A cylindrical overhead tank is filled by two pumps P1 and P2. P1 can fill the tank in 8 hr while P2 can fill the tank in 12 hr. There is a pipe P3 which can empty the tank in 8 hr. Both the pumps are opened simultaneously. The supervisor of the tank, before going out on a work, sets a timer to open P3 when the tank is half filled so that the tank is exactly filled up by the time he is back. Due to technical fault P3 opens when the tank is one-third filled. If the supervisor comes back as per the plan what percent of the tank is till empty?

• P1 and P2 can fill the tank in 24/5 hr.[In one hour these fill (1/8+1/12) part of tank].
  
  It takes 12/5 hr in filling half the tank.
  
  For remaining half of the tank P3 will open and this will takes 6 hour.
  
  [1/2=x(1/8+1/12-1/8)
  x=6hrs]
  
  Supervisor has gone out for (12/5+6) hr=42/5 hr
  
  Now, (1/3)rd tank will fill in 8/5 hr.[without P3 opening]
  
  [1/2-----12/5 hrs
  1/3-------?? ==8/5hrs
  
  42/5-8/5==34/5 hrs (because supervisor fixed time=42/5hrs)
  
  when all pipes are open,[including P3]
  6hrs -------1/2 part
  34/5 hrs---?? ==[17/30]
  
  therefore, (17/30) +[1/3] part is filled when supervisor returned.
  remaining part=1-[27/30]===1/10
  
  Which is 10% of tank.
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