A cistern can be filled by two pipes filling separately in 12 and 16 min. respectively. Both pipes are opened together for a certain time but being clogged, only 7/8 of the full quantity of water flows through the former and only 5/6 through the latter pipe. The obstructions, however, being suddenly removed, the cistern is filled in 3 min. from that moment. How long was it before the full flow began?

Both the pipes A and B can fill

of the cistern in one minute, when their is no obstruction.

With obstruction, both the pipes can fill

of the cistern in one minute.

Let the obstructions were suddenly removed after x minutes.

∴ With obstruction, x/8 of the cistern could be filled in x minutes and so the remaining of the cistern was filled without obstruction in 3 minutes,

i.e. In one minute, of the cistern was filled with obstruction.

⇒ x = 4.5 min.