8 litres are drawn from a cask full of wine a | vedclass

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(B) Let the original quantity of wine be $x$ litres.After $1$ operation,the quantity of wine left is $x(1 - 8/x)$.After $4$ operations (the initial on

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$24$

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(B) Let the original quantity of wine be $x$ litres.After $1$ operation,the quantity of wine left is $x(1 - 8/x)$.After $4$ operations (the initial one plus three more),the quantity of wine left is $x(1 - 8/x)^4$.The total volume of the mixture remains $x$ litres.The ratio of wine to water is $16:65$,so the ratio of wine to total mixture is $16:(16+65) = 16:81$.Thus,$\frac{x(1 - 8/x)^4}{x} = \frac{16}{81}$.$(1 - 8/x)^4 = (2/3)^4$.Taking the fourth root on both sides,$1 - 8/x = 2/3$.$8/x = 1 - 2/3 = 1/3$.$x = 8 	imes 3 = 24$ litres.

$8$ litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in the cask to that of water is $16:65$. How much wine did the cask hold originally? (in litres)

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