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Average Age Removal

Average Age Removal problems involve scenarios where a person leaves a group, causing the average age to change. These problems require finding the age of the person who left or the new average.

10Worksheets
200+Practice Questions
IntermediateDifficulty
2-3 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Average Age Removal

Average Age Removal problems involve scenarios where a person leaves a group, causing the average age to change. These problems require finding the age of the person who left or the new average.

Prerequisites

Average formula Sum = Average × Count Age difference concepts
Why This Matters: Average Age Removal problems appear in 1-2 questions in banking and SSC exams. They test understanding of how averages respond to removal.

How to Solve Average Age Removal Problems

1

Step 1: Calculate the present total sum using average × count

2

Step 2: Let the age of the person leaving = L

3

Step 3: New total sum = Old sum - L

4

Step 4: New average = (Old sum - L) ÷ (Old count - 1)

5

Step 5: Use given new average to solve for L

6

Step 6: Alternatively, find new average if L is known

Pro Strategy: The age of the person who left = Old average + (Old count) × (Old average - New average). The departure affects both sum and count.

Example Problem

Example: Average age of 6 persons is 25 years. One person leaves, and the average becomes 24 years. Find the age of the person who left. Solution: Step 1: Old total sum = 25 × 6 = 150 years Step 2: Let leaving age = L Step 3: New total sum = 150 - L Step 4: New average = (150 - L)/5 = 24 Step 5: 150 - L = 120 → L = 30 years Answer: The person who left is 30 years old

Pro Tips & Tricks

  • Age of person leaving = Old average + (Old count) × (Old average - New average)
  • If new average < old average, the leaving person was above average
  • If new average > old average, the leaving person was below average
  • The change in total sum = (New average - Old average) × (New count)
  • Draw a table to track sums before and after removal
  • For multiple removals, process sequentially

Shortcut Methods to Solve Faster

L = (Old avg × Old count) - (New avg × New count)
Change in sum = L = Old sum - New sum
If count changes by 1: L = (Old avg × n) - (New avg × (n-1))

Common Mistakes to Avoid

Using old count instead of new count for new average calculation
Forgetting to subtract 1 from count after removal
Misinterpreting whether average increased or decreased
Not verifying that the leaving age is within possible range

Exam Importance

Average Age Removal is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions

Ready to Master Average Age Removal?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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