The value of $$\left( {1\frac{1}{3} \div 2\frac{6}{7}{\text{ of }}5\frac{3}{5}} \right) \div \left( {6\frac{2}{5} \div 4\frac{1}{2}{\text{ of}}\,5\frac{1}{3}} \right) \times \left( {\frac{3}{4} \times 2\frac{2}{3} \div \frac{5}{9}{\text{ of }}1\frac{1}{5}} \right) = 1 + {\text{k}},$$             where k lies between:

Solution(By Examveda Team)

$$\eqalign{ & \left( {1\frac{1}{3} \div 2\frac{6}{7}{\text{ of }}5\frac{3}{5}} \right) \div \left( {6\frac{2}{5} \div 4\frac{1}{2}{\text{ of}}\,5\frac{1}{3}} \right) \times \left( {\frac{3}{4} \times 2\frac{2}{3} \div \frac{5}{9}{\text{ of }}1\frac{1}{5}} \right) = 1 + {\text{k}} \cr & \left( {\frac{4}{3} \div \frac{{20}}{7}{\text{ of}}\frac{{28}}{5}} \right) \div \left( {\frac{{32}}{5} \div \frac{9}{2}{\text{ of}}\,\frac{{16}}{3}} \right) \times \left( {\frac{3}{4} \times \frac{8}{3} \div \frac{5}{9}{\text{ of }}\frac{6}{5}} \right) = 1 + {\text{k}} \cr & \left( {\frac{4}{3} \div 4 \times 4} \right) \div \left( {\frac{{32}}{5} \div 24} \right) \times \left( {\frac{3}{4} \times \frac{8}{3} \div \frac{2}{3}} \right) = 1 + {\text{k}} \cr & \left( {\frac{4}{3} \times \frac{1}{{16}}} \right) \div \left( {\frac{4}{5} \times \frac{1}{3}} \right) = 1 + {\text{k}} \cr & \frac{1}{{12}} \div \frac{4}{{15}} \times 3 = 1 + {\text{k}} \cr & \frac{1}{{12}} \times \frac{{15}}{4} \times 3 = 1 + {\text{k}} \cr & \frac{{15}}{{16}} - 1 = {\text{k}} \cr & \frac{{ - 1}}{{16}} = {\text{k}} \cr & - 0.0625 = {\text{k}} \cr & - 0.07 < {\text{k}} > - 0.0625 \cr} $$