A cistern has three pipes A, B and C. Pipes A and B can fill it in 3 and 4 h, respectively, while pipe C can empty the completely filled cistern in 1 h. If the pipes are opened in order at 3:00 pm, 4:00 pm and 5:00 pm, respectively , at what time will the cistern be empty?
Correct Answer: 7:12 pm
Explanation:
Let the cistern gets emptied in m h after 3:pm
Work done by A in m h, by B in (m - 1) h and by c in (m - 2) h= 0
⇒ m/3 + (m - 1)/4 - (m - 2) = 0
⇒ 4m + 3(m - 1) - 12(m - 2) = 0
⇒ 5m = 21
⇒ m = 21/5 = 4.2
∴ m = 4 h 12 min
∵ Required time = 7 : 12 pm.
