Answer
$24$ amperes.
Work Step by Step
If the current $i$ varies inversely with the resistance $Z$, then
there is a nonzero constant $k$ such that
$i=\displaystyle \frac{k}{Z}$
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If $ i=30$ when $Z=8$,
substituting, we find k:
$30=\displaystyle \frac{k}{8}\quad/\times 8$
$k=240$
Thus, we write: $\displaystyle \quad i=\frac{240}{Z}.$
If $Z=10$,
$i=\displaystyle \frac{240}{10}=24$ amperes.