MnO₄^- + Br^- + H₂O $\to$MnO₂ +BrO₃^- +OH^- ; for the balanced reaction the coefficients of MnO₄^-;BrO₃^-;OH^- is respectively

$$\begin{gathered} \stackrel{+7}{\mathrm{Mn}}{\mathrm{O}}_4^{-}+{\mathrm{Br}}^{-}+{\mathrm{H}}_2\mathrm{O}\to \stackrel{+4}{\mathrm{Mn}}{\mathrm{O}}_2+\stackrel{+5}{\mathrm{Br}}{\mathrm{O}}_3^{-}+{\mathrm{OH}}^{-}; \\ 6{\mathrm{MnO}}_4^{-}+3{\mathrm{Br}}^{-}+3{\mathrm{H}}_2\mathrm{O}\to 6\stackrel{ }{\mathrm{Mn}}{\mathrm{O}}_2+\stackrel{ }{3\mathrm{Br}}{\mathrm{O}}_3^{-}+6{\mathrm{OH}}^{-}; \end{gathered}$$

$$\begin{gathered} 6{\mathrm{MnO}}_4^{-} : \stackrel{ }{3\mathrm{Br}}{\mathrm{O}}_3^{-} : 6{\mathrm{OH}}^{-} \\ 2 :1 : 2 \end{gathered}$$