Solve the following $$\frac{{24 \div \frac{3}{8}{\text{of}}\left( {8 + 2 \times \overline {7 - 3} } \right) + \left[ {\frac{2}{{11}} \div \frac{4}{{55}} - \left\{ {\frac{5}{8} + \frac{6}{{16}}} \right\}} \right]}}{{32 \div \overline {15 - 7} + 75 \div \left( {6 + 15 \div 3 + 4} \right)}}$$

Solution (By Examveda Team)

$$\eqalign{ & \frac{{24 \div \frac{3}{8}{\text{of}}\left( {8 + 2 \times \overline {7 - 3} } \right) + \left[ {\frac{2}{{11}} \div \frac{4}{{55}} - \left\{ {\frac{5}{8} + \frac{6}{{16}}} \right\}} \right]}}{{32 \div \overline {15 - 7} + 75 \div \left( {6 + 15 \div 3 + 4} \right)}} \cr & = \frac{{\left[ {24 \div \frac{3}{8}{\text{of}}\left( {8 + 2 \times 4} \right) + \left( {\frac{2}{{11}} \times \frac{{55}}{4} - \left\{ {\frac{{16}}{{16}}} \right\}} \right)} \right]}}{{32 \div 8 + 75 \div \left( {6 + 5 + 4} \right)}} \cr & = \frac{{\left[ {24 \div 6 + \left( {\frac{5}{2} - 1} \right)} \right]}}{{\left[ {4 + 75 \div 15} \right]}} \cr & = \frac{{\left[ {4 + \frac{3}{2}} \right]}}{{\left[ {4 + 5} \right]}} \cr & = \frac{{\left[ {\frac{{11}}{2}} \right]}}{9} \cr & = \frac{{11}}{{18}} \cr} $$