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Family Average

Family Average problems involve calculating or using the average age of family members. These problems often combine average concepts with individual age relationships and family composition changes.

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 Family Average

Family Average problems involve calculating or using the average age of family members. These problems often combine average concepts with individual age relationships and family composition changes.

Prerequisites

Average formula Sum = Average × Number Age progression effects on average
Why This Matters: Family Average problems appear in 1-2 questions in banking and SSC exams. They test your understanding of averages and their behavior when members are added or removed.

How to Solve Family Average Problems

1

Step 1: Use the formula: Sum of ages = Average × Number of members

2

Step 2: Calculate present total sum from given average

3

Step 3: For future averages, add n years to each person's age

4

Step 4: New total sum = Old sum + (n × number_of_members)

5

Step 5: New average = New sum ÷ New number of members

6

Step 6: For member replacement, adjust total sum accordingly

Pro Strategy: Remember that the average age increases exactly by n years when all members age by n years, provided no members are added or removed.

Example Problem

Example: Average age of a family of 5 members is 25 years. What will be the average age after 10 years? Solution: Step 1: Present total sum = 25 × 5 = 125 years Step 2: After 10 years, each of 5 members ages 10 years Step 3: New total sum = 125 + (10 × 5) = 125 + 50 = 175 years Step 4: New average = 175 ÷ 5 = 35 years Answer: 35 years Shortcut: New average = 25 + 10 = 35 years

Pro Tips & Tricks

  • New average = Old average + n (when no members change)
  • When a new member joins, new average = (Old sum + New member's age) ÷ (Old count + 1)
  • When a member leaves, new average = (Old sum - Leaving member's age) ÷ (Old count - 1)
  • Average age n years ago = Present average - n
  • Total sum = Average × Number (always remember this relationship)
  • Weighted averages appear when combining multiple families

Shortcut Methods to Solve Faster

Average after n years = Present average + n
Average n years ago = Present average - n
Total sum = Average × Count

Common Mistakes to Avoid

Adding n to average without multiplying by count for total sum
Forgetting to update the count when members change
Using average instead of sum in replacement problems
Miscalculating when multiple changes happen sequentially

Exam Importance

Family Average 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 Family Average?

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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