The value of $$\frac{\left(3\frac{1}{3} - 2\frac{1}{2}\right) \div \frac{1}{4} of 1\frac{1}{4}}{\frac{3}{10} + \frac{1}{6} \times \frac{1}{3}}$$ of $$\frac{4}{15} \div \frac{\frac{1}{3} \div \frac{1}{3} of \frac{1}{9}}{\frac{1}{9} \times \frac{1}{3} \div \frac{1}{6}}$$ is:

$$\frac{\left(3\frac{1}{3} - 2\frac{1}{2}\right) \div \frac{1}{4} of 1\frac{1}{4}}{\frac{3}{10} + \frac{1}{6} \times \frac{1}{3}}$$ of $$\frac{4}{15} \div \frac{\frac{1}{3} \div \frac{1}{3} of \frac{1}{9}}{\frac{1}{9} \times \frac{1}{3} \div \frac{1}{6}}$$

$$\Rightarrow  \frac{\left(\frac{10}{3} - \frac{5}{3}\right) \div \frac{1}{4} of \frac{5}{4}}{\frac{3}{10} + \frac{1}{6} \times \frac{1}{3}}$$ of $$\frac{4}{15} \div \frac{\frac{1}{3} \div \frac{1}{3} of \frac{1}{9}}{\frac{1}{9} \times \frac{1}{3} \div \frac{1}{6}}$$

$$\Rightarrow \frac{\frac{20-15}{6} \div \frac{5}{16}}{\frac{3}{10} + \frac{1}{18}}$$ of $$\frac{4}{15} \div \frac{\frac{1}{3} \div \frac{1}{27}}{\frac{1}{9} \times 2}$$

$$\Rightarrow \frac{\frac{5}{6} \div \frac{5}{16}}{\frac{27+5}{90}}$$ of $$\frac{4}{15} \div\frac{ 9}{\frac{2}{9} }$$

$$\Rightarrow \frac{\frac{5}{6} \times \frac{16}{5}}{\frac{32}{90}}$$ of $$\frac{4}{15} \div\frac{ 9\times 9}{2} $$

$$\Rightarrow \frac{8}{3} \times \frac{90}{32} of \frac{4}{15} \div \frac{81}{2}$$

$$\Rightarrow \frac{15}{2} \times \frac{4}{15} \div \frac{81}{2}$$

$$\Rightarrow 2 \div \frac{81}{2} $$

$$ \Rightarrow 2 \times \frac{2}{81} $$

$$\Rightarrow \frac{4}{81} $$ 

therefore Option (C) $$\frac{4}{81} $$ Ans