Introduction
In aptitude tests, some age problems are based on the concept of average age. Instead of giving individual ages directly, the question provides the average of a group or a change in average when a new member joins or leaves.
These questions test your understanding of the basic average formula: Average = (Sum of ages) ÷ (Number of persons). Once you convert the statement into equations using this idea, the problems become very easy.
Pattern: Average Age
Pattern
The key idea:
If the average age of n people is A, then their total age = n × A.
Whenever a new person joins or leaves, adjust the total age and then divide by the new number of people to get the new average.
Step-by-Step Example
Question
The average age of 4 friends is 20 years. A new friend joins the group and the new average becomes 21 years. Find the age of the new friend.
Options:
- A: 22 years
- B: 23 years
- C: 24 years
- D: 25 years
Solution
-
Step 1: Compute the total age of the original group
Average = 20, Number = 4 Total age = 4 × 20 = 80 -
Step 2: Compute the new total age after one friend joins
New average = 21, Number = 5 New total = 5 × 21 = 105 -
Step 3: Find the new friend’s age
New friend’s age = New total - Old total = 105 - 80 = 25 -
Final Answer:
25 years → Option D -
Quick Check:
(80 + 25) ÷ 5 = 105 ÷ 5 = 21 Matches the given new average ✅
Quick Variations
If a person leaves the group instead of joining, subtract their age from the total and divide by the new number to get the new average.
Sometimes the question gives the average age difference after a certain number of years. In that case, just add the extra years to everyone’s age before recalculating the average.
Trick to Always Use
- Step 1: Multiply average × number of people to get total age.
- Step 2: Adjust the total when someone joins/leaves.
- Step 3: Recalculate using the new average condition.
- Step 4: Solve for the unknown person’s age.
- Step 5: Verify by recalculating the average.
Summary
Summary
- Convert averages into total age using Total = Average × Number.
- When someone joins or leaves, adjust the total age accordingly.
- Use the new average to form the new total and solve for the unknown age.
- Always verify by recomputing the average with your final values.
Example to remember:
Average questions become simple once you convert everything into totals!
Hint: Multiply average by number of people.
Common Mistakes: Dividing instead of multiplying.