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PALLAVI

· started a discussion

· 1 Months ago

Need Explanation (Question: 39162.0 )

Help?

Question:
8 liters 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 cask to that of the water is 16:65. How much wine did the cask hold originally?
Options:
A) 18 liters.
B) 24 liters.
C) 32 liters.
D) 42 liters.
E) None of these.
Solution:

Let the quantity of the wine in the cask originally be x liters

then the quantity of wine left in cask after 4 operations 

 \(\left [ \begin{matrix}x\left ( 1-\cfrac {8}{x} \right )^4\end{matrix} \right ]\)   litaer



kanhaiya jha

· commented

· 1 Months ago

Let the quantity of the wine in the cask originally be x liters then the quantity of wine left in cask after 4 operations

=[x(1−8/x)^4] litre

[x(1−8/x)^4] = 16/81

solve it,

x=24

The ratio of the quantity of wine now left in cask to that of the water is 16:65. initially, it will be 16:81.
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