Introduction
In aptitude exams, questions often combine ages with the concept of average. These problems require finding missing ages or totals when group averages are known.
The key is to apply the Average Formula = (Sum of Ages ÷ Number of People) together with age relations.
Pattern: Age/Average Combined Problems
Pattern
Step 1: Use average × number of people = total sum of ages.
Step 2: Add or remove individuals’ ages as per the condition.
Step 3: Solve equations to find missing age(s) or group averages.
Step-by-Step Example
Question
The average age of 5 students is 15 years. When a teacher joins, the average becomes 18 years. Find the teacher’s age.
Options:
- A. 28 years
- B. 30 years
- C. 33 years
- D. 36 years
Solution
-
Step 1: Calculate total age of the students
Total age of 5 students = 5 × 15 = 75. -
Step 2: Compute total age after teacher joins
With teacher, 6 people average = 18 → total = 6 × 18 = 108. -
Step 3: Find the teacher’s age
Teacher’s age = 108 - 75 = 33. -
Final Answer:
33 years → Option C -
Quick Check:
(75 + 33) ÷ 6 = 108 ÷ 6 = 18 ✅
Quick Variations
Type 1: Average increases or decreases when someone joins/leaves → find missing person’s age.
Type 2: Combining two groups with different averages → find overall average or missing group size.
Trick to Always Use
- Shortcut: New person’s age = (New Average × New Count) - (Old Average × Old Count).
- Shortcut for combined groups: Weighted average = (Sum₁ + Sum₂) ÷ (Count₁ + Count₂).
Summary
Summary
- Average × Number = Total sum.
- When someone joins/leaves, adjust the total sum accordingly.
- Always check with Quick Check by plugging back into the average formula.
Hint: New age = (new avg × new count) - (old avg × old count).
Common Mistakes: Multiplying averages instead of adjusting sums.