This paper presents a model to study the two prominent coexisting instabilities, stimulated Raman (SRS), and stimulated Brillouin scattering (SBS) in the presence of background axial magnetic field. In the context of laser-produced plasmas, this model is very useful in the situations where a self-generated axial magnetic field is present as well as where an external axial magnetic field is applied. Due to the interplay between both the scattering processes, the behavior of one scattering process is greatly modified in the presence of another coexisting scattering process. The impact of this coexisting phenomenon and axial magnetic field on the back reflectivity of scattered beams has been explored. It has been demonstrated that the back reflectivity gets modified significantly due to the coexistence of both the scattering processes (SRS and SBS) as well as due to the axial magnetic field. Results are also compared with the three-wave interaction case (isolated SRS or SBS case).