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.

Let the number of rows be x and number of students in a row be y.Total students of the class= Number of rows × Number of students in a row = x × y = xy
Case 1
Total number of students = (x-1)(y+3) ⇒ xy = (x-1)(y+3) = xy - y + 3x - 3 ⇒ 3x - y - 3 = 0 ⇒ 3x - y = 3. (i)
Case 2
Total number of students = (x+2)(y-3) ⇒ xy = xy + 2y - 3x - 6; ⇒ 3x - 2y = -6. (ii)
Subtracting equation (ii) from (i),
⇒ (3x - y) - (3x - 2y) = 3 - (-6)
⇒ -y + 2y = 3 + 6
⇒ y = 9
By substituting value of y in (i), we get
⇒ 3x - 9 = 3
⇒ 3x = 9 + 3 = 12
⇒ x = 4
Number of rows = x = 4
Number of students in a row = y = 9
Number of total students in a class = x × y = 4 × 9 = 36