Madhu takes twice as much time as Uma to complete a work and Rahul does it in the same time as Madhu and Uma together. If all three working together can finish the work in 6 days, then the time taken by Madhu to finish the work is = ?

Answer: Option C

Suppose Uma takes x days to complete a work
Then, Madhu takes 2x days to complete the work
Uma's 1 day's work = $$\frac{1}{x}$$
Madhu's 1 day's work = $$\frac{1}{2x}$$
Rahul's 1 day's work = (Madhu + Uma)'s 1 day's work
$$\begin{array}{rl}& =\frac{1}{2x}+\frac{1}{x}\\ & =\frac{3}{3x}\end{array}$$
(Madhu + Uma + Rahul)'s 1 day's work
$$\begin{array}{rl}& =\frac{3}{3x}+\frac{1}{2x}+\frac{1}{x}=\frac{6}{3x}=\frac{3}{x}\\ & \therefore \frac{3}{x}=\frac{1}{6}\\ & \Rightarrow x=18\end{array}$$
Hence, Madhu takes (2 × 18) = 36 days to complete the work