Using the improved scission-point model, the mass distributions are calculated for induced fission of several Po and Ir isotopes. The calculated mass distributions and mean total kinetic energies of fission fragments are compared with the existing experimental data. The revealed coexistence of both symmetric and asymmetric modes in the $\ensuremath{\beta}$-delayed fission of $^{194,196}\mathrm{At}$ is in agreement with the experimental observations. The change of the shape of mass distribution with increasing $A$ of fissioning $^{A}\mathrm{Ir}$ nucleus from asymmetric for $^{185}\mathrm{Ir}$ to symmetric for $^{193}\mathrm{Ir}$ is found.