Question

Students of a school were made to stand in rows were required. If $3$ students less were standing in each row,$10$ more rows were required and if $5$ students more were standing in each row then the number of rows was reduced by $10$ . Find the number of students participating in the drill.

• A. $450$
• B. $500$
• C. $600$
• D. $750$

Answer 1

The correct option is C $600$

Let the no. of students standing in each row be $x$ and Let the no. of rows be $y$.

$\therefore$ Total no. of students participating in the drill $=xy$

As per the first given condition

$(x-3)(y+10)=xy$

$\Rightarrow xy+10x-3y-30=xy$

$\Rightarrow 10x-3y=30$ .......(1)

As per the second given condition

$(x+5)(y-10)=xy$

$\Rightarrow xy-10x+5y-50=xy$

$\Rightarrow -10x+5y=50$ .......(2)

On adding (1) and (2). we get,

$2y=80\Rightarrow y=40$

On substituting $y=40$ in (1). we get,

$10x-3\left(40\right)=30$

$\Rightarrow 10x=30+120$

$\Rightarrow 10x=150$

$\Rightarrow x=15$

Total no. of students participating in the drill$=xy=15\times 40=600$

Option C is correct.