A cistern can be filled by one of two pipes in 52 minutes and by the other pipe in 60 minutes. Both pipes are opened together for a certain time but being particularly clogged only 13/20 of the full quantity of water flows through the first pipe and only 3/4 of the full quantity of water flows through the second pipe. The obstructions, however, were suddenly removed in both the pipes after some time and the cistern got filled in 15(3/5) minutes from that moment. For how many minutes did the pipes remain clogged?