0
0

Effect of Adding/Removing a Member

Introduction

Aptitude problems में कभी-कभी समूह का average बदल जाता है जब कोई नया member जुड़ता है या कोई existing member group छोड़ देता है।

ये questions यह test करते हैं कि आप addition या removal के बाद total sum को सही तरीके से adjust कर सकते हैं और फिर नया average निकाल सकते हैं या नहीं।

Pattern: Effect of Adding/Removing a Member

Pattern

Key ideas:

Adding a member: New total = Old total + नए member का value।
New average = New total ÷ (n + 1).

Removing a member: New total = Old total - removed member का value।
New average = New total ÷ (n - 1).

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

Step-by-Step Example

Question

10 students का average age 20 years है। एक नया student जिसकी age 30 है, group में जुड़ता है। नया average age क्या होगा?

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

Solution

  1. Step 1: Old total निकालें

    Old total = 10 × 20 = 200.

  2. Step 2: नए member का value जोड़ें

    New total = 200 + 30 = 230.

  3. Step 3: Count update करें

    New count = 10 + 1 = 11.

  4. Step 4: नया average निकालें

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

  5. Final Answer:

    20.91 years → Option C

  6. Quick Check:

    जो value average से बड़ी थी वह जुड़ी - इसलिए average में थोड़ी वृद्धि होनी चाहिए। ऐसा हुआ भी ✅

Question

5 workers का average salary ₹12,000 है। एक worker जिसकी salary ₹15,000 है, group छोड़ देता है। नया average salary क्या होगा?

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

Solution

  1. Step 1: Old total निकालें

    Old total = 5 × 12,000 = 60,000.

  2. Step 2: Removed member की value घटाएँ

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

  3. Step 3: Count घटाएँ

    New count = 5 - 1 = 4.

  4. Step 4: नया average निकालें

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

  5. Final Answer:

    ₹11,250 → Option C

  6. Quick Check:

    उच्च salary वाला worker गया - इसलिए average घटना चाहिए; घट भी गया ✅

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