Tick (✓) the correct answer:
Two pipes can fill a tank in 10 hours and 12 hours respectively, while a third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time will the tank be full?
(a) 7 hrs 15 min
(b) 7 hrs 30 min
(c) 7 hrs 45 min
(d) 8 hrs
(b) 7 hours 30 minutes
Part of the tank filled by the first pipe in one hour $=\frac{1}{10}$
Part of the tank filled by the second pipe in one hour $=\frac{1}{12}$
Part of the tank filled by the third pipe in one hour $=\frac{-1}{20}$
Part of the tank filled by three pipes in one hour $=\frac{1}{10}+\frac{1}{12}-\frac{1}{20}=\frac{2}{15}$
Total time taken to fill the tank $=\frac{15}{2} \mathrm{hrs}=7$ hours 30 minutes
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