A solution contains $20\mathrm{.}0\%$ w$/$w Na$2$SO$4,15\mathrm{.}0\%$ w$/$w Na$2$CO$3,$ with the rest being water. This solution is passed through an evaporator that removes $10\mathrm{.}0\%$ of the original mass and then crystallizes $20\mathrm{.}0\%$ Na$2$SO$4$ and $30\mathrm{.}0\%$ Na$2$CO$3.$ The crystals formed are Na$2$CO$3$ per ten molecules of H$2$O and Na$2$SO$4$ per ten molecules of H$2$O$.$ Calculate the composition of the residual solution.