0
0

Effect of Adding/Removing a Member

Introduction

In aptitude problems on averages, sometimes the average of a group changes when a new member joins or an existing member leaves.

These questions test whether you can adjust the total sum correctly after the addition or removal, then recalculate the new average.

Pattern: Effect of Adding/Removing a Member

Pattern

Key ideas:

Adding a member: New total = Old total + New member’s value.
New average = New total ÷ (n + 1).

Removing a member: New total = Old total - Removed member’s value.
New average = New total ÷ (n - 1).

Shortcut: Change in average = (New/Removed value - Old average) ÷ New count.

Step-by-Step Example

Question

The average age of 10 students is 20 years. A new student aged 30 joins the group. What is the new average age?

Options:
A) 20.5 B) 20.8 C) 20.9 D) 21.0

Solution

  1. Step 1: Compute the old total

    Old total = 10 × 20 = 200.

  2. Step 2: Add the new member’s value

    New total = 200 + 30 = 230.

  3. Step 3: Update the count

    New count = 10 + 1 = 11.

  4. Step 4: Calculate the new average

    New average = 230 ÷ 11 = 20.91 (approx).

  5. Final Answer:

    20.91 years → Option C

  6. Quick Check:

    A larger-than-average value was added → average should rise slightly. It does. ✅

Question

The average salary of 5 workers is ₹12,000. One worker with salary ₹15,000 leaves the group. What is the new average salary?

Options:
A) ₹10,000 B) ₹11,000 C) ₹11,250 D) ₹12,500

Solution

  1. Step 1: Compute the old total

    Old total = 5 × 12,000 = 60,000.

  2. Step 2: Subtract the removed member’s value

    New total = 60,000 - 15,000 = 45,000.

  3. Step 3: Reduce the count

    New count = 5 - 1 = 4.

  4. Step 4: Calculate the new average

    New average = 45,000 ÷ 4 = 11,250.

  5. Final Answer:

    ₹11,250 → Option C

  6. Quick Check:

    A high-salary worker left → average should decrease. It does. ✅

Quick Variations

Adding multiple members: Add all their values to total, increase count accordingly.

Removing multiple members: Subtract their values from total, decrease count accordingly.

Mixed cases: Add some members and remove some - adjust total and count both.

Trick to Always Use

  • Step 1: Old total = average × count.
  • Step 2: Add/remove member’s value to adjust total.
  • Step 3: New average = adjusted total ÷ new count.
  • Step 4: Always check if the average should rise or fall.

Summary

Summary

Adding or removing a member affects the average because the total and count change together.

  • Adding: Total + new value, count + 1.
  • Removing: Total - removed value, count - 1.
  • Shortcut: Average change = (new - old average) ÷ new count.
  • Quick Check: If added > average → average rises; if removed > average → average falls.

Practice

(1/5)
1. The average age of 6 students is 15 years. A new student aged 21 joins the group. What is the new average?
easy
A. 15.8
B. 16.0
C. 16.2
D. 16.5

Solution

  1. Step 1: Compute the old total

    Old total = 6 × 15 = 90.

  2. Step 2: Add the new member’s age

    New total = 90 + 21 = 111.

  3. Step 3: Update the count

    New count = 6 + 1 = 7.

  4. Step 4: Calculate the new average

    New average = 111 ÷ 7 = 15.86 ≈ 15.8.

  5. Final Answer:

    15.8 → Option A

  6. Quick Check:

    Since new member > old average, average rises ✅
Hint: New avg = (old total + new value) ÷ (n+1).
Common Mistakes: Dividing by 6 instead of 7 after adding the member.
2. The average salary of 5 workers is ₹10,000. A worker earning ₹12,000 leaves. What is the new average salary?
easy
A. 9,000
B. 9,200
C. 9,500
D. 9,800

Solution

  1. Step 1: Compute the old total

    Old total = 5 × 10,000 = 50,000.

  2. Step 2: Subtract the leaving member’s salary

    New total = 50,000 - 12,000 = 38,000.

  3. Step 3: Update the count

    New count = 5 - 1 = 4.

  4. Step 4: Calculate the new average

    New average = 38,000 ÷ 4 = 9,500.

  5. Final Answer:

    9,500 → Option C

  6. Quick Check:

    One higher salary left → average decreases ✅
Hint: Subtract the leaving salary and divide by (n-1).
Common Mistakes: Forgetting to reduce the count after removing a member.
3. The average score of 8 players is 40 runs. A new player scores 56 runs and joins. What is the new average score?
easy
A. 41
B. 41.8
C. 42.5
D. 43

Solution

  1. Step 1: Compute the old total

    Old total = 8 × 40 = 320.

  2. Step 2: Add the new player’s score

    New total = 320 + 56 = 376.

  3. Step 3: Update the count

    New count = 8 + 1 = 9.

  4. Step 4: Calculate the new average

    New average = 376 ÷ 9 = 41.78 ≈ 41.8.

  5. Final Answer:

    41.8 → Option B

  6. Quick Check:

    New member > old avg → average increases ✅
Hint: Add the new member’s score and divide by updated count.
Common Mistakes: Dividing by 8 instead of 9 after addition.
4. The average weight of 12 boys is 50 kg. If one boy of 60 kg leaves the group, what is the new average weight?
medium
A. 49
B. 49.1
C. 49.5
D. 50

Solution

  1. Step 1: Compute the old total

    Old total = 12 × 50 = 600.

  2. Step 2: Subtract the leaving boy’s weight

    New total = 600 - 60 = 540.

  3. Step 3: Update the count

    New count = 12 - 1 = 11.

  4. Step 4: Calculate the new average

    New average = 540 ÷ 11 = 49.09 ≈ 49.1.

  5. Final Answer:

    49.1 → Option B

  6. Quick Check:

    Heavier boy left → average decreases ✅
Hint: If leaving value > average → average decreases.
Common Mistakes: Subtracting weight but not reducing the count.
5. The average marks of 15 students is 48. If a student with 60 marks joins, what is the new average?
medium
A. 48.7
B. 49
C. 49.5
D. 50

Solution

  1. Step 1: Compute the old total

    Old total = 15 × 48 = 720.

  2. Step 2: Add the new student’s marks

    New total = 720 + 60 = 780.

  3. Step 3: Update the count

    New count = 15 + 1 = 16.

  4. Step 4: Calculate the new average

    New average = 780 ÷ 16 = 48.75 ≈ 48.7.

  5. Final Answer:

    48.7 → Option A

  6. Quick Check:

    New student has more than 48 → average rises ✅
Hint: Change in average = (new value - old avg) ÷ (n+1).
Common Mistakes: Using old count instead of new count.

Mock Test

Ready for a challenge?

Take a 10-minute AI-powered test with 10 questions (Easy-Medium-Hard mix) and get instant SWOT analysis of your performance!

10 Questions
5 Minutes