Question

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. Find the average age of the team.

• A. 23 years
• B. 26 years
• C. 50 years
• D. None of these

Hint:

For average problems, convert statements to total sums (average $\times$ count) and set up a simple linear equation.

Answer 1

The Correct Option is A

Let the average age of the whole team be $A$. Then total age $S=11A$.
Excluding captain (26) and keeper (29), the remaining 9 have average $A-1$, so sum $=9(A-1)=9A-9$.
Hence \[ 11A=(9A-9)+26+29=9A+46 \;\Rightarrow\; 2A=46 \;\Rightarrow\; A=\boxed{23}. \] 

Answer 2

Instead of directly writing the total-age equation for the whole team, we can use a deviation (shortcut) approach comparing the excluded pair's ages to the team average, and check each option.

1. Option A (23 years): Let the average age of the whole team be \(A\). The captain (\(26\)) and wicket-keeper (\(29\)) have a combined age of \(55\). If the remaining \(9\) players' average drops by exactly \(1\) year when these two are removed, the excess of the removed pair's age over "twice the average" must equal the total drop spread over the remaining \(9\) players: \[ 55-2A=9\times1=9\;\Rightarrow\;2A=46\;\Rightarrow\;A=23. \] This matches option A.
2. Option B (26 years): Substituting \(A=26\) gives \(55-52=3\ne9\), so this does not satisfy the deviation condition and is incorrect.
3. Option C (50 years): This is far too large an average given the captain and keeper are only \(26\) and \(29\), so it is incorrect.
4. Option D (none of these): Since option A satisfies the deviation equation exactly, this option is incorrect.

The deviation-based shortcut confirms the team's average age is \(23\) years.

Hence, the correct answer is option A: 23 years.