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.

Ans.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

Case 1 :

Total number of students = (x – 1) (y + 3)
\(xy = (x – 1) (y + 3)\)
\(=> xy = xy – y + 3x – 3\)
\(=> 3x – y – 3 = 0\)
\(=> 3x – y = 3\)… (1)

Case 2 :

Total number of students = (x + 2) (y – 3)
\(xy = xy + 2y – 3x – 6\)
\(=> 3x – 2y = –6\)… (2)

Subtracting equation (2) from (1):
y = 9

Substituting the value of y in equation (1):
\(3x – 9 = 3\)
\(3x = 9 + 3 = 12\)
x = 4

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

Hence, Total number of students in a class = xy = 36