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# 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