The value of
$$3\frac{1}{5} \div 4\frac{1}{2}  of  5\frac{1}{3} - 2\frac{1}{3}  of  \left\{\frac{3}{7} - \left(1\frac{4}{15} - \frac{13}{30}\right) \times 1\frac{1}{5}\right\}$$ is:

Given Equation : 

$$3\frac{1}{5} \div 4\frac{1}{2} of 5\frac{1}{3} - 2\frac{1}{3} of \left\{\frac{3}{7} - \left(1\frac{4}{15} - \frac{13}{30}\right) \times 1\frac{1}{5}\right\}$$

Lets Solve this as per the rule of BODMAS : 

$$\therefore\ \frac{16}{5}\div\frac{9}{2}of\ \frac{16}{3}-\frac{7}{3}of\left\{\frac{3}{7}-\left(\frac{19}{15}-\frac{13}{30}\right)\times\ \frac{6}{5}\right\}$$

$$\therefore\ \frac{16}{5}\div24-\frac{7}{3}of\left\{\frac{3}{7}-\frac{\left(38-13\right)}{30}\times\ \frac{6}{5}\right\}$$

$$\therefore\ \frac{16}{5}\times\ \frac{1}{24}-\frac{7}{3}of\left\{\frac{3}{7}-\frac{25}{30}\times\ \frac{6}{5}\right\}$$

$$\therefore\ \frac{2}{15}-\frac{7}{3}of\left\{\frac{3}{7}-1\ \right\}$$

$$\therefore\ \frac{2}{15}-\frac{7}{3}of\left\{-\frac{4}{7}\right\}$$

$$\therefore\ \frac{2}{15}+\frac{4}{3}$$

$$\therefore\ \frac{22}{15}$$

$$\therefore\ 1\frac{7}{15}$$

Hence, Option D is correct.