Question

The ratio of the number of boys to that of girls in a group becomes $2:1$when $15$ girls leave. But afterwards when $45$ boys also leave, the ratio becomes $1:5$ . Originally the number of girls in the group was

• A. $20$
• B. $30$
• C. $40$
• D. $50$

Answer 1

The correct option is C $40$

Let the number of boys and girls be x and y respectively.
Then, $\frac{x}{y-15}=\frac{2}{1}and\frac{x-45}{y-15}=\frac{1}{5}\Rightarrow \frac{x}{2}=(y-150)......\left(1\right)and5(x-45)=y-15....\left(2\right)$
From eq. (1) and (2)
$5(x-45)=\frac{x}{2}\Rightarrow 10x-450=x\Rightarrow 9x=450\Rightarrow x=50$
$\therefore Fromeq.\left(1\right),y-15=25\Rightarrow y=40$