The average age of 5 family members is 25 years. Including the servant increases the average age by 40%. What is the servant's age?
Aptitude
Average
Difficulty: Medium
Choose an option
Answer
Correct Answer: 85 yr
Explanation
Introduction / Context:Average increase by a percentage upon adding one member suggests the new average equals old average times (1 + percentage). Use totals to get the added person’s age precisely.
Given Data / Assumptions:
- 5 members, mean 25 ⇒ total = 125.
- Including servant: 6 persons; mean increases by 40% ⇒ new mean = 25 * 1.4 = 35.
Concept / Approach:New total = new mean * new headcount = 35 * 6. Servant's age = new total − old total.
Step-by-Step Solution:
New total = 35 * 6 = 210 Old total = 125 Servant's age = 210 − 125 = 85 yearsVerification / Alternative check:With servant 85, total becomes 210; average 210 / 6 = 35, which is exactly 40% above 25.
Why Other Options Are Wrong:90, 73, 55: Do not produce a new average of 35 when recomputed.
Common Pitfalls:Adding 40% of the total instead of 40% of the average, or applying the 40% to only one person's age erroneously.
Final Answer:85 yr