(a) 1800 litres
Part of the tank that can be filled by the two filler taps = \(\big(\frac{1}{30}+\frac{1}{20}\big)\)
= \(\frac{2+3}{60}\) = \(\frac{5}{60}\) = \(\frac{1}{12}\)
\(\therefore\) The two taps can fill the tank in 12 minutes.
\(\Rightarrow\) Half of the tank will be filled in 6 minutes
\(\Rightarrow\) The time taken by the remaining half of the tank to be filled when the outlet pipe is open = (24 – 6) min = 18 min.
\(\Rightarrow\) Part of that half of the tank that can be emptied in 1 hour
= \(\frac{1}{6}\) - \(\frac{1}{18}\) = \(\frac{1}{9}\)
\(\therefore\) Time taken to empty half of the cistern = 9 minutes
\(\therefore\) Capacity of the tank = 100 × 9 × 2 = 1800 litres.
