Question

A cricket team consist of 11 players with an average age of 32 years, the average age of the first five players is 40 years and the average age of the last 5 players is 26 years. The age of the coach of the team is 8 years more than the age of the sixth player, then find the average age of the coach and the sixth player of the team?
1. 23 years
2. 26 years
3. 32 years
4. 30 years

Answer 1

Correct Answer - Option 2 : 26 years

Given:

Average age of 11 players = 32 years

Average age of first five players = 40 years

Average age of last five players = 26 years

Age of coach = age of sixth player + 8 years

Formula Used:

Average = Sum of all the values/ Total number of values

Calculation:

The average age of 11 players = 32 years

⇒ Total age of 11 players = 32 × 11 years

⇒ 352 years      ----(i)

The average age of first five players = 40 years

⇒ Total age of first five players = 40 × 5 years

⇒ 200 years      ----(ii)

The average age of last five players = 26 years

⇒ Total age of last five players = 26 × 5 years

⇒ 130 years      ----(iii)

Age of sixth player = Total age of 11 players – (Total Age of first 5 players + Total age of last five players)

Putting values from equation (i), (ii) and (iii)

⇒ Age of sixth player = 352 – (200 + 130) years

⇒ 352 – 330 years

⇒ 22 years

Age of coach = Age of sixth player + 8 years

⇒ 22 + 8 years

⇒ 30 years

Average age of coach and sixth player = (30 + 22)/2 years

⇒ 52/2 years

⇒ 26 years

∴ The average age of coach and the sixth player is 26 years.