Simplify : $${{{5 \over 3} \times {7 \over {51}}{\text{ of }}{{17} \over 5} - {1 \over 3}} \over {{2 \over 9} \times {5 \over 7}{\text{ of }}{{28} \over 5} - {2 \over 3}}}$$

Solution (By Examveda Team)

$$\eqalign{ & {\text{According to question,}} \cr & \frac{{\frac{5}{3} \times \frac{7}{{51}}{\text{ of }}\frac{17}{5} - \frac{1}{3}}}{{\frac{2}{9} \times \frac{5}{7}{\text{ of }}\frac{{28}}{5} - \frac{2}{3}}}\, \cr & \Rightarrow \frac{{\frac{5}{3} \times \frac{7}{{51}} \times \frac{17}{5} - \frac{1}{3}}}{{\frac{2}{9} \times \frac{5}{7} \times \frac{{28}}{5} - \frac{2}{3}}}\, \cr & \Rightarrow \frac{{\frac{5}{3} \times \frac{7}{{15}} - \frac{1}{3}}}{{\frac{2}{9} \times 4 - \frac{2}{3}}} \cr & \, \Rightarrow \frac{{\frac{7}{9} - \frac{1}{3}}}{{\frac{8}{9} - \frac{2}{3}}} \cr & \, \Rightarrow \frac{{\frac{{7 - 3}}{9}}}{{\frac{{8 - 6}}{9}}} \cr & \Rightarrow \frac{4}{2} \cr & \Rightarrow 2 \cr} $$