Pipes A and B can fill a tank in 18 minutes and $22\frac{1}{2}$ minutes, respectively while pipe C can empty the full tank in 12 minutes. A and are opened together for 6 minutes and then closed. Now C is opened. C alone will empty the tank in _____.

$7\frac{1}{5}$ minutes

A+ = 18 min, B+ = \( {22 }_{2 }^{1 } \) min, C- = 12 min,

⇒ A + B were opened for 6 min = (10 + 8) x 6 = 18 x 6 = 108 units,

⇒ Time required by C to empty 108 units of tank = \(\frac{108}{15}\) = $7\frac{3}{15}$  = $7\frac{1}{5}$ minutes