In a farm, in addition to $48$ hens, there are $42$ sheep and $11$ oxen with some shepherds. If the total number of feet is $224$ more than the number of heads, find the number of shepherds.

Let the number of shepherds be $x$.First, let's find the total number of heads:
$$\text{Total heads}=48\text{ (hens)}+42\text{ (sheep)}+11\text{ (oxen)}+x\text{ (shepherds)}$$
$$\text{Total heads}=101+x$$
Next, let's find the total number of feet:Hens have $2$ feet each: $48\times 2=96$ Sheep have $4$ feet each: $42\times 4=168$ Oxen have $4$ feet each: $11\times 4=44$ Shepherds have $2$ feet each: $x\times 2=2x$ $
$\text{Total feet}=96+168+44+2x=308+2x$$Accordingtothegivencondition:$$\text{Total feet}=\text{Total heads}+224$ $
$$308+2x=(101+x)+224$$
$$308+2x=325+x$$
$$2x-x=325-308$$
$$x=17$$
Thus, the number of shepherds is $17$.