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

Hint:
Here we will first assume the number of parrots purchased by Chandani. Then we will find the number of parrots that flew away and died, and then this obtained value we will find the number of parrots that remained. Using the given conditions we will find the value of the number of parrots sold. Then we will find the value of the unsold parrots and equate it to 33. We will solve the equation to get the number of parrots purchased by Chandani.

Complete Step by Step Solution:
Let the number of parrots purchased by Chandani be \[x\].
It is given that the \[20\% \] flew away and \[5\% \] died from the number of parrots purchased by her. So we will find out the number of parrots that flew away and died. Therefore, we get
Number of parrots flew away and died \[ = \dfrac{{\left( {20 + 5} \right)}}{{100}} \times x = \dfrac{1}{4}x\]
Now we will find the remaining parrots by subtracting the number of parrots that flew away and died from the total number of parrots. Therefore, we get
Remaining number of parrots \[ = x - \dfrac{1}{4}x = \dfrac{3}{4}x\]
It is given that of the remaining, \[45\% \] were sold. So, now we will find the number of parrots sold by multiplying the percentage sold with the remaining number of parrots. Therefore, we get
Number of parrots sold \[ = \dfrac{{45}}{{100}} \times \dfrac{3}{4}x = \dfrac{{27}}{{80}}x\]
Now we will find the number of parrots which are not sold by subtracting the number of parrots sold by the number of remaining parrots. Therefore, we get
Number of unsold parrots \[ = \dfrac{3}{4}x - \dfrac{{27}}{{80}}x = \dfrac{{33}}{{80}}x\]
It is given that at the end 33 parrots remain which means the number of unsold parrots is equal to 33. Therefore, we get
\[\dfrac{{33}}{{80}}x = 33\]
On cross multiplication, we get
\[ \Rightarrow 33x = 33 \times 80\]
Dividing both sides by 33, we get
\[ \Rightarrow x = \dfrac{{33 \times 80}}{{33}} = 80\]

Hence the number of parrots purchased by Chandani is 80.

Note:
Here, we might make a mistake by considering 33 as the remaining parrots after some parrots flew away and died. Then we might calculate \[45\% \] of 33 to find the number of parrots sold. Thus, we will give us the wrong answer. So, 33 is the number of parrots that remained after selling the remaining parrots. To find the remaining amount of anything we have to subtract the value from the total value to get the value of the remaining amount of the item.