$\left(\frac{3}{4}\right)^{th}$ of a cistern is filled by a pipe in 12 mins. Time taken by the pipe to fill half of the cistern is :

8 mins

The correct answer is Option (3) → 8 mins

Rate of filling = $\frac{\frac{3}{4}Cisterns}{12\,minutes}=\frac{3}{4×12}=\frac{3}{48}=\frac{1}{16}$ Cistern per minute

$Time = \frac{\frac{1}{2}Cisterns}{\frac{1}{16}Cisterns\,minutes}=8\,minute$