Question

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

Answer 1

Let the number of students in each row be $x$, and number of rows be $y$.
Total number of students $=xy$
From the first condition, we get
$(x-3)(y+10)=xy$
$xy+10x-3y-30=xy$
$10x-3y=\mathrm{30...........}\left(i\right)$
From the second condition we get
$(x+5)(y-10)=xy$
$xy-10x+5y-50=xy$
$-10x+5y-50=0$
$\therefore$ $-10x+5y=\mathrm{50..........}\left(ii\right)$
Adding equations $\left(i\right)$ and $\left(ii\right)$
$10x-3y=30$
$-10x+5y=50$
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$2y=80$
$y=40$
Substituting $y=40$ in equation $\left(ii\right)$ we get
$-10x+5y=50$
$-10x+5\times 40=50$
$-10x+200=50$
$\therefore$ $-10x=50-200$
$\therefore$ $-10x=-150$
$\therefore$ $10x=150$
$\therefore$ $x=15$
The number of students $=xy$
$=15\times 40$
$=600$
Total number of students participating in the drill are $600$