The metal which is obtained from both sea-water and ores from the earth's solid crust is:

The metal which is obtained from both sea water and ores from the earth's solid crust is magnesium.

Magnesium. Magnesium is the only metal that can be extracted directly from seawater, and it is present there in seawater at a concentration of around 1,000 parts per million. ${\mathrm{MgCl}}_2$ is abundant in seawater, and the Dow sea water technique is used to extract Mg from it.

Carnallite may also be used to extract Mg.

Hence, option A is correct.