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} $
$\Rightarrow \frac{4x}{5(y - 44)} = \frac{5}{2}$
$\Rightarrow 8x = 25 y - 1100\,...(ii)$
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.
$\therefore 50 - 10 - z = 60 - 44$
$z = 40- 16= 24$