A body A floats with $$50\%$$ of volume submerged in a liquid B and $$75\%$$ of its volume submerged in a liquid C. What is the ratio of the densities of A, B and C? What fraction of the body A will be seen above the surface of a homogenous mixture of equal volumes of the liquids B and C?

PLACEHOLDER ANSWER - the question has two answers. For floating, $$\rho_A = 0.5\rho_B = 0.75\rho_C$$, so $$\rho_A \colon \rho_B \colon \rho_C = 3 \colon 6 \colon 4$$. A mixture of equal volumes has density $$\frac{6 + 4}{2} = 5$$ units, so the fraction submerged is $$\frac{3}{5}$$ and the fraction above the surface is $$\frac{2}{5}$$.