The reaction of aqueous $KMn{O}_4$ with $H_2{O}_2$ in acidic conditions gives

$\text{ Hydrogen peroxide is oxidised to }{\mathrm{H}}_2\mathrm{O}\text{ and }{\mathrm{O}}_2$

$2{\mathrm{KMnO}}_4+3{\mathrm{H}}_2{\mathrm{SO}}_4+5{\mathrm{H}}_2{\mathrm{O}}_2⟶{\mathrm{K}}_2{\mathrm{SO}}_4+2{\mathrm{MnSO}}_4$$+8{\mathrm{H}}_2\mathrm{O}+5{\mathrm{O}}_2$

  $\text{ or, }2{\mathrm{MnO}}_4^{-}+5{\mathrm{H}}_2{\mathrm{O}}_2+6{\mathrm{H}}^{+}⟶2{\mathrm{Mn}}^{2+}+8{\mathrm{H}}_2\mathrm{O}+5{\mathrm{O}}_2$