The binary ruthenium pnictides RuAs and RuP exhibit metal-insulator (MI) transition below 200 K and 270 K, respectively, and show an evidence of pseudogap formation in their metallic state accompanied with superstructure formation at 280 K and 330 K. The MI transition and pseudogap formation are suppressed with Rh doping in Ru1-xRhxAs and Ru1-xRhxP. Furthermore, Rh-doping leads to superconductivity in both of them. The optimally doped Ru0.75Rh0.25As and Ru0.55Rh0.45P show superconductivity at Tc = 1.8 K and 3.7 K, respectively. It would be of interest to further investigate the superconducting properties of Ru0.75Rh0.25As and Ru0.55Rh0.45P using muon spin relaxation and rotation (µSR) technique to explore the nature of the superconducting gap, pairing symmetry and time reversal symmetry below TC. We therefore propose to carry out µSR study on Ru0.75Rh0.25As and Ru0.55Rh0.45P.