Let $V$ be the volume of the block. When block floats in water, then $V_{\mathrm{block} }g=\left(\frac{4}{5}v\right){\rho }_{\mathrm{water} }g$

or $P_{\mathrm{block}}=\frac{4}{5}{\rho }_{\mathrm{water} }.....\left(\mathrm{i}\right)$

When block floats in liquid.

$V{\rho }_{\mathrm{block} }g=V{\rho }_{\mathrm{liquid}}g$

${\rho }_{\mathrm{block} }={\rho }_{\mathrm{liquid} }$

${\rho }_{\mathrm{liquid} }=\frac{4}{5}{\rho }_{\mathrm{water} }$ [from Eq. (i)]

$=\frac{4}{5}\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$

$=800 \mathrm{kg} {\mathrm{m}}^{-3}$