The average age of 6 members of a family is 20 years. If the age of a servant is also included, the average age increases by 25%. What is the age (in years) of the servant?

Introduction / Context:
This is an averages and totals question. Average is total sum divided by number of items (people). When a new person is included, both the total sum and the number of people change. Because the new average is given as a percentage increase of the old average, you can compute the new average directly. Then compute the new total sum and subtract the original total to isolate the servant's age. This approach is systematic and avoids guesswork.

Given Data / Assumptions:

• Average age of 6 family members = 20 years
• Servant added, total people = 7
• Average increases by 25% (relative increase)
• Let servant age = S years

Concept / Approach:
Original total = 6 * 20. New average = 20 * (1 + 25/100) = 25. New total = 7 * 25. Servant age is the difference between new total and original total.

Step-by-Step Solution:
Original total age = 6 * 20 = 120 New average = 20 * 1.25 = 25 New total age (7 people) = 7 * 25 = 175 Servant age S = 175 - 120 = 55

Verification / Alternative check:
If the servant is 55, the new total is 120 + 55 = 175, and the new average is 175/7 = 25. Since 25 is 25% more than 20 (because 20 + 25% of 20 = 20 + 5 = 25), the statement is satisfied exactly.

Why Other Options Are Wrong:
30 and 35 are too small; they cannot raise the average from 20 to 25. 50 gives total 170 and average 170/7 = 24.285..., not 25. 45 gives average 165/7 = 23.571..., also not 25.

Common Pitfalls:
Thinking “increase by 25%” means adding 25 years, forgetting the number of people becomes 7, or using 25% of the new average instead of 25% of the old average.

Final Answer:
The servant's age is 55 years.