Question

The captain of a cricket team of 11 members is 35 years old and the wicket-keeper is 5 years older than the captain. If the ages of these two are excluded, the average age of the remaining players is three years less than the average age of the whole team. What is the average age of the whole team?

• A. 24 years
• B. 28 years
• C. 26 years
• D. 25 years

Answer 1

Answer:

A. 24 years

Age of captain = 35
Age of wicketkeeper = 35 + 5 = 40
Let the average age of all players be x
When captain & wicketkeeper excluded average age is 'x – 3’ years
Age of whole team = 11 × x = 11x
Age of team when captain and wicket keeper excluded = 9(x- 3)
⇒ 11x - (35 + 40) = 9(x - 3)
⇒ 11x = 9x - 27 + 75
⇒ 2x = 75 - 27
⇒ 2x = 48
⇒ x = 24

Alternate Method
Let the average age be x
let the average age be 'x - 3' when captain and wicket keeper are exclude
Total age of team = 11 × x = x
[11x - (35 + 40)]/9 = x - 3
⇒ 11x - 75 = 9x - 27
⇒ 2x = 48
⇒ x = 24