The densities of ice and water at 0°C and 1 bar are $0.96$ and $0.99 \mathrm{gm} {\mathrm{cm}}^{-3}$, a respectively. If the percentage of occupied space in ice is .x, then the percentage of empty space in water is :

The ratio of occupied space to total space determines density.

$\frac{\mathrm{density} \mathrm{of} {\mathrm{H}}_2\mathrm{O}}{\mathrm{density} \mathrm{of} \mathrm{ice}}=\frac{\mathrm{\%} \mathrm{of} \mathrm{occupiedspace} \mathrm{in} {\mathrm{H}}_2\mathrm{O}}{\mathrm{\%} \mathrm{of} \mathrm{occupiedspace} \mathrm{in} \mathrm{Iu}}$

$\frac{d_{{\mathrm{H}}_2\mathrm{O}}}{d_{\text{ice }}}=\frac{{\mathrm{OS}}_{{\mathrm{H}}_2\mathrm{O}}}{{\mathrm{O}}_{ice}}$

 $0\cdot {\mathrm{S}}_{{\mathrm{H}}_2\mathrm{O}}=0.{\mathrm{S}}_{\mathrm{ice}}$ $\mathrm{x}\frac{{\mathrm{d}}_{{\mathrm{H}}_2\mathrm{O}}}{{\mathrm{d}}_{\text{ice }}}=\mathrm{x}\times \frac{0.99}{0.96}=\frac{33}{32}\mathrm{x}$

% of empty space in ${\mathrm{H}}_2\mathrm{O}$

$=100-\mathrm{\%}$of occupide space in ${\mathrm{H}}_2\mathrm{O}$$=\left(100-\frac{33}{32}x\right)$