Two pipes A and B can fill a tank in 12 min and 18 minutes respectively. There is also an outlet C. If all the three pipes are opened together, the tank is full in 9 minutes. How much time will be taken by C to empty the full tank ?

$Acanfilla\text{\hspace{0.17em}\hspace{0.17em}tank}=12\min \Rightarrow for1\min =\frac{1}{12}$

$Bcanfilla\text{\hspace{0.17em}\hspace{0.17em}tank}=18\min \Rightarrow for1\min =\frac{1}{18}$

$Ccanemptythe\text{\hspace{0.17em}\hspace{0.17em}tank}=x\min \Rightarrow for1\min =\frac{1}{x}$

$\therefore A+B-C=\frac{1}{9}$

$\frac{1}{12}+\frac{1}{18}-\frac{1}{x}=\frac{1}{9}$

$\frac{3x+2x-36}{36x}=\frac{1}{9}$

$5x-36=\frac{36x}{9}$

$5x-36=4x$

$x=36$

$\therefore \text{'}C\text{'}canemptythe\text{\hspace{0.17em}\hspace{0.17em}tank}=36\text{\hspace{0.17em}\hspace{0.17em}minutes}$