A simple compass can be made by attaching a small bar magnet to the top of a cork floating in water. What fraction of a plain cork will be submerged when floating in water, assuming the density of cork is $0\mathrm{.}24$ x $10^3$ kg$/$m$^3.$

If the cork has a mass of $11\mathrm{.}3$ g and a $20\mathrm{.}5$ g magnet, made of iron with a density of $7\mathrm{.}80$ g$/$cm$^3,$ is placed on it$,$ what fraction of the cork will be submerged? Assume that only the cork is submerged $-$ the magnet is out of the water.