4 gallons are drawn out of a cask containing special liquid and is then filled with water. Now 6 gallons of mixture is drawn from the cask and it is again filled with water. If the quantity of special liquid now in the cask be to the quantity of water in it as 1:2, how much does the cask hold?

Dear Student ,
Please find below the solution to the asked query :

Let the cask hold x gallons of special liquid .Now , 4 gallons of special liquid are taken out .Quantity of special liquid present = x-4 gallonsAmount of water present =4 gallons .Ratio of special liquid to water in mixture=x-44Now , 6 gallons of mixture is drawn out .So , Special liquid drawn out =x-4x×6=6x-4x gallonsWater drawn out =4x×6=24x gallonsAmount of special liquid present =x-4-6x-4x=xx-4-6x-4x=x2-4x-6x+24x=x2-10x+24x gallonsAmount of water present =4-24x=4x-24x gallons .A.T.Qx2-10x+24x4x-24x=12x2-10x+244x-24=122x2-20x+48=4x-242x2-24x+72=0x2-12x+36=0x2-6x-6x+36=0xx-6-6x-6=0x-6x-6=0So , x=6Hence Cask can hold 6 litres of water .
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