**Solve the following question and mark the best possible option.**

The average age (in years) of a class is twice the number of students in the class. A student, X leaves the class and the average age is still twice the number of students in the class. Now another student Y leaves the class and the average is still twice the number of students in the class. If the ratio of the ages of X and Y is 19: 17, then find the average age of the class, if one more student Z of age 16 years leaves the class.

#### Options

10

15

16

18

#### Solution

Let the number of students in the class be n

Total age = n x 2n = 2n^{2}

When X leaves, the total age = (n - 1) x 2(n - 1) = 2(n - 1)^{2}

X's age = 2n^{2} - 2(n -1)^{2}

When Y leaves the total age = (n - 2) x 2(n - 2) = 2(n - 2)^{2}Y's age = 2(n - 1)^{2} - 2(n - 2)^{2}

Therefore, Ratio of ages of X and Y.

⇒ `( 2n^2 - 2(n - 1)^2)/(2(n - 1)^2 - 2(n - 2)^2) = 19/17`

⇒ `(n^2 - (n^2 - 2n + 1))/((n^2 - 2n + 1) - (n^2 - 4n + 4)) = 19/17`

⇒ `(2n - 1)/(2n - 3) = 19/17`

⇒ n = 10.

When z leaves, total age = 2(n - 2)^{2} - 16 = 2(8)^{2} - 16 = 112

Avarage age = `112/7` = 16