A container is filled with a mixture of milk and water in the ratio 7 : 3. Some quantity of the mixture is removed and replaced with pure water. After this operation, the ratio of milk to water becomes 1 : 1. What fraction of the original mixture was removed and replaced?
2/7
Removing a fraction f of the mixture and replacing it with water reduces the milk by the same fraction, while the total quantity stays the same.
Milk initially = 7/10 of the mixture
Milk after replacement = (7/10)(1 – f)
For ratio 1 : 1, milk = 1/2 of the mixture
(7/10)(1 – f) = 1/2
1 – f = 5/7
f = 2/7
Check: Take 70 L (49 L milk, 21 L water). Remove 20 L: milk = 49 – 14 = 35 L, water = 21 – 6 + 20 = 35 L, so the ratio is 1 : 1.
Hence, 2/7.
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