Nine litres are drawn from a cask full of wine and it is then filled with water. Nine litres of the mixture are drawn and the cask is again filled with water. The quantity of wine now left in the cask is to that of the water in it as 16:9. How much does the cask hold?
A. 36 litres
B. 27 litres
C. 45 litres
D. 63 litres
E. 54 litres

• By applying the formula (x(1-(9/x))^2) We can also say x(1-(9/x))^2 : x : : 16 : 25 And by solving this eqn. We get the value of x=45. So, the option is C)45
• 8 years agoHelpfull: Yes(3) No(2)
• we have a formula
  if a container contains x units 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)
  
  From this assume intially x units are there after
  two times replacement with 9 litres
  we get
  x(1-(9/x)^2)
  so the ratio becomes
  x(1-(9/x)^2)/x =16/9
  by solving that
  we get x=27
  ans :option b
• 9 years agoHelpfull: Yes(1) No(5)
• Let there be x litres in the cask.
  
  After n operations,
  
  Water left in vessel / Original quantity = (1 – 9/x)n
  
  16/25 = (1 – 9/x)2
  
  4/5 = 1 – 9/x
  
  ∴ x = 45 litres.
• 4 years agoHelpfull: Yes(1) No(0)