From a cask full of alcohol 4 litres of alcohol is drawn and the cask is filled with water. again four litres of the mixture is drawn and the cask is again filled with water. the quantity of alcohol now left in the cask to that of water in it is 36:13.find the capacity of the cask.
Answers
Let volume of the container = xx gallons Initially, container is full of wine and therefore quantity of wine = xx gallons 4 gallons of wine is taken out and 4 gallons of water is added Quantity of wine in the container now = (x−4)(x−4) gallons 4 gallons of mixture is taken out and 4 gallons of water is added to the mixture Quantity of wine removed = 4(x−4)x4(x−4)x Quantity of wine in the container now =(x−4)−4(x−4)x=x(x−4)−4(x−4)x=x2−4x−4x+16x=x2−8x+16x=(x−4)−4(x−4)x=x(x−4)−4(x−4)x=x2−4x−4x+16x=x2−8x+16x Total quantity will remain same as xxgallons Now we have (x2−8x+16x)x=3649x2−8x+16x2=364949x2−392x+784=36x213x2−392x+784=0 x=392±√(−392)2−4×13×7842×13=392±√153664−4076826=392±√11289626=392±33626=28 or 2.2(x2−8x+16x)x=3649x2−8x+16x2=364949x2−392x+784=36x213x2−392x+784=0 x=392±(−392)2−4×13×7842×13=392±153664−4076826=392±11289626=392±33626=28 or 2.2 xx must be greater than 4. So we take xx = 28.