Two pipes, P and Q can fill a cistern in 12 and 15 minutes respectively. If both are opened together and at the end of 3 minutes, the first is closed, how much longer will the cistern take to fill?

Let the amount of work in filling a cistern equivalent to 60 units

Pipe P takes 12 minutes to fill 60 units

P's 1 minute work = 5 units

Q takes 15 minutes to fill 60 units

Q's 1 minute work = 4 units

If both work together than (P+Q)'s 1 minute work = 9 units

they both are opened for 3 minutes and the amount of units filled = 9 x 3 = 27 units

Now it is given that pipe P is closed

so amount of time taken by pipe Q to fill the tank = $$\frac{33}{4}$$ = 8.25 minutes = 8 $$\frac{1}{4}$$ minutes