What's the best way to master Average Replacement Age Problems quickly?

Master Average Replacement Age Problems by understanding the core concepts first, practicing regularly with our worksheets, and applying the shortcut techniques provided.

Average Replacement

Average Replacement problems involve scenarios where a family member is replaced by another person (often of different age), causing the average age to change. These problems test your understanding of how averages respond to replacements.

10Worksheets

200+Practice Questions

AdvancedDifficulty

3-4 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 Replacement

Prerequisites

Average formula Sum = Average × Count Age difference concepts

Why This Matters: Average Replacement problems appear in 1-2 questions in banking and SSC mains exams. They test advanced average concepts.

How to Solve Average Replacement Problems

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

Step 2: Let the age of the person leaving = L, person joining = J

Step 3: New total sum = Old sum - L + J

Step 4: New average = New total sum ÷ Count (if count unchanged)

Step 5: If count changes, adjust denominator accordingly

Step 6: Use the change in average to find the difference between J and L

Pro Strategy: Focus on the change in total sum. The difference between joining and leaving ages equals the change in total sum (count × change in average).

Example Problem

Example: Average age of 5 family members is 30 years. A member aged 40 leaves and a new member joins, making the average 28 years. Find the age of the new member. Solution: Step 1: Old total sum = 30 × 5 = 150 years Step 2: Let new member's age = x Step 3: New total sum = 150 - 40 + x = 110 + x Step 4: New average = (110 + x)/5 = 28 Step 5: 110 + x = 140 → x = 30 years Answer: New member is 30 years old

Pro Tips & Tricks

Change in total sum = Count × Change in average (when count same)
J - L = Count × (New avg - Old avg)
If count changes, use: New sum = Old sum - L + J
When multiple replacements happen, process sequentially
The replaced person's age affects the total sum directly
Draw a table to track sums before and after replacement

Shortcut Methods to Solve Faster

J = L + Count × (New avg - Old avg)

If average increases, J > L; if decreases, J < L

For one replacement: New sum = Old sum + (J - L)

Common Mistakes to Avoid

Forgetting to subtract the leaving person's age

Using old count instead of new count when count changes

Misinterpreting whether average increased or decreased

Not accounting for multiple replacements in sequence

Practice Worksheets

Practice makes perfect! Work through these worksheets to master Average Replacement. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.

Worksheet 1 Beginner Beginner level - Perfect for building foundational understanding

Worksheet 2 Beginner Beginner level - Perfect for building foundational understanding

Worksheet 3 Beginner Beginner level - Perfect for building foundational understanding

Worksheet 4 Intermediate Intermediate level - Test your understanding with moderate difficulty

Worksheet 5 Intermediate Intermediate level - Test your understanding with moderate difficulty

Worksheet 6 Intermediate Intermediate level - Test your understanding with moderate difficulty

Worksheet 7 Advanced Advanced level - Challenge yourself with complex problems

Worksheet 8 Advanced Advanced level - Challenge yourself with complex problems

Worksheet 9 Advanced Advanced level - Challenge yourself with complex problems

Worksheet 10 Advanced Advanced level - Challenge yourself with complex problems