The average age of a committee of 9 members increases by 3 years when two men aged 42 and 44 years are replaced by two women. What is the average age of these two women?

Correct — C. Turn the rise in average into a rise in total.

Rise in the committee's total age: 9 × 3 = 27 years
Age of the two men removed: 42 + 44 = 86 years
The women replace the men and add the rise: 86 + 27 = 113 years

Average of the two women: 113 ÷ 2 = 56.5 years → option (c)

Why the others are wrong

• (a)
  50.5 years — Two women averaging 50.5 total 101, only 15 more than the men's 86. Spread over 9 members that lifts the average by 15⁄9 ≈ 1.67 years, not 3.
• (b)
  46.5 years — 46.5 each totals 93, just 7 above the men's 86, so the average would rise by 7⁄9 ≈ 0.78 years. The men themselves average 43.
• (d)
  60.5 years — 60.5 each totals 121, 35 above the men's 86. That lifts the 9-member average by 35⁄9 ≈ 3.89 years, more than the 3 stated.

Change in average × group size = change in total. The committee still has 9 members after the swap, so a 3-year rise in the average means the total age went up by 27 years.

Nobody else changed, so the whole 27 years comes from the women being older than the men they replaced. The women's total = the men's total + 27.

Key facts

• Change in total = number of members × change in average.
• Here 9 × 3 = 27, so the two women together are 27 years older than the two men.
• Shortcut: the women's average = the men's average + 27 ÷ 2 = 43 + 13.5 = 56.5.

Common traps

• Adding the 3-year rise to the men's average (43 + 3 = 46). The rise belongs to all 9 members, not to the two women.
• Forgetting that two people share the 27-year rise: the women's total is 113, and their average is half of it.

No directly related past PYQ was found.