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. Reduce these statements in the form of linear equations assuming number of rows to be 'x' and number of students in a row to be 'y'.

• A. $-3x+y=-2$ $x-2y=6$
• B. $x-y=3$ $3x+2y=5$
• C. $3x-y=3$ $3x-2y=-6$
• D. None of the above

Answer 1

The correct option is C

$3x-y=3$

$3x-2y=-6$

Let the number of rows be x and number of students in a row be y.
Total students of the class = Number of rows $\times$ number of students in a row
= xy
Using the information given in the question,
Condition 1
Total number of students = (x-1)(y+3)
$\Rightarrow xy=(x-1)(y+3)$
$\Rightarrow xy=xy-y+3x-3$
$\Rightarrow 3x-y=3\left(i\right)$
Condition 2
Total number of students = (x+2) (y-3)
$xy=xy+2y-3x-6$
$3x-2y=-6\left(ii\right)$