4. 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 the number of rows be A and the number of students in a row be B. Total number of students = Number of rows x Number of students in a row =AB Using the information, that is given, First Condition: Total number of students = (A – 1) ( B + 3) Or AB = ( A – 1 )(B + 3) = AB – B + 3A – 3 Or 3A – B – 3 = 0 Or 3A – Y = 3 – – – – – – – – – – – – – (1) Second condition: Total Number of students = (A + 2 ) ( B – 3 ) Or AB = AB + 2B – 3A – 6 Or 3A – 2B = -6 – – – – – – – – – (2) When equation (2) is subtracted from (1) (3A – B) – (3A – 2B) = 3 – (-6) -B + 2B = 3 + 6B = 9 By using the equation (1) we get, 3A – 9 =3 3A = 9+3 = 12 A = 4 Number of rows, A = 4 Number of students in a row, B = 9 Number of total students in a class = AB = 4 x 9 = 36