Two pipes can fill a tank in 5 minutes and 6 minutes respectively and a third pipe empties the full tank in 10 minutes. How much time will be taken to fill the tank if all pipes open simultaneously?

A 30/11 min

B 3/10 min

C 3.52 min

D 15/4 min

E 11/30 min

Correct Answer: Option D

Tank filled by first, second and third pipe in 1 minute = 1/5, 1/6 and (-1/10) respectively.

{Negative sign for the pipe which is making the tank empty instead of filling}

∴ Total part filled in 1 min \(= \left( {\frac{1}{5} + \frac{1}{6} - \frac{1}{{10}}} \right) = \frac{8}{{30}} = \frac{4}{{15}}\)

∴ Time taken to fill the tank \(= \frac{{15}}{4} = 3\frac{3}{4}min\)

Hence, required time to fill the tank completely is 15/4 minutes.