A cistern has 3 pipes A,B and C. A and B can fill the tank in 15 and 18 minutes respectively whereas all three simultaneously take 45 minutes. Let flow of water in every pipe change directions for two minutes after every five minutes of regular flow,beginning with regular flow. How much time will now be taken to fill the empty tank?

• 
  A takes = 15 min to fill the tank , so in 1 min =1/15, 5 min = 5/15
  B " = 18 min , 1 min =1/18, 5 min =5/18
  now calculate for C,
  1/A+1/B+1/C=1/45 => 1/15+1/18+1/c=1/45, solving we get C= -0.1
  what is its mean -0.1, it means C doing -ve work w.r.t A & B.
  C takes 10min to empty the tank , in 1 min -0.1 5 min= -0.5
  
  So, in 5 min (A+B+C) =10/90 wk,
  now its turn for reverse 2 min wk = 4/90 (approx.)
  it means in 7 min wk= 11/90-4-90=6/90
  7min---------6/90
  x-------------1 full tank
  solving for x.x=(90*7)/6
  total time = 105 min is correct ans
• 7 years agoHelpfull: Yes(1) No(0)
• Ans: 108 min.
  Basically u can assume that A,B,C are 3 persons for convenience.
  A takes = 15 min for 100% work , so in 1 min =100/15= 6.66%, 2 min= 13.32%, 5 min = 33.30% work
  B " = 18 min " " , 1 min =100/18= 5.55%, 2 min= 11.10%, 5 min = 27.75% work
  now calculate for C,
  1/A+1/B+1/C=1/45 => 1/15+1/18+1/c=1/45, solving we get C= -10% ??
  what is its mean -10%, it means C doing -ve work w.r.t A & B.
  C takes -100% work in 10min, in 1 min -10%, in 2 min = -20%, in 5 min= -50%
  
  So, in 5 min (A+B+C) = 11% wk,
  now its turn for reverse 2 min wk = (-4.5%) (approx.)
  it means in 7 min wk= 11-4.5 = 6.5%
  so, in 7*15 min wk = 6.5*15 = 97.5 % (rem = 100%-97.5= 2.5%)
  in next 2-3 min he will do rem 2.5 % work
  total time = 7*15+ 2.5min= 107.5 or 108 min .......:-)
• 8 years agoHelpfull: Yes(0) No(0)