Question

In a zoo, there are rabbits and pigeons. If their heads are counted, these are $90$ while their legs are $224$. Find the number of pigeons in the zoo.

• A. $70$
• B. $68$
• C. $72$
• D. $22$

Answer 1

Answer: (B)

$\left(68\right)$

Let no. of Pigeons$=P$
no. of Rabbits $=R$
Then, according to question, if their heads counted their total count is $225$
$\Rightarrow P+R=\mathrm{90........}\left(i\right)$
When their legs counted then their count is $224$
$\Rightarrow 2P+4R=\mathrm{224......}\left(ii\right)$
Here, $2$ represent each Pigeons contains $2$ legs and $4$ represents each Rabbit contains $4$ legs.
Solving equation(i) and (ii):
Substitute $P=90-R$ in equation(ii), we get
$\Rightarrow 2(90-R)+4R=224$
$\Rightarrow 180-2R+4R=224$
$\Rightarrow 180+2R=224$
$\Rightarrow 2R=224-180$
$\Rightarrow 2R=44$
$\therefore R=22$
Substitute $R=22$ in equation $P=90-R$, we get
$\Rightarrow P=90-22$
$\therefore P=68$
Hence, the number of pigeons is $68$ and the number of rabbit is $22$