A vessel contains a mixture of milk and water in the ratio 4:1. A certain quantity of this mixture is removed and replaced with an equal quantity of water. After this process, the ratio of milk to water in the new mixture becomes 2:3. What percentage of the original mixture was removed and replaced with water?
Show answer & explanation
Correct answer: A
Explanation
Given:
Initial Ratio (Milk : Water) = 4 : 1
Final Ratio (Milk : Water) = 2 : 3
According to the formula:
After removing a portion of the mixture and adding water once:
Remaining fraction of milk = (New milk ratio / Old milk ratio)
Old milk fraction = 4 / (4 + 1) = 4/5
New milk fraction = 2 / (2 + 3) = 2/5
Remaining fraction = (2/5) ÷ (4/5) = 1/2
Fraction removed = 1 − 1/2 = 1/2
Percentage = (1/2) × 100 = 50%