Simplify : 1/3 + 1/4 [ 2/5 - 1/2 ]12/3\, of 3/4 - 3/4\, of 4/5 = ?

Answer: Option A

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