A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank (in litres) is

• 5760 litres
  
  Let capacity of the tank be x litres.
  Inlet pipe can fill 4*60=240 litres in 1 hr.
  Leakage per hour = x/6 litres.
  Given when tank is full and inlet is opened, tank is empty in 8 hrs.
  => Quantity (Full tank + Filling in 8 hrs) = Quantity (Leakage in 8 hrs)
  => x + 240*8 = 8*(x/6)
  => 6x + 11520 = 8x
  => x = 5760
• 7 years agoHelpfull: Yes(15) No(1)
• Work done by the inlet in 1 hour = 1/6 − 1/8 = 1/24
  Work done by inlet in 1 min= 1/24 ∗ 1/60 = 1/1440
  Volume of 1/1440 part = 4 liters
  Volume of whole = (1440 * 4) litres = 5760 litres.
• 7 years agoHelpfull: Yes(5) No(0)
• when the tank is full and the inlet pipe is opened water is leaked out of the tank as,
  1/4-1/6=1/24
  therefore in every 1hour 24litres of water is leaked out.
  the rate of water is 4litres a minute
  therefore, capacity of tank is=24*60*4=5760litres
• 7 years agoHelpfull: Yes(3) No(0)
• 5760 litre is the correct answer
• 7 years agoHelpfull: Yes(1) No(0)
• a part empty the tank =1//8-1/6=2/48=>1/24 inhour
  in min( 24*60=1440)
  inlet pipe fills 4 lit a min
  capacity can hold the tank=4*1440=5760lit
• 6 years agoHelpfull: Yes(1) No(0)
• ans :1440 L
• 7 years agoHelpfull: Yes(0) No(3)
• ans is 4320 litrs
  
  let the discharge capacity of the tank be L/360 lit per min
  
  also the filling capacity of the tank be given as 4 lit per min
  
  after 6 hrs due to filling the tank cant get emptied then water in the tank = 4*(6*60min)= 1440 lit
  
  also after 2 hrs the tank is filled = 4*(2*60)=480 lit
  
  then water in tank after 8hrs =1440+480=1920 lit
  
  if only discharge tap is opened then the tank empties in 6 hrs
  
  if both filling and discharge happens simultaneously then this 1920 lit get emptied in 2 hrs to make tank fully empty
  
  hence cumulative discharge capacity = 1920/(2*60) = 16 lit/min
  
  above capacity is cumulative i.e considering filling and discharge at the same time (as in relative velocity
  approach)
  
  actual discharge = 16-4 = 12 lit/min
  
  hence tank capacity = 12 lit/min * 360min = 4320 litre
• 7 years agoHelpfull: Yes(0) No(6)
• time taken to fill the tank by inlet=-(1/8)+(1/6)
  total volume=4/(1/60)*24=5760
• 6 years agoHelpfull: Yes(0) No(0)
• outlet can empty it in 6 hrs;
  inlet can fill 240 lts in 1 hr:
  when the inlet and oulet both are open then it is taking 8 hrs(when the tank is already full);
  let x be the full tank capacity ?
  x+(240*8)=this ltrs of water is finishes by 8 hours.(we know that it can empty in 6 hours so now we ll find for 8 hrs)=
  (x/6)*8+=x+(240*8)=ans
• 6 years agoHelpfull: Yes(0) No(0)
• let L be the leak and I be inlet
  suppose capacity be 24
  now L->-6 hours hence efficiency will be -4l
  4l/min =240l/hour
  then efficiency after inlet is open =24/-8=-3l(both are open at present)
  efficiency of inlet will be -3+4=1l/hour
  this 1 l corresponds to 240l /hour thus -3l will make 720l/hour
  as tank is completely empty in 8 hours so in 8 hours 8*720 =5760l
  note :negative sign is for emptying.
• 5 years agoHelpfull: Yes(0) No(0)
• A-Inlet
  B-leakage
  
  take there 1hr efficiency so,
  A- 4*60=240L
  B- x/6 ( x is the capacity of tank in Ltrs)
  Now as given
  it takes 8 hours to empty the tank when both of them are opened so,
  
  X/(X/6 - 240) = 8
  X= 5760ltrs
• 5 years agoHelpfull: Yes(0) No(0)