Question

14 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 cask to that of the water is 81:175. How much wine did the cask originally hold?

• A. 42 L
• B. 70 L
• C. 81 L
• D. 56 L

Answer 1

The correct option is D 56 L

Quantity of wine left $=(1-x{)}^4=\frac{81}{256}$,where x is $\left(\frac{removedquantity}{originalquantity}\right)$ of wine We get $(1-x{)}^4=(3/4{)}^4\Rightarrow x=\frac{1}{4}$ Therefore, quantity of wine in the cask originally $=14\times 4=56$L