Express the following as a vulgar fraction.

​$$0.0\overline{13}+0.\overline{32}$$​​

Correct option is C

Given:

​$$0.0\overline{13}+0.\overline{32}$$​​

Solution:

Let x = 0.0131313…

Then 10x = 0.131313

1000x = 13.1313…

1000x - 10x = 13.131313… - 0.131313

990x = 13

x = $$\frac{13}{990}$$​​

Let y = 0.323232…

100y = 32.323232..

100y - y = 32.3232.. - 0.323232…

99y = 32

y = $$\frac{32}{99}$$ 

then, 

​$$0.0\overline{13}+0.\overline{32}$$​​

​$$= \frac{13}{990} + \frac{32}{99}$$​​

​$$= \frac{13 + 320}{990}$$​​

​$$= \frac{333}{990}$$​​

​$$=\frac{111}{330}$$​​