Coach added raises the average by 20%: The average age of four players is 18.5 years. If the coach is included, the average increases by 20%. What is the coach’s age?
Aptitude
Average
Difficulty: Medium
Choose an option
Answer
Correct Answer: 37 years
Explanation
Introduction / Context:An average increased by a percentage indicates a multiplicative change to the mean. Convert to totals before and after adding the coach to find their age.Given Data / Assumptions:
- Players: 4 with average 18.5 years ⇒ total 74.
- Including coach: 5 people; new average = 18.5 * 1.20 = 22.2 years.
Concept / Approach:Coach’s age = (new average * 5) − old total.Step-by-Step Solution:
Old total (players) = 4 * 18.5 = 74New total with coach = 5 * 22.2 = 111Coach’s age = 111 − 74 = 37 yearsVerification / Alternative check:Average check with ages consistent: (74 + 37) / 5 = 111/5 = 22.2 years, which is 20% higher than 18.5.Why Other Options Are Wrong:
- 28, 31, 34 years: Too small to raise the average by the stated 20% with count increasing to 5.
Common Pitfalls:Adding 20% of total instead of 20% of average, or forgetting that headcount increases from 4 to 5.Final Answer:
37 years