Question

The students of a class are made to be stand in a row. If 3 students are extra in a row, then there would be 1 row less. If 3 students are less in a row there would be 2 more rows. Find the number of students in the class

Answer 1

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

= xy

condition(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 (1)

Condition (2)

Total number of students
= (x + 2) (y − 3)

xy = xy + 2y − 3x − 6

3x − 2y = −6 (2)

solving equations we get

(3x − y) − (3x − 2y) = 3 − (−6)

− y + 2y = 3 + 6

y = 9

By using equation (1), we obtain

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 = xy = 4 × 9 = 36