Question

The average age of a class of 20 students is 12 years. Out of which one student whose age is 10 year left the class and two new boys entered the class. The average of the class remains the same and the difference between the ages of new boys is 4 year. What will be the age of younger one .

Answer 1

The average age of $20$ students is $12$ years.

$\therefore$ Total age of $20$ students $=20\times 12=240years$

It is given that, student who is $10years$ old left the class.

$\therefore$ Total age of $19$ students $=240-10=230years$

An then $2$ new students entered and average remain same.

$\therefore$ Total age of $21$ students $=21\times 12=252years$

$\Rightarrow$ Total age of $2$ new students who entered in the class $=252-230=22years$

Let $x$ and $y$ be the two new students.

$\therefore$ $x+y=22$ ------ ( 1 )

According to the question,

$x-y=4$ ----- ( 2 )

Now adding $\left(1\right)$ and $\left(2\right)$, we get,

$x=13$

Putting value of $x$ in equation ( 1 ) we get,

$y=9$

$\therefore$ The age of younger one is $9years$.