The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 29 years old. If the ages of these two players are excluded, the average age of the remaining 9 players is one year less than the average age of the whole team. What is the average age of the entire team?

Introduction / Context:
This question involves average age in a sports team, a very common pattern in aptitude tests. The twist is that the removal of two members changes the average of the remaining players in a known way. The goal is to convert the information about averages into algebraic equations involving total ages, and then solve for the unknown team average.

Given Data / Assumptions:

• Total number of team members = 11.
• Age of the captain = 26 years.
• Age of the wicket keeper = 29 years.
• Average age of remaining 9 players is one year less than the average age of the whole team.
• We need the average age of all 11 players.

Concept / Approach:
When you know an average, you can always write total = average * number of items. Here, let the unknown team average be A. Then the total age of all 11 players is 11A. We know the ages of two specific players, so we can subtract them to get the total age of the remaining 9 players. Using the fact that the remaining players have an average of A - 1, we can form an equation and solve for A.

Step-by-Step Solution:
Let the average age of the whole team be A years.Total age of all 11 players = 11 * A.Ages of captain and wicket keeper together = 26 + 29 = 55 years.Total age of the remaining 9 players = 11A - 55.Average age of these 9 players is given as (A - 1) years.So, (11A - 55) / 9 = A - 1.Multiply both sides by 9: 11A - 55 = 9A - 9.Bring like terms together: 11A - 9A = -9 + 55, so 2A = 46.Therefore, A = 23 years.

Verification / Alternative check:
If the average is 23, total age of 11 players = 11 * 23 = 253. After removing the captain and wicket keeper, remaining total = 253 - 55 = 198. Average of 9 players = 198 / 9 = 22, which is exactly one year less than 23. This matches the statement in the problem, so the solution is correct.

Why Other Options Are Wrong:
At 20 or 21 years, the numbers do not satisfy the relationship that removing two players reduces the average by exactly one year. At 25 years, the remaining players would not average 24 years. Only 23 years gives a consistent solution for all conditions given in the question.

Common Pitfalls:
Common errors include mixing up the number of players (using 10 instead of 9 for the remaining group), or assuming the difference in ages of the removed players directly affects the change in average. The correct method is always to set up total sums using the average formula and then solve the resulting linear equation carefully.

Final Answer:
The average age of the entire team is 23 years.