Hello, anjana!

This one was tricky to set-up . . .

Students of a class are made to stand in rows.

(a) If there are 4 more students in each row, there would be 2 rows less.

(b) If there are 4 less students in each row, there would be 4 more rows.

Find the number of students.

Let = number of students in the class.

Let = number of students in each row.

Let = number of rows.

Then we have: .[1]

. . This is the original seating: in each row and rows.

Case (a): 4 more students per row, 2 fewer rows.

Then we have: . n + 4)(r - 2)" alt="X \:=\n + 4)(r - 2)" />[2]

Case (b): 4 less students per row, 4 more rows.

Then we have: . n-4)(r + 4)" alt="X\:=\n-4)(r + 4)" />[3]

Equate [1] and [2]: . n + 4)(r - 2)\quad\Rightarrow\quad 2r - n \:=\:4" alt="nr \:=\n + 4)(r - 2)\quad\Rightarrow\quad 2r - n \:=\:4" />

Equate [1] and [3]: . n - 4)(r + 4)\quad\Rightarrow\quad r - n \:=\:-4" alt="nr\:=\n - 4)(r + 4)\quad\Rightarrow\quad r - n \:=\:-4" />

Solve this system of equations and we get: .

Therefore: .

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Check

Orignally, the 96 students were seated 12 in each row.

. . There were rows.

With 4 more in each row, there were 16 in each row.

. . There were rows . . . two less rows.

With 4 less in each row, there were 8 in each row.

. . There were rows . . . 4 more rows.

We nailed it!