How do you solve average questions in aptitude tests?

The core formula is simple, but aptitude tests usually ask you to apply it in reverse or track how it changes.

A worked example: finding a missing value

Question: The average of 5 numbers is 24. Four of the numbers are 18, 22, 25, and 30. What is the fifth number?

Solution: Total sum = 24 × 5 = 120. Sum of the four known numbers = 18+22+25+30 = 95. Fifth number = 120 − 95 = 25.

A worked example: average shifting with a new entry

Question: The average age of 20 students is 15 years. If the teacher, aged 40, is included, what's the new average?

Solution: Original total = 15 × 20 = 300. New total with teacher = 300 + 40 = 340. New average = 340 ÷ 21 ≈ 16.19 years.

Key insight

Always convert an average back into a total (average × count) before doing anything else — trying to manipulate averages directly, without going through the total, is where most mistakes happen.