Two pipes A and B can fill a cistern in 15 hours and 25 hours respectively. Another pipe C can empty the full tank in 30 hours. If all the pipes are opened together, then the time needed to fill the cistern fully is :

$12\frac{7}{11}$ hours $13\frac{7}{11}$ hours $11\frac{7}{11}$ hours $13\frac{8}{11}$ hours

$13\frac{7}{11}$ hours