The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older than the captain. If the ages of these two players are excluded, the average age of the remaining 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 age based question uses the idea of removing two members from a group and seeing how the average changes. We know the ages of the captain and the wicket keeper, and we are told that when they are removed, the average age of the remaining nine players is one year less than the overall team average. From this, we have to find the average age of the whole cricket team of 11 players.

Given Data / Assumptions:
- Total number of team members = 11.
- Age of the captain = 26 years.
- Age of the wicket keeper = 26 + 3 = 29 years.
- If these two players are excluded, 9 players remain.
- The average age of the 9 remaining players is 1 year less than the average age of the whole team.
- Let the average age of the whole team be A years.

Concept / Approach:
The average age of the whole team, multiplied by 11, gives the total age of all members. When we remove the captain and the wicket keeper, we subtract their ages from this total to get the sum of ages of the remaining nine players. Dividing that new total by 9 gives their average, which is given as A - 1. Setting up this equation allows us to solve for A.

Step-by-Step Solution:
Step 1: Total age of all 11 players = 11 * A.Step 2: Combined age of captain and wicket keeper = 26 + 29 = 55 years.Step 3: Total age of the remaining 9 players = 11 * A - 55.Step 4: Average age of the remaining 9 players is given as A - 1.Step 5: Therefore, (11 * A - 55) / 9 = A - 1.Step 6: Multiply both sides by 9 to remove the denominator: 11A - 55 = 9A - 9.Step 7: Rearrange terms: 11A - 9A = 55 - 9, so 2A = 46.Step 8: Hence A = 46 / 2 = 23 years.

Verification / Alternative Check:
If the average age of the team is 23 years, total age of 11 players is 11 * 23 = 253 years. Removing the captain and wicket keeper removes 55 years, leaving 253 - 55 = 198 years for 9 players. Their average becomes 198 / 9 = 22 years, which is indeed one year less than 23. This confirms that our value for A is consistent with the given condition.

Why Other Options Are Wrong:
If the team average were 20, 21 or 25 years, the resulting average of the remaining 9 players would not be exactly one year less than the overall average when the given ages of 26 and 29 are subtracted. Only an average of 23 years satisfies the equation and the described situation.

Common Pitfalls:
Some learners mistakenly subtract 2 from the average instead of 1, or they forget that the total age reduces by the sum of both removed players. Others divide by 11 instead of 9 after removal. To avoid such errors, always compute totals first, then use the correct number of players in each average.

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