$300 \mathrm{gm} 30\% (\mathrm{w}/\mathrm{w}) \mathrm{NaOH}$ solution is mixed with  $500 \mathrm{gm} 40\% (\mathrm{w}/\mathrm{w}) \mathrm{NaOH}$ solution. What is $\% (\mathrm{w}/\mathrm{v}) \mathrm{NaOH}$ if density of final solution is $2 \mathrm{gm}/\mathrm{mL}$?

30% (w/w) of 300 g of NaOH  $=300\times \frac{30}{100}=90\mathrm{g}$

40% (w/w) of 500 g of NaOH$=500\times \frac{40}{100}=200\mathrm{g}$

Total volume of solution$=\frac{\text{ Mass of solution }}{\text{ Density of solution }}$

$=\frac{800}{2}=400\mathrm{mL}$

%(w/v) volume of NaOH $=\frac{90+200}{400}\times 100=72.5$
 

$$\begin{gathered} \frac{300\times 0.30+500\times 0.4}{\frac{800}{2}}\times 100 \\ =72.5\mathrm{\%} \end{gathered}$$