A measurement of the ratios of the effective decay widths of ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ and ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{K}^{+}$ decays over that of ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ decays is performed with the LHCb experiment using proton--proton collisions at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of $6\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$. These observables give access to the charm mixing parameters ${y}_{CP}^{\ensuremath{\pi}\ensuremath{\pi}}\ensuremath{-}{y}_{CP}^{K\ensuremath{\pi}}$ and ${y}_{CP}^{KK}\ensuremath{-}{y}_{CP}^{K\ensuremath{\pi}}$, and are measured as ${y}_{CP}^{\ensuremath{\pi}\ensuremath{\pi}}\ensuremath{-}{y}_{CP}^{K\ensuremath{\pi}}=(6.57\ifmmode\pm\else\textpm\fi{}0.53\ifmmode\pm\else\textpm\fi{}0.16)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, ${y}_{CP}^{KK}\ensuremath{-}{y}_{CP}^{K\ensuremath{\pi}}=(7.08\ifmmode\pm\else\textpm\fi{}0.30\ifmmode\pm\else\textpm\fi{}0.14)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, where the first uncertainties are statistical and the second systematic. The combination of the two measurements is ${y}_{CP}\ensuremath{-}{y}_{CP}^{K\ensuremath{\pi}}=(6.96\ifmmode\pm\else\textpm\fi{}0.26\ifmmode\pm\else\textpm\fi{}0.13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, which is four times more precise than the previous world average.