Question

The students of a class are made to stand in rows. If $1$ students are extra in a row, there would be $2$ row less. If $1$ students are less in a row there would be $3$ rows more. Find the number of students in the class.

Answer 1

Let the number of rows be $x$ rows and the number of students in each row be $y$ students .

Then the total number of students in $a$ class =$xy$ students.

$\therefore$ According to the question ,

$(x-2)(y+1)=xy\Rightarrow xy+x-2y-2=xyx-2y=2⟶\left(i\right)$

And

$(x+3)(y-1)=xy\Rightarrow xy-x+3y-3=xy-x+3y=3⟶\left(ii\right)x-2y=2-x+3y=3$

On adding , $y=5$ students.

putting the value of $y$ in equation $⟶\left(i\right)$

$x-2\left(5\right)=2x=12$ rows.

$\therefore$ Total number of students in $a$ classroom $=(12\times 5)$students $=60$ students.