Two pipes can fill a tank in 12 hours and 4 hours respectively. A third pipe alone can empty the completely filled tank in 5 hours. If all the three pipes are opened simultaneously, then how much time ( in hours) will it take for the empty tank to get filled ?

$7\frac{1}{2}$

Total capacity = Efficiency × Time

When all the three pipes are open , Net capacity = 5 + 15 - 12 = 8

Time = \(\frac{60}{8}\)

= \(\frac{15}{2}\)

The correct answer is option (1) : $7\frac{1}{2}$