The value of $${\text{0}}{\text{.}}\overline 2 + {\text{0}}{\text{.}}\overline 3 + {\text{0}}{\text{.}}\overline {32} $$     is :

Solution (By Examveda Team)

$$\eqalign{ & 0.\overline 2 + 0.\overline 3 + 0.\overline {32} \cr & = \frac{2}{9} + \frac{3}{9} + \frac{{32}}{{99}} \cr & = \frac{{22 + 33 + 32}}{{99}} \cr & = \frac{{87}}{{99}} \cr & = 0.\overline {87} \cr} $$