6 gallons of wine are drawn from a cask and replaced by 6 gallons of water. 6 gallons
of the mixture are drawn next and again replaced by 6 gallons of water. If the ratio of
wine to water in the cask is now 81:19, then what was the quantity of wine (in
gallons) in the cask at the beginning of the operation? (There was no water in the cask
at first)

• The ratio provided here is not correct.
• 10 years agoHelpfull: Yes(0) No(6)
• Let the initial capacity of cask= c
  After replacement the rest wine =
  c(1-6/c)^2
  And the quantity of water = c-c(1-6/c)^2
  Ratio of rest wine to water = 81:19
  (1-6/c)^2/{1-(1-6/c)^2} = 81:19
  19(1-6/c)^2 =81{1-(1-6/c)^2}
  100(1-6/c)^2=81
  (1-6/c)^2==81/100
  1-6/c==9/10
  6/c==1+9/10
  C==10*6/19
  C==60/19
  C==
• 9 years agoHelpfull: Yes(0) No(2)