A block of wood floats in water with ( 4 / 5 ) ^ th ~of its volume...

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

or ${P}_{block} = \dfrac{4}{5}{ρ}_{water}..... \left(i\right)$

When block floats in liquid.

$V{ρ}_{block}g = V{ρ}_{liquid}g$

${ρ}_{block} = {ρ}_{liquid}$

${ρ}_{liquid} = \dfrac{4}{5}{ρ}_{water}$ [from Eq. (i)]

$= \dfrac{4}{5} \times {10}^{3}$ kgm^{- 3}$</p><p>$= 800kgm^{- 3}$</p>$