If $$\frac{a}{{1 - 2a}}$$  $$+$$ $$\frac{b}{{1 - 2b}}$$  $$+$$ $$\frac{c}{{1 - 2c}}$$  = $$\frac{1}{2}{\text{,}}$$  then the value of $$\frac{1}{{1 - 2a}}$$  $$+$$ $$\frac{1}{{1 - 2b}}$$  $$+$$ $$\frac{1}{{1 - 2c}}$$  is?

Solution (By Examveda Team)

$$\eqalign{ & \frac{a}{{1 - 2a}} + \frac{b}{{1 - 2b}} + \frac{c}{{1 - 2c}} = \frac{1}{2} \cr & {\text{Multiply by 2 both side}} \cr & \Rightarrow \frac{{2a}}{{1 - 2a}} + \frac{{2b}}{{1 - 2b}} + \frac{{2c}}{{1 - 2c}} = 1 \cr & {\text{Adding 3 both side}} \cr} $$
$$ \Rightarrow 1 + \frac{{2a}}{{1 - 2a}} + 1 + \frac{{2b}}{{1 - 2b}} + 1 + $$       $$\frac{{2c}}{{1 - 2c}} = $$  $$1 + 3$$
$$ \Rightarrow \frac{1}{{1 - 2a}} + \frac{1}{{1 - 2b}} + \frac{1}{{1 - 2c}} = 4$$