In 1 min both pipes can fill,

$\Rightarrow \frac{1}{20}+\frac{1}{30}=\frac{1}{12}$^th part of the cistern---Eq1

Similarly,

In 10 min only second pipe can fill,

$\Rightarrow \frac{1}{30}\times 10=\frac{1}{3}$^rd part of the cistern

Part of cistern filled by both the pipes,

$\Rightarrow 1-\frac{1}{3}=\frac{2}{3}$

According to eqution 1, $\frac{1}{12}$^th part will be filled in 1 min

So, $\frac{2}{3}$rd part will be filled in...

$\Rightarrow 12\left(\frac{2}{3}\right)=8 \mathrm{minutes}$

Therefore, firstpipe should be turned off after 8 min

Hence option D is correct.