Question

A man has some hens and cows. If the number of heads be $48$ and the number of feet
be $140$, how many cows are there?

Answer 1

Let the number of hens and cows be $x$ and $y$ respectively.

As, we know that there is $1$ head for all animals.

No.of feet for hen $=2$

No. of feet for cow $=4$

As per the question, we have

$x+y=48\dots \dots \left(i\right)$

and, $2x+4y=140$

$\Rightarrow x+2y=70\dots \dots \left(ii\right)$
Subtracting $eq.\left(i\right)$ from $eq.\left(ii\right)$, we have

$x+2y-(x+y)=70-48$
$\Rightarrow y=22$
Hence, the number of cows is $22$.