The average age of 12 men in a group is increased by 2 years when two men…
2025
The average age of 12 men in a group is increased by 2 years when two men whose ages are 20 years and 22 years, are replaced by new members. What is the average age of the new men included?
- A.
35
- B.
33
- C.
31
- D.
29
Attempted by 12 students.
Show answer & explanation
Correct answer: B
When a fixed number of members in a group is replaced and the group's average changes, the total sum of ages changes by (change in average) × (number of members in the group). That total change lets us recover the combined age of the new members from the combined age of those removed.
Number of men in the group = 12; the average age rises by 2 years after the replacement.
So the total age of the group increases by 12 × 2 = 24 years.
The two men removed had ages 20 and 22 years, whose combined age is 20 + 22 = 42 years.
Since the replacement raises the total by 24 years, the combined age of the two new men is 42 + 24 = 66 years.
Average age of the new men = 66 ÷ 2 = 33 years.
Check: if the original average was A, the original total was 12A. After replacement the total becomes 12A − 42 + 66 = 12A + 24, so the new average is A + 2 — exactly the 2-year rise stated in the question, confirming 33 is correct.
