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Age Change Impact on Average

Introduction

In some average age problems, the focus is not only on the group’s average, but on how the average changes when a member is replaced or someone new joins the group. These are slightly trickier than direct average questions because they involve comparing the before-and-after effect of the change.

The key is to calculate the difference in averages and use it to find the age of the person who joined, left, or was replaced.

Pattern: Age Change Impact on Average

Pattern

The key idea:

If the average increases or decreases when someone joins or is replaced, the total change in sum of ages is equal to (change in average × number of people).

Using this, we can directly calculate the missing person’s age.

Step-by-Step Example

Question

The average age of 5 friends is 20 years. One of them, Raj, leaves the group and is replaced by Rohan. The average age becomes 21 years. Find Rohan’s age if Raj was 18 years old.

Options:

  • A: 20 years
  • B: 21 years
  • C: 22 years
  • D: 23 years

Solution

  1. Step 1: Write the original total.

    Total age of 5 friends = 5 × 20 = 100

  2. Step 2: Write the new total after change.

    New total age = 5 × 21 = 105

  3. Step 3: Find the difference in totals.

    Increase in total = 105 - 100 = 5

  4. Step 4: Relate this change to Raj and Rohan.

    Rohan’s age = Raj’s age + increase = 18 + 5 = 23

  5. Final Answer:

    23 years → Option D

  6. Quick Check:

    New total = 100 - 18 + 23 = 105 → New average = 105 ÷ 5 = 21 ✅

Quick Variations

If the average decreases instead of increasing, subtract the difference from the leaving person’s age to find the new person’s age.

If a question says someone joins a group without mentioning replacement, simply compare the old total and new total using the change in average.

Trick to Always Use

  • Step 1: Multiply average × number of people to find total.
  • Step 2: Recalculate new total using the new average.
  • Step 3: Compare both totals to find the difference.
  • Step 4: Use the difference to calculate the missing person’s age.
  • Step 5: Verify by recalculating the new average.

Summary

Summary

The Age Change Impact on Average pattern is solved by:

Change in total age = Change in average × Number of people

  • Step 1: Compute the original total age.
  • Step 2: Compute the new total after replacement.
  • Step 3: Compare totals to identify the difference.
  • Step 4: Use this difference with given data to find the missing age.
  • Step 5: Verify with the average condition.

With practice, average-change problems become extremely easy to solve!

Practice

(1/5)
1. The average age of 4 friends is 20 years. One new friend joins and the new average becomes 21. What is the age of the new friend?
easy
A. 25
B. 24
C. 23
D. 26

Solution

  1. Step 1: Compute the old total age.

    Old total = 4 × 20 = 80.

  2. Step 2: Compute the new total with 5 friends.

    New total = 5 × 21 = 105.

  3. Step 3: Find the new friend’s age.

    New friend = 105 - 80 = 25.

  4. Final Answer:

    25 → Option A

  5. Quick Check:

    (80 + 25) ÷ 5 = 21 ✅
Hint: New member = (new_avg × new_count) - old_total.
Common Mistakes: Forgetting to multiply the averages by the group size before comparing totals.
2. The average age of 6 players is 22. One player aged 28 is replaced by a new player and the new average becomes 21. What is the age of the new player?
easy
A. 22
B. 20
C. 24
D. 26

Solution

  1. Step 1: Compute the old total.

    Old total = 6 × 22 = 132.

  2. Step 2: Compute the new total.

    New total = 6 × 21 = 126.

  3. Step 3: Find the remaining total after removing the replaced player.

    Remaining = 132 - 28 = 104.

  4. Step 4: Compute the new player’s age.

    New player = 126 - 104 = 22.

  5. Final Answer:

    22 → Option A

  6. Quick Check:

    (104 + 22) ÷ 6 = 21 ✅
Hint: New = new_total - (old_total - replaced_age).
Common Mistakes: Not removing the replaced person before calculating the new member’s age.
3. The average age of 5 children is 12 years. A new child joins and the average becomes 13. What is the age of the new child?
medium
A. 16
B. 18
C. 17
D. 15

Solution

  1. Step 1: Compute the old total.

    Old total = 5 × 12 = 60.

  2. Step 2: Compute the new total with 6 children.

    New total = 6 × 13 = 78.

  3. Step 3: Find the new child’s age.

    New child = 78 - 60 = 18.

  4. Final Answer:

    18 → Option B

  5. Quick Check:

    (60 + 18) ÷ 6 = 13 ✅
Hint: New child = new_total - old_total.
Common Mistakes: Using the difference of averages directly instead of converting to totals.
4. The average age of 8 men is 25 years. One man leaves and the average drops to 24. What was the age of the man who left?
medium
A. 31
B. 30
C. 32
D. 29

Solution

  1. Step 1: Compute the old total.

    Old total = 8 × 25 = 200.

  2. Step 2: Compute the new total after one leaves.

    New total = 7 × 24 = 168.

  3. Step 3: Compute the age of the man who left.

    Left = 200 - 168 = 32.

  4. Final Answer:

    32 → Option C

  5. Quick Check:

    (200 - 32) ÷ 7 = 24 ✅
Hint: Left = old_total - new_total.
Common Mistakes: Forgetting to reduce the count when computing the new total.
5. The average age of a cricket team of 11 players is 24. If the captain’s age is included, the average increases by 1. What is the age of the captain?
hard
A. 34
B. 35
C. 36
D. 37

Solution

  1. Step 1: Compute the old total.

    Old total = 11 × 24 = 264.

  2. Step 2: Compute the new total with the captain.

    New total = 12 × 25 = 300.

  3. Step 3: Find the captain’s age.

    Captain = 300 - 264 = 36.

  4. Final Answer:

    36 → Option C

  5. Quick Check:

    (264 + 36) ÷ 12 = 25 ✅
Hint: New member’s age = new_total - old_total.
Common Mistakes: Not increasing the number of people when computing the new average.

Mock Test

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