Answer
$x=25 \mathrm{~km} .$
Work Step by Step
The Curie temperature for iron is $770^{\circ} \mathrm{C}$. If $x$ is depth at which the temperature has this value, then $10^{\circ} \mathrm{C}+\left(30^{\circ} \mathrm{C} / \mathrm{km}\right) x=770^{\circ} \mathrm{C}$. Therefore,
$$
x=\frac{770^{\circ} \mathrm{C}-10^{\circ} \mathrm{C}}{30^{\circ} \mathrm{C} / \mathrm{km}}\\=25 \mathrm{~km} .
$$
