Simplify $$\frac{\left[\frac{3}{5} of \left(15\frac{2}{3}-33\frac{1}{3}\right)+\frac{1}{3}\left(18\frac{3}{4} of 7\frac{1}{5}\div15\times2\right)\right]\times5}{3^{2}\times5+1}$$.

Given Equation : 

$$\frac{\left[\frac{3}{5} of \left(15\frac{2}{3}-33\frac{1}{3}\right)+\frac{1}{3}\left(18\frac{3}{4} of 7\frac{1}{5}\div15\times2\right)\right]\times5}{3^{2}\times5+1}$$.

Lets solve it as per rule of BODMAS. 

$$\frac{\left[\frac{3}{5}of\left(\frac{47}{3}-\frac{100}{3}\right)+\frac{1}{3}\left(\frac{75}{4}of\ \frac{36}{5}\div15\times2\right)\right]\times5}{3^2\times5+1}.$$

$$\frac{\left[\left(\frac{3}{5}\times\ -\frac{53}{3}\right)+\frac{1}{3}\left(\frac{75}{4}\times\ \frac{36}{5\times\ 15}\times\ 2\right)\right]\times5}{3^2\times5+1}.$$

$$\frac{\left[\left(\left(-\frac{53}{5}\right)+6\right)\right]\times5}{3^2\times5+1}.$$

$$\frac{-23}{3^2\times5+1}$$

$$\frac{-23}{46}=-\frac{1}{2}$$

Hence, Option B is correct.