Numerical answer
A vessel contains 60 litres of a milk–water mixture in the ratio 7 : 3. Twenty litres of the mixture are drawn off and replaced with water. How many litres of pure milk must now be added so that the ratio of milk to water becomes 3 : 2?
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Answer: 20
Initially: milk = 42 L, water = 18 L.
Drawing off 20 L (one-third of the mixture) removes one-third of each: remaining milk = 28 L, water = 12 L. Adding 20 L water makes water = 32 L. Milk stays 28 L.
Let m litres of milk be added: (28 + m) / 32 = 3/2 → 28 + m = 48 → m = 20.
Tip: When a mixture is drawn off, each component falls in the same proportion; only the replacing liquid changes the ratio. The water quantity (32 L) is fixed from then on, so work from it.
Drawing off 20 L (one-third of the mixture) removes one-third of each: remaining milk = 28 L, water = 12 L. Adding 20 L water makes water = 32 L. Milk stays 28 L.
Let m litres of milk be added: (28 + m) / 32 = 3/2 → 28 + m = 48 → m = 20.
Tip: When a mixture is drawn off, each component falls in the same proportion; only the replacing liquid changes the ratio. The water quantity (32 L) is fixed from then on, so work from it.
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