To calculate the density of a body and a liquid based on buoyancy, the weights of the body in air, water, and another liquid are essential. The body weighs 7.55 kg in air, 5.17 kg in water, and 6.35 kg in a certain liquid, with the density of water given as 1000 kg/m^3. The discussion highlights the need to clarify whether the provided values are weights in Newtons or masses in kilograms. Using the buoyant force and the principle of Archimedes, the densities can be derived from the weight differences in various mediums. Accurate calculations depend on understanding the correct units for weight and mass.