Question

Chandani purchased some parrots. $20\%$ flew away and $5\%$ died. Of the remaining, $45\%$ were sold. Now, $33$ parrots remain. How many parrots had Chandani purchased?

Answer 1

Let's consider total number of parrots $=x$,
$\Rightarrow$ Number of parrots left $=20\%$ of $x$$=\frac{20x}{100}$ $=\frac{x}{5}$
Number of parrots died $=5\%$ of $x=\frac{5x}{100}=\frac{x}{20}$

$\Rightarrow$ Remaining parrots $=x-(\frac{x}{5}+\frac{x}{20})$

$=x-\frac{4x+x}{20}$

$=\frac{20x-5x}{20}$

$=\frac{15x}{20}$

$=\frac{3x}{4}$

Number of parrots sold on remaining $=45\%$ of $\frac{3x}{4}$

$=\frac{45}{100}\times \frac{3x}{4}$

$=\frac{27x}{80}$

It is given that, the remaining parrots after sold $=33$

$\Rightarrow \frac{3x}{4}-\frac{27x}{80}=33$

$\Rightarrow \frac{60x-27x}{80}=33$

$\Rightarrow \frac{33x}{80}=33$

$\Rightarrow x=\frac{33\times 80}{33}$

$\Rightarrow x=80$

Therefore, Chandani purchased $80$ parrots