷ 4 = 19.5

Answer: 19.5

Q2. The average age of 30 students in a class is 14 years. When the teacher's age is included, the average rises by 1 year. Find the teacher's age.

Total age of 30 students = 30 × 14 = 420
New average = 15 for 31 people, so total = 31 × 15 = 465
Teacher's age = 465 − 420 = 45

Answer: 45 years

Q3. The average of 11 numbers is 50. The average of the first six numbers is 49 and the average of the last six numbers is 52. Find the sixth number.

Sum of all 11 numbers = 11 × 50 = 550
Sum of first six = 6 × 49 = 294
Sum of last six = 6 × 52 = 312
The sixth number is counted in both groups, so 294 + 312 = 550 + sixth number
Sixth number = 606 − 550 = 56

Answer: 56

Shortcuts that save time

When one value joins a group, add (change in average × new count) to the old average to get the new value directly. This skips the totals step and saves time, so you are less likely to rush and misread an option.
In 'last six and first six' overlap questions, count how many positions are shared before you calculate. Spotting the overlap first avoids the most common wrong answer.
If every value changes by the same amount, the average changes by that amount. You do not need to recompute the whole sum, which cuts the chance of an arithmetic slip.

Where this appears

SSC CGL Tier-1	Quantitative Aptitude section
SSC CHSL Tier-1	Quantitative Aptitude section
SSC MTS	Numerical and Mathematical Ability section
RRB NTPC CBT-1	Mathematics section
Bank PO/Clerk Prelims	Quantitative Aptitude section

Averages

Practice Set

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1 of 1 (adapting live)Medium

The average of 4 numbers is 73. If 3 of the numbers are 56, 69, 85, find the remaining number.

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