Two pipes, P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes, P is turned off. In how many more minutes will Q fill the cistern?

P can fill cistern in 12 minutes
P fills cistern in 1 minute = 1/12 part

Q can fill cistern in 15 minutes
Q fills cistern in 1 minute = 1/15 part
P and Q together can fill cistern in 1 minute,
=1/12 + 1/15 = 9/60 part
So, they can together fill cistern in 3 minute,
= 3 × 9/60 = 9/20 part
Rest Cistern
= 1− 9/20
= 11/20 part
cistern must be filled by Q in (11/20) ÷ (1/15)
= 8 minutes 15 seconds