55 cows can graze a field in 16 days.

Let x be the number of cows that can graze the field in 10 days .

Since the number of cows and the number of days taken by them to graze the field are in inverse variation, we have:

$16 \times 55=10 \times x$

$\Rightarrow x=\frac{16 \times 55}{10}$

$=88$

$\therefore$ The required number of cows is 88