Question

the average age of 5 teachers of a school was 48.From them a teacher of age 56 retired and a new teacher came.The present average is 46.What is the age of the new teacher?

Answer 1

The age of the new teacher is 46 years

Step-by-step explanation:

$\textbf{Formula of Average=}\frac{\textbf{Sum of quantity}}{\textbf{number of quantity}}$

$\text{So, by above formula the sum of ages of teachers= Average x Number of teachers}$

$\text{average age = 48 and number of teachers =5, (given)}$

$\textbf{So, the Sum of ages = 48 x 5 = 240}$

$\text{A teacher of age 56 is retired so the sum of age of remaining for teachers is 240 - 56 = 186}$

$\textbf{Let the age of new teacher = X}\\\\\text{present average age = 46 (given)}$

$\text{So putting each value in the formula of average, for the new average}$

$\textbf{46 = }\frac{\textbf{184 + X}}{\textbf{5\\}}$

$\text{multiplying both sides by 5 and then subtracting 184 from both sides}$

$\text{above equation becomes}$

$\textbf{ (46 x 5) - 186 = X}$$\textbf{So, X = 230 -184 = 46 years }$

$\textbf{So the correct answer is 46 years }$