A paint mixture containing $25\mathrm{.}0$ wt$\%$ of a pigment and the balance binders $($which help the

pigment stick to the surface$)$ and solvents $($which ensure that the paint stays in liquid form$)$ costs

$$20\mathrm{.}00/$kg$.$ Another paint mixture containing $12\mathrm{.}0$ wt$\%$ pigment costs $$14\mathrm{.}00/$kg$.$ If a paint retailer sells a

blend containing $17$ wt$\%$ pigment, for how much $($$$/$kg$)$ should it be sold to yield a $20\%$ profit?