A solid shell loses half its weight in water. Relative density of shell is 5.0. What fraction of its volume is hollow?

Let x fraction of its volume is hollow. Then weight of shell

$=(\mathrm{V}-x\mathrm{V})\times 5.0\times 1000\times \mathrm{g}$

Weight of water displaced $=\mathrm{V}\times 1000\times \mathrm{g}$

Weight of water displaced = loss in weight

$\therefore \mathrm{V}\times 1000\times \mathrm{g}=\frac{1}{2}(\mathrm{V}-xV)\times 5.0\times 1000\times \mathrm{g}$

Solving this we get, $x=\frac{3}{5}$