A vessel contains a mixture of milk and water in the ratio of 5:3 respectively. How much of the mixture…
The correct choice is: “1/5” Milk is 5/8 of the mixture. Removing a fraction x of the mixture removes the same fraction of the milk, and the replacement is pure water, so…
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A vessel contains a mixture of milk and water in the ratio of 5:3 respectively. How much of the mixture must be siphoned off and replaced with water, so that the mixture may be half milk and half water?
Answer and explanation
Correct answer D
The correct choice is: “1/5”
Milk is 5/8 of the mixture. Removing a fraction x of the mixture removes the same fraction of the milk, and the replacement is pure water, so the milk left is (5/8)(1 − x) of the vessel.
We need milk = 1/2: (5/8)(1 − x) = 1/2, so 1 − x = 4/5 and x = 1/5.
Check with 8 litres: 5 L milk, 3 L water. Remove 1.6 L (1/5): milk falls to 4 L and water to 2.4 L; adding 1.6 L of water gives 4 L milk and 4 L water.
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