The captain of a cricket team of 11 members is 26 years old and the…
2023
The captain of a cricket team of 11 members is 26 years old and the wicketkeeper 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?
- A.
20
- B.
30
- C.
23
- D.
12
Attempted by 34 students.
Show answer & explanation
Correct answer: C
Answer: 23 years.
Let the average age of the whole team be x years. Then the total age of 11 players is 11x.
The captain is 26 and the wicketkeeper is 29, so together they are 55 years. The remaining 9 players have average (x − 1), so their total age is 9(x − 1) = 9x − 9.
Set up the equation for total ages: 11x = 55 + (9x − 9).
Simplify: 11x = 9x + 46, so 2x = 46.
Solve: x = 23.
Check: Total = 11 × 23 = 253. Subtract the two ages 253 − 55 = 198; average of remaining 9 players = 198/9 = 22, which is indeed one year less than 23.
Therefore the average age of the team is 23 years.