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 \[ 11A=(9A-9)+26+29=9A+46 \;\Rightarrow\; 2A=46 \;\Rightarrow\; A=\boxed{23}. \]