students of a class are made to stand in rows. if 4 students are extra in a row, there would be two rows less. if 4 students are less in a row, there would be four more rows.find the number of students in the class.

Suppose the number of students in each row is x and the number of rows be y.
Then, total number of students in the class = $\mathrm{number} \mathrm{of} \mathrm{students} \mathrm{in} \mathrm{each} \mathrm{row}\times \mathrm{number} \mathrm{of} \mathrm{rows} = xy$
Now according to the question we have;
When 4 students are extra in a row;
Total number of students = $\left(x+4\right)\left(y-2\right)$
$$\begin{gathered} \Rightarrow xy = \left(x+4\right)\left(y-2\right) \\ \Rightarrow xy = xy-2x+4y-8 \\ \Rightarrow 2x-4y = -8 \\ \Rightarrow x-2y = -4 ...\left(\mathrm{i}\right) \end{gathered}$$
When 4 students are less in a row;
Total number of students = $\left(x-4\right)\left(y+4\right)$
$$\begin{gathered} \Rightarrow xy = \left(x-4\right)\left(y+4\right) \\ \Rightarrow xy = xy+4x-4y-16 \\ \Rightarrow 4x-4y = 16 \\ \Rightarrow x-y = 4 ...\left(\mathrm{ii}\right) \end{gathered}$$
Subtracting (ii) from (i) we get;
$$\begin{gathered} x-2y-x+y = -4-4 \\ \Rightarrow -y = -8 \\ \Rightarrow y = 8 \end{gathered}$$
Putting the value of y in either of (i) or (ii) we get;
$$\begin{gathered} x-8 = 4 \\ \Rightarrow x = 12 \end{gathered}$$
Therefore total number of students in the class = $12\times 8 = 96$