Question

The average age of child in a class of 30 is 11. The average including the teacher is 12 How old is the teacher ?​

Answer 1

$\small\texttt{Let the age of the teacher be x.}$

$\small\mathtt{Av. \; age \; of \; children = \large\frac{Sum \; of \; ages \; of \; children}{No. \; of \; students}}$

$\small\implies\mathtt{11 = \large\frac{Sum \; of \; ages \; of \; children}{30}}$

$\small\mathtt{\implies Sum \; of \; ages \; of \; children = 11×30}$

$\therefore\texttt{ The sum of ages of children is 330}$

$\small\texttt{Av. \; after \; adding \; teacher's \; age,}$

$\mathtt{New \; av. = \large \frac{Sum \; of \; ages \; of \; children \; + \; age \; of \; teacher}{No. \; of \; students \; + \; 1}}$

$\small\implies\mathtt{12= \large\frac{330+x}{31}}$

$\small\implies\mathtt{330+x = 12×31}$

$\small\implies\mathtt{330+x = 372}$

$\small\implies\mathtt{x = 372-330}$

$\small\implies\mathtt{x = 42}$

$\small\texttt{Hence, the age of the teacher is 42 yrs.}$