Students are made to stand in rows. If one student is extra in a row there would be 2 rows less. If one student is less in a row there would be 3 rows more. Find the number of students in the class.

Ans: No. of rows be y

Let the number of students be x

Number of students in the class will be = xy

One student extra, 2 rows less

(x + 1) (y - 2) = xy

xy - 2x + y -2 = xy

-(-2x + y -2) = 0

+2x - y = -2 -------------- (1)

One student less, three more rows

(x - 1) (y + 3) = xy

xy + 3x - y -3 = xy

3x - y = 3 ---------------------(2) From (1) & (2)

2x - y = -2 X 3

3x - y = 3 X -2

Solve it , to get ... y = 12 and x = 5

∴ Number of student = xy

= 12 X 5

= 60 students