Question

Students of a school were made to stand in rows 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. 400
• B. 500
• C. 600
• D. 700

Answer 1

The correct option is C 600

Let the number of students standing in each row be $x$ and let the number of rows be $y$. Then the number of students participating in the drill will be $xy$.

It is given that if $3$ students were less standing in each row then $10$ more rows were required, therefore, we have:

$(x-3)(y+10)=xy\Rightarrow x(y+10)-3(y+10)=xy\Rightarrow xy+10x-3y-30=xy\Rightarrow 10x-3y=xy-xy+30\Rightarrow 10x-3y=30.......\left(1\right)$

Also, it is given thatif $5$ students more were standing in each row then the number of rows reduced by $10$, therefore, we have:

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

Now adding equations 1 and 2 we get:

$(10x-3y)+(-10x+5y)=30+50\Rightarrow 10x-3y-10x+5y=80\Rightarrow 2y=80\Rightarrow y=\frac{80}{2}\Rightarrow y=40$

Substitute the value of $y$ in equation 1 as follows:

$10x-(3\times 40)=30\Rightarrow 10x-120=30\Rightarrow 10x=30+120\Rightarrow 10x=150\Rightarrow x=\frac{150}{10}\Rightarrow x=15$

Now let us find $xy$:

$x\times y=15\times 40=600$

Hence, the number of students participating in the drill are $600$.