Two taps P and Q can fill a cistern in 30 and 20 minutes respectively. Both P and Q were opened for a few minutes after which P was closed. The rest of the cistern was filled by Q in 5 minutes. After how many minutes was pipe P closed?

Tap $P$ fills the cistern in 30 minutes.

Tap $Q$ fills the cistern in 20 minutes.

$Q$ fills the rest of the cistern in 5 minutes after $P$ is closed. 

Formula Used:​

Capacity = Rate to fill  $$\times$$ time taken

Solution: 

LCM of 30 and 20 = 60 

Let the capacity of the tank be 60 unit.

So,  Rate of tap P = $$\frac{60}{30} = 2 \,unit/min.$$ 

Rate of tap Q = $$\frac{60}{20} = 3 \, unit/min.$$ 

Now, Q fill the remaining in 5 minutes 

So, filled portion by Q alone = $$5 \times 3 = 15 \, unit$$ 

Portion filled by both P + Q, earlier = 60 - 15 = 45 unit,

Time taken to fill by P + Q = $$\frac{45}{5} = 9 \, min.$$ 

Thus, P is closed after 9 minutes.