Question

The students of a class are made to stand in rows . If 4 students are extra in each row there would be 2rows less . If 4students are less in each row there would be 4 rows more.Find the no of students in the class

Answer 1

The number of students = constant = xy

Let students in each row = X

and rows = y

$(x + 4)(y - 2) = xy \\ xy - 2x + 4y - 8 = xy \\ - 2x + 4y - 8 = 0 \\ - 2x + 4y = 8 \\ 2x - 4y = - 8 \\ x - 2y = - 4 \: ...............(i)$

$(x - 4)(y + 4) = xy \\ xy + 4x - 4y - 16 = xy \\ 4x - 4y = 16 \\ x - y = 4 \: ..............(ii)$

On subtracting equations 2 from 1, we get,

$- y = - 8 \\ y = 8$

Substituting y in our second equation,

$x = 4 + y \\ x = 4 + 8 \\ x = 12$

Number of students = xy

$= 12 \times 8 \\ = 96$

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