Simplify : $$\frac{{\frac{1}{3} + \frac{1}{4}\left[ {\frac{2}{5} - \frac{1}{2}} \right]}}{{1\frac{2}{3}\,{\text{of }}\frac{3}{4} - \frac{3}{4}\,{\text{of }}\frac{4}{5}}} = ?$$

$$\eqalign{ & {\text{According to question,}} \cr & \frac{{\frac{1}{3} + \frac{1}{4}\left[ {\frac{2}{5} - \frac{1}{2}} \right]}}{{1\frac{2}{3}\,{\text{of }}\frac{3}{4} - \frac{3}{4}\,{\text{of }}\frac{4}{5}}} \cr & \Rightarrow \frac{{\frac{1}{3} + \frac{1}{4}\left[ {\frac{{4 - 5}}{{10}}} \right]}}{{\frac{5}{3}\, \times \frac{3}{4} - \frac{3}{4}\, \times \frac{4}{5}}} \cr & \Rightarrow \frac{{\frac{1}{3} - \frac{1}{4} \times \frac{1}{{10}}}}{{\frac{5}{4} - \frac{3}{5}}} \cr & \Rightarrow \frac{{\frac{{40 - 3}}{{120}}}}{{\frac{{25 - 12}}{{20}}}} \cr & \Rightarrow \frac{{37}}{{120}} \times \frac{{20}}{{13}} \cr & \Rightarrow \frac{{37}}{{78}} \cr} $$