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The Average Age (In Years) of a Class is Twice the Number of Students in the Class. Then Find the Average Age of the Class, If One More Student Z of Age 16 Years Leaves the Class. - Mathematics

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MCQ

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

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Solution

Let the number of students in the class be n
Total age = n x 2n = 2n2
When X leaves, the total age = (n - 1) x 2(n - 1) = 2(n - 1)2
X's age = 2n2 - 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

Concept: Average and Age
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