students of a class are made …

Let the number of rows be x and the number of students in each row be y.
Then, the total number of students = xy.

Case I When there are 4 more students in each row.
Then, number of students in each row = {tex}(y + 4){/tex}.
And, number of rows = {tex}(x - 2).{/tex}
Total number of students = {tex}(x - 2) (y + 4){/tex}
{tex}\therefore{/tex} {tex}(x - 2)(y + 4) = xy{/tex}
{tex}\Rightarrow{/tex} {tex}4x - 2y = 8{/tex}
{tex} \Rightarrow{/tex}{tex}2x - y = 4.{/tex} ...(i)

Case II When 4 students are removed from each row.
Then, number of students in each row = {tex}(y - 4).{/tex}
And, number of rows = {tex}(x + 4).{/tex}
Total number of students = {tex}(x + 4)(y - 4){/tex}
{tex}\therefore{/tex} {tex}(x + 4)(y - 4) = xy{/tex}{tex} \Rightarrow{/tex} {tex}4y - 4x = 16{/tex}
{tex}\Rightarrow{/tex}{tex}4(y - x) = 16{/tex} {tex}\Rightarrow{/tex}{tex}(y - x)= 4{/tex}. ...(ii)
Adding (i) and (ii), we get {tex}x = 8{/tex}
Putting {tex}x = 8{/tex} in (ii), we get
{tex}y - 8 = 4{/tex} {tex}\Rightarrow{/tex} {tex}y = 12.{/tex}
Thus, {tex}x = 8\ and\ y = 12{/tex}.
This shows that there are 8 rows and there are 12 students in each row.
Hence, the number of students in the class = {tex}xy = 8\times12 = 96{/tex}.