A tank can be filled by a tap in 12 minutes and by another tap in 30 minutes. Both the taps are kept open for 6 minutes and then the first tap is shut off. After this, the tank will be filled in     

A tap can be filled a tank = 12 minuts $\Rightarrow$ for 1 minute $=\frac{1}{12}$

another  tap can be filled a tank = 30 minutes $\Rightarrow$ for 1 minute $=\frac{1}{30}$

part of  the tank filled in 6 minutes $=6\times [\frac{1}{12}+\frac{1}{30}]=6\times \left[\frac{5+2}{60}\right]=\frac{7}{10}parts$

$\begin{array}{l}\text{Remaining\hspace{0.17em}\hspace{0.17em}}parts=1-\frac{7}{10}=\frac{3}{10}parts\\ \frac{1}{30}partof\text{\hspace{0.17em}\hspace{0.17em}tank\hspace{0.17em}}filled\Rightarrow 1\text{\hspace{0.17em}\hspace{0.17em}minute}\\ \frac{3}{10}parthastobefilled\Rightarrow x\text{\hspace{0.17em}\hspace{0.17em}minutes}\\ \frac{3}{10}\times 30=x\Rightarrow x=9\text{\hspace{0.17em}\hspace{0.17em}minutes}\end{array}$