there r 'N' students in one class whose average age is 19 and if 2 students leave their avg age 18 now what is average age of two students who left ?
Hello, arunachalam.s!
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There are $\displaystyle n$ students in one class whose average age is 19.
If two students leave, the average age of the class is 18.
What is average age of two students who left?
Let $\displaystyle S$ = sum of the ages of all $\displaystyle n$ students.
Then: .$\displaystyle \frac{S}{n} \,=\,19 \quad\Rightarrow\quad S \:=\:19n$ .[1]
Let $\displaystyle x$ = sum of the ages of the two students.
Then the other $\displaystyle n-2$ students have a sum of $\displaystyle S - x$ years.
. . Hence: .$\displaystyle \frac{S-x}{n-2} \:=\:18 \quad\Rightarrow\quad x \:=\:S - 18n + 36$ .[2]
Substitute [1] into [2]: .$\displaystyle x \:=\:19n - 18n + 36 \quad\Rightarrow\quad x \:=\:n + 36
$
The average age of the two students is: .$\displaystyle \frac{x}{2} \:=\:\frac{n+36}{2}$