The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less.

Let the number of rows be x and number of students in a row be y.
Total number of students in the class = Number of rows x Number of students in a row
= xy


According to the question,
Total number of students = (x - 1) (y + 3)
xy = (x - 1) (y + 3)

= xy - y + 3x - 3
3x - y - 3 = 0
3x - y = 3 ... (1)

Total number of students = (x + 2) (y - 3)
xy = xy + 2y - 3x - 6
3x - 2y = -6 ... (2)

Subtracting equation (2) from (1), we obtain:
y = 9

Substituting the value of y in equation (1), we obtain:
3x - 9 = 3
3x = 9 + 3 = 12
x = 4

Number of rows = x = 4
Number of students in a row = y = 9

Total number of students in a class = xy = 4 x 9 = 36