• # question_answer 19) A cistern has two inlets A and B which .can fill it in 12 minutes and 15 minutes respectively. An outlet C can empty the full cistern in 10 minutes. If all the three pipes then are opened together in the empty cistern, time taken to fill the cistern completely is _____. A)  20 minutes                 B)         10 minutes     C)         15 minutes                 D)         5 minutes

Part of cistern filled by inlets A and B together in one minute $=\frac{1}{12}+\frac{1}{15}=\frac{5+4}{60}=\frac{9}{60}$ and part of cistern emptied by outlet C in 1 minute $=\frac{1}{10}$ So, part of the cistern filled in one minute when all three pipes are opened simultaneously, $=\frac{9}{60}-\frac{1}{10}=\frac{9-6}{60}=\frac{3}{60}=\frac{1}{20}$ So, time required to fill the cistern = 20 mins.