Two taps P and Q can separately fill a cistern in 36 minutes and 45 minutes respectively. After both the taps are opened simultaneously by what time (in minutes) the pipe Q should be closed so that the cistern is completely filled in 27 minutes?

A

$$11\frac{1}{2}$$

B

$$12\frac{1}{2}$$

C

$$12\frac{1}{4}$$

D

$$11\frac{1}{4}$$