Pipes A and B can fill a tank in 16 hours and 24 hours, respectively, whereas pipe C can empty the full tank in 40 hours. All three pipes are opened together, but pipe A is closed after 10 hours. After how many hours will the remaining part of the tank be filled?

$12\frac{1}{2}$

A+ = 16 hrs, B+ = 24 hrs, C- = 40 hrs,

⇒ A + B + C opened for 10 hours and then A was closed = (15 + 10 - 6) x 10 = 19 x 10 = 190 units,

⇒ Remaining = 240 - 190 = 50 units,

⇒ Time required by B + C to fill the remaining tank = \(\frac{50}{10-6}\) = \(\frac{50}{4}\) = \( {12 }_{2 }^{ 1} \) hrs.