Students of a class are made …

Let the number of students be x and the number of rows be y.
Number of students in each row = {tex}x\over y{/tex}
According to the question, when one student is extra in each row, there are 2 rows less i.e., when each row has {tex}\left( \frac { x } { y } + 1 \right){/tex} students, the number of rows is {tex}(y - 2).{/tex}
{tex}\therefore{/tex} Total number of students = No. of rows {tex}\times{/tex}No. of students in each row
{tex}\Rightarrow x = \left( \frac { x } { y } + 1 \right) ( y - 2 ){/tex}
{tex}\Rightarrow x = x - \frac { 2 x } { y } + y - 2 {/tex}
{tex}\Rightarrow - \frac { 2 x } { y } + y - 2 = 0{/tex}....(i)
According to the question, If one student is less in each row, then there are 3 rows more i.e., when each row has {tex}\left( \frac { x } { y } - 1 \right){/tex}students, the number of rows is {tex} (y + 3).{/tex}
{tex}\therefore{/tex}  Total number of students = No. of rows {tex}\times{/tex}No. of students in each row
{tex}\Rightarrow x = \left( \frac { x } { y } - 1 \right) ( y + 3 )\\ \Rightarrow x = x + \frac { 3 x } { y } - y - 3 {/tex}
{tex}\Rightarrow \frac { 3 x } { y } - y - 3 = 0{/tex}....(ii)
Putting {tex}\frac { x } { y } = u{/tex} in equation (i) and equation (ii), we get
{tex}\Rightarrow{/tex} -2{tex}u{/tex}+ {tex}y{/tex} {tex}-2=0 {/tex} ...(iii)
{tex}\Rightarrow{/tex} 3{tex}u{/tex} - {tex}y{/tex}{tex}- 3=0{/tex} .....(iv)
Adding (iii) and (iv), we get
{tex}\Rightarrow u - 5 = 0\\ \Rightarrow u = 5{/tex}
Putting u in eq.(iii), we get
{tex}\Rightarrow -10 + y -2 = 0 {/tex}
{tex}\Rightarrow y =12{/tex}
Now, Substituting u value, we get
{tex}\Rightarrow \frac { x } { y } = 5\\ \Rightarrow \frac { x } { 12 } = 5\\ \Rightarrow x = 60{/tex}
Therefore, the number of students in the class is 60.