One sixth of a cistern is filled by pipe at the rate of 6 lit/h, 4/6th of a cistern is filled by pipe at the rate of 8 lit/h and rest at the rate of 4 lit/h. Find the average rate of pipe at which tank will completely get filled.?

Option 1 : 6.54 lit/hr

Let the total capacity of a cistern be ‘m’ litres.

Average rate = total litres/total time taken

⇒ Time taken by a pipe to fill 1/6^th of a cistern = (m/6)/6 = m/36 hr

⇒ Time taken by a pipe to fill 5/6^th of a cistern = (4m/6)/8 = m/12 hr

⇒ Rest part of a cistern remain to fill = m {1 – (1/6 + 4/6)} = m (1 – 5/6)

⇒ Rest part of a cistern remain to fill = m/6

⇒ Time taken by a pipe to fill rest of cistern = (m/6)/4 = m/24 hr

Total time taken by a pipe to fill cistern completely =

= (m/36 + m/12 + m/24) hr

= m

= 11m/72

Average rate to fill cistern completely =

⇒ a = Total capacity of a cistern/Total time taken by a pipe to fill cistern completely

⇒ a = m/ (11m/72)                            

⇒ a = 72/ 11 lit/hr

⇒ a = 6.54lit/hr