Two \(5\) molal solutions are prepared by dissolving a non-electrolyte, non-volatile solute separately in the solvents \(X\) and \(Y\). The molecular weights of the solvents are \(M_X\) and \(M_Y\), respectively where \(M_X\, = \frac{3}{4} M_Y\). The relative lowering of  vapour pressure of the solution in \(X\) is \(''m''\) times that of the solution in \(Y\). Given that the number of moles of solute is very small in comparison to that of solvent, the value of \(''m''\)  is

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.