Simplify 3.$$\bar{36}$$-2.$$\bar{05}$$+1.$$\bar{33}$$

Let say, $$0.\overline{36\ }=x\ ,0.\overline{05\ }=y\ and\ \ 0.\overline{33\ }=z.$$

So, $$36.\overline{36\ }=100x\ $$

or,$$36+x=100x\ .$$

or,$$x=\frac{36}{99}.$$

and, $$y=0.\overline{05\ }$$

or,$$100y=5+0.\overline{05\ }=5+y.$$

or,$$y=\frac{5}{99}.$$

and,

$$z=0.\overline{33\ }$$

or,$$100z=33+0.\overline{33}=33+z.$$

or,$$z=\frac{33}{99}.$$

So,

$$3.\overline{36}-2.\overline{05}+1.\overline{33}$$

$$=3+x-2-y+1+z.$$

$$=3+\frac{36}{99}-2-\frac{5}{99}+1+\frac{33}{99}.$$

$$=2+\frac{36-5+33}{99}.$$

$$=2+\frac{64}{99}.$$

$$=2+0.\overline{64}=2.\overline{64}.$$

A is correct choice.