The value of $$\frac{(0.\overline{29} \div 0.\overline{32}) \times 6.6}{0.\overline{95} \div 1.\overline{05} \times 1.\overline{2}}$$​ is

Correct option is C

Given:

​$$\frac{(0.\overline{29} \div 0.\overline{32}) \times 6.6}{0.\overline{95} \div 1.\overline{05} \times 1.\overline{2}}$$​​

Formula Used:
For a two-digit recurring decimal:

​$$0.\overline{ab}=\frac{ab}{99}$$​​

Solution:

​$$\frac{(0.\overline{29} \div 0.\overline{32}) \times 6.6}{0.\overline{95} \div 1.\overline{05} \times 1.\overline{2}} \\ \ \\ = \frac{(\frac{29}{99} \div \frac{32}{99}) \times 6.6}{\frac{95}{99} \div \frac{105 -1}{99} \times \frac{12-1}{9}}\\ \ \\ = \frac{(\frac{29}{32} ) \times \frac{66}{10}}{\frac{95}{104} \times \frac{11}{9}}\\ \ \\ = \frac{29}{32} \times \frac{33}{5} \times \frac{104} {95} \times \frac{9}{11} \\ \ \\ = \frac{10179}{1900} \\ \ \\ \approx 5.4$$​​