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 = x
and the number of students in each row = y
`therefore` Total number of students in the class = xy
According to the I condition,
(y + 3) (x - 1) = xy (no. of students in each row `xx` no. of rows = total students)
implies xy - y + 3x - 3 = xy
implies 3x - y = 3 ...(1)
According to the II condition,
(y - 3) (x + 2) = xy
implies xy + 2y - 3x - 6 = xy
implies 3x - 2y = - 6
Subtracting equation (2) from equation (1), we have
y = 9
Put y = 9 in equation (1), we get
3x - 9 = 3 implies 3x = 12 implies x = 4
`therefore` Total number of students in the class = xy = 4 `xx` 9 = 36.