An unknown volume of $40\%$ $(\mathrm{w}/\mathrm{w})\mathrm{NaOH}$ solution of specific gravity 1.6 is diluted until specific gravity of the solution becomes 1.1. The strength of resulting solution is:

Let $1000 \mathrm{mL}$ of ${\mathrm{sol}}^{\mathrm{n}}$  is taken

${\text{ mass of sol }}^{\mathrm{n}}=1600\mathrm{g}\left(640\mathrm{gNaOH}+960{\mathrm{gH}}_2\right.\text{ C }$ 

$\text{ Let }V\mathit{ }{\mathrm{mL}}_2 \text{ of }{\mathrm{H}}_2\mathrm{O}$ is added (Assume ${\rho }_{{\mathrm{H}}_2\mathrm{O}}=1\mathrm{g}/\mathrm{c}$ 

$1.1=\frac{1600+V}{1000+V}\Rightarrow V=5000\mathrm{mL}$

$$\begin{gathered} \mathrm{\%}w/w=\frac{640}{6600}\times 100=9.7\mathrm{\%} \\ \mathrm{\%}w/v=\frac{640}{6000}\times 100=10.67\mathrm{\%} \end{gathered}$$