Difficulty: Easy
Correct Answer: 34 yrs
Explanation:
Introduction / Context:
This question explores how the average age changes when an additional member (the coach) is included in a team. We are given the average age of 11 players, and after including the coach, the new average age of 12 people increases by 1 year. Using average and total age relationships, we can easily compute the coach's age.
Given Data / Assumptions:
Concept / Approach:
Average is given by:
average age = total age / number of persons.
We first compute the total age of the 11 players from their average. Then we compute the total age of all 12 people from the new average. The difference between these two totals is the age of the coach.
Step-by-Step Solution:
Step 1: Total age of the 11 players.
Total(players) = 11 * 22 = 242 years.
Step 2: New average age after adding the coach = 23 years.
Number of persons now = 12.
Total(players + coach) = 12 * 23 = 276 years.
Step 3: Age of the coach = total(players + coach) − total(players).
Coach's age = 276 − 242 = 34 years.
Verification / Alternative check:
Check: If the coach is 34, adding him to the 11 players gives total age 242 + 34 = 276.
Average age = 276 / 12 = 23 years, which is exactly 1 year more than the players' average (22), satisfying the given condition.
Why Other Options Are Wrong:
If the coach were 33 years old, total would be 242 + 33 = 275, giving an average of 275 / 12 ≈ 22.92, not exactly 23.
Similarly, coach ages of 35, 36, or 38 would give higher totals and correspondingly higher averages than 23 years.
Common Pitfalls:
Some students confuse the direction of the average change and try to subtract rather than add when computing the total age with the coach.
Others may mistakenly multiply by 11 instead of 12 when computing the new total based on the new average.
Final Answer:
The age of the coach is 34 yrs.
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