The complex oxide ${\mathrm{Pb}}_{0.55}{\mathrm{Cd}}_{0.45}{\mathrm{V}}_{2}{\mathrm{O}}_{5}$ was synthesized and investigated by means of x-ray powder diffraction, electron diffraction, magnetic susceptibility measurements, and band structure calculations. Its structure is similar to that of $M{\mathrm{V}}_{2}{\mathrm{O}}_{5}$ compounds ($M=\mathrm{Na}$, Ca), giving rise to a spin system of coupled $S=1∕2$ two-leg ladders. Magnetic susceptibility measurements reveal a spin gap-like behavior with $\ensuremath{\Delta}\ensuremath{\approx}270\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and a spin singlet ground state. Band structure calculations suggest ${\mathrm{Pb}}_{0.55}{\mathrm{Cd}}_{0.45}{\mathrm{V}}_{2}{\mathrm{O}}_{5}$ to be a system of weakly coupled dimers in perfect agreement with the experimental data. ${\mathrm{Pb}}_{0.55}{\mathrm{Cd}}_{0.45}{\mathrm{V}}_{2}{\mathrm{O}}_{5}$ provides an example of the modification of the spin system in layered vanadium oxides by cation substitution. Simple correlations between the cation size, geometrical parameters, and exchange integrals for the $M{\mathrm{V}}_{2}{\mathrm{O}}_{5}$-type oxides are established and discussed.