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?

Given data

• Team size = 11 players
• Captain's age = 26; Wicket keeper's age = 26 + 3 = 29
• Excluding these two, the average age of remaining 9 players is one year less than the average age of the whole team

Let the team's average be A years

Step 1: Write the sums
Total age of team = 11ASum of remaining 9 = 11A − (26 + 29) = 11A − 55

Step 2: Use the condition on averages
Average of remaining 9 = (11A − 55) ÷ 9 = A − 1⇒ 11A − 55 = 9A − 9⇒ 2A = 46 ⇒ A = 23 years

Check

• Remaining 9 average = A − 1 = 22 years.
• Sum of remaining 9 = 9 × 22 = 198; add captain and keeper: 198 + 26 + 29 = 253; 253 ÷ 11 = 23 ✓

Final Answer
Average age of the team is 23 years.