Two pipes can fill a tank in 15 hours and 4 hours, respectively, while a third pipe can empty it in 12 hours. How long (in hours) will it take to fill the empty tank if all the three pipes are opened simultaneously?

$ \frac{30}{7}$

A+ = 15 hrs, B+ = 4 hrs, C- = 12 hrs,

⇒ Time required by A + B + C to fill the tank completely = \(\frac{60}{4+15-5}\) =  \(\frac{60}{14}\) =  \(\frac{30}{7}\) hrs.