Two pipes A and B can fill a cistern in 12 and 16 minutes respectively. Both pipes are opened together but 4 minutes before the cistern is full pipe A stop working. How much time will the cistern take to fill?

9\(\frac{1}{7}\) min

Pipe  A can fill = 12 minutes 

Pipe  B can fill = 16 minutes 

LCM of 12 and 16 = 48 ( total work ) 

Efficiency of pipe A = \(\frac{48}{12}\) = 4 

Efficiency of pipe B = \(\frac{48}{16}\) = 3

 total efficiency ( A + B ) = 7 

 Let A work for 4 minutes more = 4 × 4 = 16 

 then total work done by ( A + B ) = 48 + 16 = 64 

time taken = \(\frac{64}{7}\) = 9\(\frac{1}{7}\)