Given,

Weight of body in water is \(\frac{1}{3}\) of total weight in air,

Mean, buoyancy force in water is \(\frac{2}{3}\) of total weight in air

Volume of body, \(V\)

Density of water and body, \(\rho_w\ and\, \rho_b\)

Apply Archimedes principle

Buoyancy force \(=\) weight of water displaces \(=\frac{2}{3}\) weight of body in air

\(\rho_{ w } Vg =\frac{2}{3} \rho_{ b } Vg\)

\(\rho_{ b }=1.5 \rho_{ w }\)

Density of body is \(1.5\) time the density of water.