The students of a class are made to stand in rows. If 3 student 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.
Given:
The students of a class are made to stand in rows. If 3 student 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.
To do:
We have to find the number of students in the class.
Solution:
Let the number of rows be $x$ and the number of students in each row be $y$.
This implies,
Total number of students $=xy$
If 3 student are extra in a row, there would be 1 row less.
$\Rightarrow (x+3)(y-1)=xy$
$xy-x+3y-3=xy$
$x=3y-3$....(i)
If 3 students are less in a row there would be 2 rows more.
$\Rightarrow (x-3)(y+2)=xy$
$xy+2x-3y-6=xy$
$2x=3y+6$
$2(3y-3)=3y+6$ (From (i))
$6y-6=3y+6$
$6y-3y=6+6$
$3y=12$
$y=\frac{12}{3}$
$y=4$
$\Rightarrow x=3(4)-3$ (From (i))
$x=12-3$
$x=9$
$\Rightarrow xy=9\times4=36$
Therefore, the number of students in the class is 36.
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