Average age increases after replacing three men with three women: A committee has 11 persons. Replacing men aged 32, 34, and 33 by three women increases the committee’s average age by 2 years. What is the average age of the three women?

Introduction / Context:
When a group’s average increases after replacement without changing the headcount, the total age increases by (increase in average) * (group size). That increase must come from the difference between the incoming and outgoing members’ totals.

Given Data / Assumptions:

• Total persons remain 11
• Average increases by 2 years → total age increases by 11 * 2 = 22 years
• Outgoing men: 32, 34, 33 (sum = 99)

Concept / Approach:
Let W be the sum of the three women’s ages. Then W − 99 = 22 → W = 121. The average of the three women is W / 3.

Step-by-Step Solution:
Increase in total = 22W − 99 = 22 → W = 121Average (women) = 121 / 3 = 40 1/3 years

Verification / Alternative check:
Replacing 99 by 121 raises the committee total by 22, which across 11 members raises the mean by exactly 2 years.

Why Other Options Are Wrong:
40, 41, and 39 2/3 do not produce the exact +22 total change; 411/3 is a misread of the mixed fraction needed here (correct is 401/3).

Common Pitfalls:
Confusing “sum increases by 22” with “each woman is 22 years older” or misreading mixed fractions. Always compute totals first.

Final Answer:
401/3 yr