$$ 1.\overline{27} + 0.\overline{94} $$

Let say,

$$x=\overline{.27}\ and\ y=\overline{.94\ }\ .$$

So,we can rewrite it as,

$$x=.27\overline{27\ }\ and\ \ y=.94\overline{94\ }\ .$$

or,$$100x=27.\overline{27\ }\ and\ \ 100y=94.\overline{94\ }\ .$$

or,$$100x=27+.\overline{27\ }\ and\ \ 100y=94+.\overline{94\ }\ .$$

or,$$100x=27+x\ and\ \ 100y=94+y\ .$$  (as $$x=\overline{.27\ }\ and\ \ y=\overline{.94\ }\ .$$)

or,$$99x=27\ and\ 99y=94.$$

or,$$x=\frac{\ 27}{99}\ and\ \ y=\frac{94\ }{99}.$$

So,$$1.\overline{27\ }+.\overline{94\ }=1+x+y.$$

or,$$1.\overline{27\ }+.\overline{94\ }=1+\frac{27\ }{99}+\frac{94\ }{99}.$$

or,$$1.\overline{27\ }+.\overline{94\ }=\frac{220\ }{99}=2.22222222.....=2.\overline{2\ }.$$

B is correct choice.