Two solutions A and B are prepared by dissolving 1 g of non-volatile solutes X and Y, respectively in 1 kg of water.…

Strategy:\n> Depression in freezing point ($\Delta T_f$) is inversely proportional to the molar mass ($M$) of the solute when common masses of solute and solvent are used ($\Delta T_f \propto \\frac{1}{M}$).\n\nStep 1: Express $\Delta T_f$ in terms of molar mass\nFor solution A and B, mass ($w=1\\text{g}$) and mass of solvent ($W=1\\text{kg}$) are the same.\n$\Delta T_f = K_f \cdot \\frac{w}{M \cdot W} \implies \Delta T_f \propto \\frac{1}{M}$\n\nStep 2: Relate the ratios\nGiven ratio $\\frac{\Delta T_{f,A}}{\Delta T_{f,B}} = \\frac{1}{4}$.\nSince $\Delta T_f \propto \\frac{1}{M}$, then $\\frac{M_X}{M_Y} = \\frac{\Delta T_{f,B}}{\Delta T_{f,A}}$.\n$\\frac{M_X}{M_Y} = \\frac{4}{1} = 4$\n\nStep 3: Express as 1 : X\n$M_X : M_Y = 1 : 0.25$.\n\n$\boxed{\\text{Answer: (2) 1 : 0.25}}$