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, 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)

$24$

Let the total number of girls and boys are $b$ and $g.$

We have, $\frac{4b}{5g}=\frac{2}{3}\dots eqn\left(1\right)$

And $\frac{4b}{5(g-44)}=\frac{5}{2}\dots eqn\left(2\right)$

From equation 1 and equation 2, we get

$8b=25g-(44\times 25)\Rightarrow 8\times \frac{5g}{6}=25g-44\times 25\Rightarrow g=60\to b=50$

let $x$ number of boys leave and the ratio is equal, we get

$\frac{4}{5}\times 50-x=60-44=16\Rightarrow x=24$