Question

The average age of 11 players of a cricket team is decreased by 2 months when two of them aged 17 years and 20 tears are replaced by two new players . The average age of the new players is

• A. 17 years 1 month
• B. 17 years 7 months
• C. 17 years 11 months
• D. 18 years 3 months

Answer 1

The correct option is B 17 years 7 months

Let the average age of 11 players be x.
Then, total age of 11 players = 11x
Total age of 9 players = 11x - (17 + 20) = 11x - 37
Let y be the total age of the 2 new players.
Then $\frac{11x-37+y}{11}=x-\frac{1}{6}=\frac{6x-1}{6}$
$\Rightarrow 66x-222+6y=66x-11$
$\Rightarrow 6y=-11+222=211y=\frac{211}{6}years$
$\therefore$ Average of the two players = $\frac{y}{2}=\frac{211}{12}=17$ years 7 months.