Let the total capacity of a tank be ‘m’ lit. Average rate = total distance/time taken ⇒ Time taken by a pipe to fill 1/4th of a tank = (m/4)/12 = m/48 hr ⇒ Time taken by a pipe to fill 2/3rd of a tank = (2m/3)/32 = m/48 hr ⇒ Rest part of a tank remain to fill = m {1 - (1/4 + 2/3)} = m (1 - 11/12) ⇒ Rest part of a tank remain to fill = m/12 Given, The rest at the rate of ‘a’ lit/hr: ⇒ Time taken by a pipe to fill rest of cistern = (m/12)/a = m/12a hr Total time taken by a pipe to fill cistern completely = = (m/48 + m/48+ m/12a) hr = (m/12) × (1/4 + 1/4 + 1/a) = (m/12) × = /24a Average rate to fill cistern completely - ⇒ Total capacity of a cistern/Total time taken by a pipe to fill cistern completely ⇒ 8 = (m/{/24a}) ⇒ 8 = 24a/(a + 2) ⇒ 8a + 16 = 24a ⇒ 16a = 16 ⇒ a = 1 lit/hr The value of a is 1 lit/hr.