Two pipes A and B can fill a cistern in 36 and 54 minutes respectively. Both pipes are opened together, after how many minutes should B be turned off, so that the cistern be fill in 24 minutes?

Question: Two pipes A and B can fill a cistern in 36 and 54 minutes respectively. Both pipes are opened together, after how many minutes should B be turned off, so that the cistern be fill in 24 minutes?

Solution:
A can fill the cistern in 36 minutes
So in 1 min A can fill the cistern = 1/36 th part
In 24 min, A can fill the cistern = 24/36 = 2/3 rd

∴ Remaining part = 1 - (2/3) = 1/3 rd

As B can fill full cistern in 54 minutes
So it will fill 1/3 rd part in = (1/3) × 54) = 18 minutes.