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?

Answer: Option D

P can fill cistern in 12 minutes
P fills cistern in 1 minute = $$\frac{1}{12}$$
Q can fill cistern in 15 minutes
Q fills cistern in 1 minute = $$\frac{1}{15}$$ part
P and Q together can fill cistern in 1 minute,
$$=\frac{1}{12}+\frac{1}{15}\Rightarrow \frac{9}{60}$$    part
So, they can together fill cistern in 3 minute,
$$=3\times \frac{9}{60}\Rightarrow \frac{9}{20}$$    part
Rest Cistern = $$1-\frac{9}{20}$$  = $$\frac{11}{20}$$  part
$$\frac{11}{20}$$ part cistern must be filled by Q in
$$\frac{\frac{11}{20}}{\frac{1}{15}}=8\frac{1}{4}$$   minutes

Alternatively,
Pipe P can fill cistern in one minute = $$\frac{100}{12}$$ = 8.33%
Pipe Q can fill cistern in one minute = $$\frac{100}{15}$$ = 6.66%
(P + Q) together can fill the cistern in one minute = 15%;
In 3 minutes cistern is filled = 45%
P become off, then rest of cistern will be filled by Pipe Q in = $$\frac{55}{6.66}$$ = $$8\frac{1}{4}$$ minutes.