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

1 $\frac{37}{78}$ $\frac{{37}}{{78}}$
2 $\frac{37}{13}$ $\frac{{37}}{{13}}$
3 $\frac{74}{78}$ $\frac{{74}}{{78}}$
4 $\frac{74}{13}$ $\frac{{74}}{{13}}$

Answer:- 1

Explanation:-

Solution:

\begin{aligned} According to question \\ \frac{\frac{1}{3} + \frac{1}{4} [\frac{2}{5} - \frac{1}{2}]}{1 \frac{2}{3} of \frac{3}{4} - \frac{3}{4} of \frac{4}{5}} \\ \Rightarrow \frac{\frac{1}{3} + \frac{1}{4} [\frac{4 - 5}{10}]}{\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{aligned}

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