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Let's analyze the problem:

We have a cricket team of 11 members. The captain is 26 years old, and the wicket-keeper is 3 years older, making him 29 years old. The average age of the remaining players (after excluding the captain and wicket-keeper) is one year less than the average age of the whole team.

Let's denote:
- \( x \) as the average age of the whole team.
- The total age of all 11 players is \( 11x \).

The total age of the remaining 9 players (after excluding the captain and wicket-keeper) is \( 11x - 26 - 29 = 11x - 55 \).

The average age of these 9 players is given as \( x - 1 \).

Thus, we can write the equation:
\[
\frac{11x - 55}{9} = x - 1
\]

Now let's solve this equation for \( x \):

1. Multiply both sides by 9:
\[
11x - 55 = 9(x - 1)
\]

2. Simplify the right-hand side:
\[
11x - 55 = 9x - 9
\]

3. Subtract \( 9x \) from both sides:
\[
2x - 55 = -9
\]

4. Add 55 to both sides:
\[
2x = 46
\]

5. Divide by 2:
\[
x = 23
\]

Thus, the average age of the whole team is **23 years**.

Would you like further clarification or details on this solution?

Here are 5 related questions to consider:
1. What if the captain and wicket-keeper were both 2 years younger, how would the average change?
2. How does the average age change if an additional player is added?
3. What is the total age of the team based on this average?
4. How would the equation change if there were 12 players instead of 11?
5. Can you find the individual ages of the remaining players based on this information?

**Tip:** When solving average problems, always set up an equation based on the definition of average (sum divided by number of items) for better clarity.

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two 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 team?

Solve the average age problem for a cricket team where the ages of the captain and wicket-keeper are excluded. This problem involves averages and algebraic equations, perfect for Grades 8-10 students.

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