Question

In a classroom, one-fifth of the boys leave the class and the ratio of the remaining boys to girls is $2:3$. If further $44$ girls leave the class, then class the ratio of boys to girls is $5:2$. How many more boys should leave the class so that the number of boys equals that of girls?

• A. 16
• B. 24
• C. 30
• D. 36

Answer 1

Answer: (B)

Let the number of boys and girls
in classroom is $x$ and $y$, respectively.
Given, $\frac{x-x/5}{y}=\frac{2}{3}$
$\Rightarrow \frac{4x}{5y}=\frac{2}{3}$
$\Rightarrow \frac{x}{y}=\frac{5}{6}...(i)$
Also, $\frac{x-x/5}{y-44}=\frac{5}{2}$
$\Rightarrow \frac{4x}{5(y-44)}=\frac{5}{2}$
$\Rightarrow 8x=25y-1100...(ii)$
From Eqs. (i) and (ii), we get
$x=50,y=60$
Let $z$ number of boy leaves so number of boys and number of girls are equal.
$\therefore 50-10-z=60-44$
$z=40-16=24$