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