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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

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Number of hours inlet A requires to fill the cistern : 10hours 

Number of hours inlet B requires to fill the cistern : 12hours 

Number of hours outlet C requires to empty the cistern : 20hours

Part of the cistern filled by inlet A in one hour: \(\frac{1}{10}\)

Part of the cistern filled by inlet B in one hour: \(\frac{1}{12}\)

Part of the cistern emptied by outlet C in one hour: \(\frac{1}{20}\)

Work done by pipes A, B and C together in one hour: \(\frac{1}{10}+\frac{1}{12}-\frac{1}{20}=\frac{8}{60}=\frac{2}{15}\)

∴ They can fill the cistern together in \(\frac{15}{2}\) hours = 7 hrs 30 min

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