A measurement of the ratios of the effective decay widths of $D^0\to {\pi }^{-}{\pi }^{+}$ and $D^0\to K^{-}{K}^{+}$ decays over that of $D^0\to K^{-}{\pi }^{+}$ 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 $6{\mathrm{fb}}^{-1}$. These observables give access to the charm mixing parameters $y_{CP}^{\pi \pi }-y_{CP}^{K\pi }$ and $y_{CP}^{KK}-y_{CP}^{K\pi }$, and are measured as $y_{CP}^{\pi \pi }-y_{CP}^{K\pi }=(6.57\pm 0.53\pm 0.16)\times {10}^{-3}$, $y_{CP}^{KK}-y_{CP}^{K\pi }=(7.08\pm 0.30\pm 0.14)\times {10}^{-3}$, where the first uncertainties are statistical and the second systematic. The combination of the two measurements is $y_{CP}-y_{CP}^{K\pi }=(6.96\pm 0.26\pm 0.13)\times {10}^{-3}$, which is four times more precise than the previous world average.