Find the value of * in the following. $${\text{1}}\frac{2}{3} \div \frac{2}{7} \times \frac{*}{7} = 1\frac{1}{4} \times \frac{2}{3} \div \frac{1}{6}$$

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let,}} \cr & \frac{5}{3} \div \frac{2}{7} \times \frac{x}{7} = \frac{5}{4} \times \frac{2}{3} \div \frac{1}{6} \cr & {\text{Then,}} \cr & \frac{5}{3} \times \frac{7}{2} \times \frac{x}{7} = \frac{5}{4} \times \frac{2}{3} \times 6 \cr & \Leftrightarrow \frac{5}{6}x = 5 \cr & \Leftrightarrow x = \left( {\frac{{5 \times 6}}{5}} \right) \cr & \Leftrightarrow x = 6 \cr} $$