A vessel is filled to its capacity with pure milk. Ten litres are withdrawn from it and replaced by water. This procedure is repeated again. The vessel now has 32 litres of milk. Find the capacity of the vessel (in litres).

• Assume that a container contains x of liquid from which y units are taken out and replaced
  
  by water. After n operations, the quantity of pure liquid=x(1−y/x)^n
  quantity of pure liquid is 32 lit
  i,e 32=x(1-10/x)^2
  =>(x(x-10)^2)/x^2=32
  =>(x-10)^2=32x
  x^2+100-20x=32x
  =>x^2+100-52x=0
  by factorization
  (x-2)(x-50)=0
  therefore x=50 or 2....since 2 is not possible practically bcaz present milk level is 32
  x=50....
• 9 years agoHelpfull: Yes(18) No(0)
• let milk is 100 liter
  then it is replaced by 10 liter of water so the mix will be 90 lit milk and 10 lit water
  again it is replaced by 10 lit of water so
  mix will be
  81 lit milk + 19 lit water
  so for 81 lit of milk in the mix the total amount is 100 lit intially so
  for 32 lit there will be (100/81) *32= 39.5 lit ans
• 10 years agoHelpfull: Yes(7) No(7)
• let the capacity of the vassel be xlitres.
  then
  x(1-10/x)^2=32
  solve x from here.
• 10 years agoHelpfull: Yes(3) No(7)
• total capacity= 32+20=52
• 10 years agoHelpfull: Yes(3) No(4)
• x(x-10/x)^2 = 32,
  x=2 & x=50,
  2 cannot be possible so the correct answer is 50.
• 9 years agoHelpfull: Yes(3) No(0)
• 50ltr is the capacity of vessel
• 10 years agoHelpfull: Yes(2) No(1)
• capacity of vessel is 32 litre.
• 10 years agoHelpfull: Yes(1) No(2)
• plz solve this question....
• 10 years agoHelpfull: Yes(0) No(2)
• 39.5 lt. is the answer...
• 10 years agoHelpfull: Yes(0) No(4)
• hai anand may i knw how it is 81 lit of milk
• 10 years agoHelpfull: Yes(0) No(1)
• 37 litres
  
• 9 years agoHelpfull: Yes(0) No(2)