Question

the average age of adult class is 40 years. 12 new student with an average age of 32 years join the class thereby decreasing the average of the class by 4 year the original strength of class was

Answer 1

$\textbf{Answer}$

$\textbf{Suppose}$ the original strength of class is x, which means there were x number of students in the class.

Since $\textbf{average age was 40 years}$ for x students,
=> $\textbf{Total age of x students = 40x}$


$\textbf{Then 12 new students joined,}$
Average age of students = 32 years
=> Total age of 12 students = 12×32
$\textbf{Total age of 12 students = 384}$


$\textbf{Lets calculate total average of all}$ students,
$\textbf{Total no. of students}$ after 12 students joined = $\textbf{x+12}$
$\textbf{New students decrease}$ the average of the class by 4.
=> $\textbf{Overall Average = 40-4 = 36}$
Overall average = {(40x) + 384}/(x+12)
=> {(40x) + 384}/(x+12) = 36

=> 40x + 384 = 36x + 432

=> 40x - 36x = 432 - 384

=> 4x = 48

=> x = 12

=> In the beginning,there were 12 students.

$\textbf{Original Strength of class was 12}$

$\textbf{Hope My Answer Helped}$
$\textbf{Thanks}$

Answer 2

Suppose the original strength of class is x, which means there were x number of students in the class.

Since \textbf{average age was 40 years}average age was 40 years for x students,
=> \textbf{Total age of x students = 40x}Total age of x students = 40x 


\textbf{Then 12 new students joined,}Then 12 new students joined, 
Average age of students = 32 years
=> Total age of 12 students = 12×32
\textbf{Total age of 12 students = 384}Total age of 12 students = 384 


\textbf{Lets calculate total average of all}Lets calculate total average of allstudents,
\textbf{Total no. of students}Total no. of students after 12 students joined = \textbf{x+12}x+12 
\textbf{New students decrease}New students decrease the average of the class by 4.
=> \textbf{Overall Average = 40-4 = 36}Overall Average = 40-4 = 36 
Overall average = {(40x) + 384}/(x+12)
=> {(40x) + 384}/(x+12) = 36

=> 40x + 384 = 36x + 432

=> 40x - 36x = 432 - 384

=> 4x = 48

=> x = 12

=> In the beginning,there were 12 students.

\textbf{Original Strength of class was 12}Original Strength of class was 12