Question

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

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