$4$ oxen or $12$ cows can graze a field in $32$ days. How long would $7$ oxen and $3$ cows take to graze the same field?

The correct option is D: $16$ days

$4$ oxen $=12$ cows

$\Rightarrow 1$ oxen $=\frac{12}{4}=3$ cows

$\Rightarrow 7\text{oxen}\equiv 3\times 7\text{cows}=21\text{cows}$

$\Rightarrow$ $(7$ oxen $+$ 3 cows) $\equiv$ $(21$ cows $+$ 3 cows) $=24$ cows

Now, $12$ cows can graze the field in $32$ days.

So, $1$ cow can graze the field in $(32\times 12)$ days.
[less cows, more days, inverse relation]

$24$ cows can graze the field in $\frac{32\times 12}{24}=16$ days
[more cows, less days, inverse relation]

Hence, $7$ oxen and $3$ cows can graze the field in $16$ days.