Replacing a 25-year-old woman with Priyanka decreases the average age of 30 women by 3 months (0.25 year). What is Priyanka's age?

Introduction / Context:Average change due to replacement equals (new member's value − old member's value) divided by group size. A decrease in the average indicates the newcomer is younger than the outgoing member by (drop * group size).

Given Data / Assumptions:

• Group size constant = 30.
• Outgoing age = 25 years.
• Average decreases by 0.25 year.

Concept / Approach:Total decrease = drop in average * group size = 0.25 * 30. Newcomer's age = outgoing age − total decrease, since the new total is lower by that amount across the group.

Step-by-Step Solution:

Verification / Alternative check:If the new average is lower by 0.25, across 30 women the total age must be 7.5 years less; replacing 25 by 17.5 decreases the total by 7.5, exactly as required.

Why Other Options Are Wrong:20, 30, 22: None yields a 7.5-year reduction in total; they would cause different average shifts.

Common Pitfalls:Subtracting 0.25 directly from 25 (getting 24.75), forgetting that the 0.25 drop applies across all 30 members.

Final Answer:17.5 yr