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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?

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Detailed Solution

Let's assume that the number of parrots purchased by Chandani is

x

. It is estimated that 20% flew away and 5% died from the number of parrots purchased by her. So let's find out the number of parrots that flew away and died. Hence, we get
Number of parrots flew away and died =

\frac{(20 + 5)}{100} \times x = \frac{1}{4} x

Remaining number of parrots =

x - \frac{1}{4} x = \frac{3}{4} x

It is given that of the remaining, 45% were sold.
Number of parrots sold =

\frac{45}{100} \times \frac{3}{4} x = \frac{27}{80} x

Number of unsold parrots =

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

It is given that at the end 33 parrots remain meaning that the number of unsold parrots is equal to 33. So, we get
⇒

\frac{33}{80} x = 33

⇒

33 x = 33 \times 80

⇒

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

= 80

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