A solution is obtained by mixing $200 \mathrm{g}$ of $30\%$ and $300 \mathrm{g}$ of $20\%$ solution by weight. What is the percentage of solute in the final solution? 

Solute in $200 \mathrm{g}$of $30\%$ solution = 60 g

Solute in 300 g of $20\%$ solution = 60 g

Total grams of solute = $120 \mathrm{g} \left(60 \mathrm{g}+60 \mathrm{g}\right)$ 

Total grams of solution $= 200 \mathrm{g}+ 300 \mathrm{g}= 500 \mathrm{g}$

$\%$ of solute in the final solution =$\frac{\mathrm{Weight} \mathrm{of} \mathrm{solute}}{\mathrm{Weight} \mathrm{of} \mathrm{solution}} \times 100=\frac{120 \mathrm{g}}{500 \mathrm{g}}\times 100=24\%$