Molality(m) can be defined as the number of moles of solute dissolved in 1 Kg of the solvent,
         $Molality\left(m\right) = \frac{Number of moles of solute}{Mass of solvent in Kg}$
Mole fraction of a component in a solution is the ratio of the number of moles of that component to the total number of moles of all the components,
      For a binary solution of A & B,
          $$\begin{gathered} Mole fraction of A \left(X_A\right) = \frac{n_A}{n_A + n_B} \\ Mole fraction of B\hspace{0.17em}\left(X_B\right) = \frac{n_B}{n_A + n_B} \\ Moreover, \\ Total mole fraction of all the components of a solution is \mathbf{1} \\ i.e, X_A + X_B = 1 \\ \frac{X_A}{X_B}= \frac{n_A}{n_B}= \frac{Moles of solute}{Moles of solvent} \\ = \frac{w_A\times m_B}{w_B\times m_A} \\ \frac{{\mathbf{X}}_{\mathbf{A}}\mathbf{\times }\mathbf{1000}}{{\mathbf{X}}_{\mathbf{B}}\mathbf{\times }{\mathbf{m}}_{\mathbf{B}}}\mathbf{=}\frac{{\mathbf{w}}_{\mathbf{A}}\mathbf{\times }\mathbf{1000}}{{\mathbf{w}}_{\mathbf{B}}\mathbf{\times }{\mathbf{m}}_{\mathbf{A}}}\mathbf{=}\mathit{m} \\ OR \\ \frac{{\mathbf{X}}_{\mathbf{A}}\mathbf{\times }\mathbf{1000}}{\mathbf{1}\mathbf{ }\mathbf{-}\mathbf{ }{\mathbf{X}}_{\mathbf{A}}}\mathbf{=}\mathit{m} \end{gathered}$$