Discussion
Rajesh has a container which has a mixture of wine and water in it. Wine and water are in the ratio 4:1. Rajesh spills some of the mixture by accident. He then replaces the spilled amount with water of same quantity. But now the wine to water ratio became 3:2. How much water did Rajesh add?
Answer: C
Take the container as 5 units: 4 of wine and 1 of water. Spilling a fraction \( f \) removes that fraction of the wine as well, and the water poured back keeps the total at 5.
\[ \text{wine left} = 4(1 - f) \]
The new ratio 3 : 2 means the wine is now 3 of the 5 units:
\[ 4(1 - f) = 3 \quad\Longrightarrow\quad 1 - f = \frac{3}{4} \quad\Longrightarrow\quad f = \frac{1}{4} \]
So a quarter of the mixture was replaced by water. Spilling removes wine and water in their existing proportion, which is what makes the wine shrink by the factor \( 1-f \).
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