Question

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

Answer 1

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

therefore total number of students $=xy$.

if one student is extra in a row, there will be $2$ rows less.

the number of students in 1 row $=y+1$ and the number of rows $=x-2$.

therefore the number of students $=(x-2)(y+1)$

$\therefore (x-2)(y+1)=xy$

$\to xy-2y+x-2=xy$

$\to x-2y=\mathrm{2..........}(1$)

if 1 student is less in a row there would be 3 rows more.

therefore

($y-1\left)\right(x+3)=xy$

$\to xy-x+3y-3=xy$

$\to -x+3y=3..........\left(2\right)$

adding equation ($1$) and equation ($2):$

$y=5$

and $x-2\times 5=2$

$x-10=2$

$\to x=10+2=12$

thus the number of students in the class $=xy=12\times 5=60$