The captain of a cricket team of 11 members is 26 years old and the wicket-keeper is 3 years older than the captain. If the average age of the remaining 9 members is one year less than the average age of the whole team then the average age of the whole team is:?

Option 2 : 23 years

Concept used :

Total age = average age × number of players

Given :

Age of captain = 26 years

Total number of members = 11

Solution :

Let the average age of the whole team be x

Total age of whole team = 11 × x = 11x      -----(1)

Age of wicket-keeper = 26 + 3 = 29 years

The average age of team other than captain and wicket-keeper = (x - 1) years

Total age of team other than captain and wicket-keeper = 9 × (x - 1)      -----(2)

From (1) and (2) we get

11x = (x - 1)9 + 26 + 29

⇒ 11x = 9x - 9 + 55

⇒ 11x - 9x = 46

⇒ 2x = 46

∴ x = 23 years