Question

The king took a glass filled with red wine and drank $\frac{1}{5}$ of its contents. When the king looked away, the court jester refilled the glass by adding water to the remaining red wine and then stirred it. The king drank $\frac{1}{4}$ of this liquid mixture. When the king looked away again, the court jester refilled the cup with more water and stirred it. The king then drank $\frac{1}{3}$ of this liquid mixture. When the king looked away for the third time, the court jester refilled the cup with more water. What percent of this final mixture is red wine?

• A. 50%
• B. 40%
• C. 30%
• D. 25%

Answer 1

The correct option is B

40%

Method 1:
Let the capacity of glass be 100 ml.

$\begin{array}{ccc}& RedWine& Water\\ Initial& 100& 0\\ Afterthefirstoperation& 80& 20\\ Afterthesecondoperation& 60& 40\\ Afterthethirdoperation& 40& 60\end{array}$

Method 2: Quantity of red wine left after 3 operations, when the glass originally contains $100\%$ wine from which $\frac{1}{5},\frac{1}{4}$ and $\frac{1}{3}$ of total wine are taken out each time and replaced is
$=(1-\frac{1}{5})(1-\frac{1}{4})(1-\frac{1}{3})=40\%$