Two liquids of densities 1 g/cm3 and 3g/cm3 are mixed in equal volumes. A cube of external dimension 20 cm has an inner cubical portion of side 10 cm whose density is twice that of the outer portion. if this cube is just floating in the liquid mixture, find the density of the inner portion. if the density of the inner portion is half of this value, what fraction of the volume of the cube will be submerged?