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. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.

Solution :

Let students in each row be x.

And Let number of rows be y.

then, total number of students = xy

Case 1 : When 3 students are extra in a row, then number of rows becomes (y – 1)

xy = (x + 3)(y – 1)

\(\implies\)  x – 3y + 3 = 0               …….(1)

Case 2 : When 3 students are less in the row, then the number of rows becomes (y + 2)

xy = (x – 3)(y + 2)

\(\implies\)  2x – 3y – 6 = 0                ……..(2)

Solving equation (1) and (2), we get

x = 9, y = 4

Hence, the number of students is 36.