Calculate E^o_cell corresponding to each compound undergoing disproportionation reaction. The reaction for which E^o_cell comes out + ve is spontaneous.

HBrO $\to$ Br₂, E^o_HBrO/Br2 = 1.595 V

HBrO $\to$ BrO₃^–, E^o_BrO3^-/HBrO = 1.595 V

E^o_cell for the disproportionation of HBrO,

E^o_cell = E^o_HBrO/Br2 - E^o_BrO3^-/HBrO

= 1.595 - 1.5

= 0.095 V = + ve

So, E^o_cell > 0

So, $\Delta$G^o < 0 (Spontaneous)