Average age rises by 20% when adding the head of family: The average age of 4 family members is 25 years. When the head of the family is included (making 5 people), the average increases by 20%. Find the age of the head.

Introduction / Context:Adding one member to a group changes the average depending on how that member compares to the current mean. Here the mean increases by a percentage, letting us work with totals cleanly.

Given Data / Assumptions:

• Average of 4 = 25 → current total = 100
• New average rises by 20% → new average = 25 * 1.20 = 30
• New count = 5

Concept / Approach:Compute the new total from the new average and count, then subtract the old total to get the head’s age.

Step-by-Step Solution:New total = 5 * 30 = 150Head’s age = 150 − 100 = 50 years

Verification / Alternative check:Check average with 5 people: (100 + 50) / 5 = 150 / 5 = 30, exactly 20% above 25.

Why Other Options Are Wrong:45, 55, and 60 would not give a 20% rise to 30; 40 keeps the average too low.

Common Pitfalls:Applying 20% to the total incorrectly or to just one person’s age; the percentage applies to the average (hence to the total proportionally).

Final Answer:50 yr