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