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20 litres of a mixture contains milk and water in the ratio 5 : 3. If 4 litres of this mixture be replaced by 4 litres of milk, then the ratio of milk to water in the new mixture would beA 2 : 1 B 7 : 3 C 8 : 3 D 4 : 3

Question

20 litres of a mixture contains milk and water in the ratio 5 : 3. If 4 litres of this mixture be replaced by 4 litres of milk, then the ratio of milk to water in the new mixture would beA 2 : 1 B 7 : 3 C 8 : 3 D 4 : 3

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Solution

The initial mixture contains 20 litres of liquid, with milk and water in the ratio of 5:3. This means that the mixture contains 12.5 litres of milk and 7.5 litres of water (because 5/820 = 12.5 and 3/820 = 7.5).

If 4 litres of this mixture is replaced by milk, the amount of milk becomes 12.5 - 45/8 + 4 = 14.5 litres (because 4 litres of the mixture contains 45/8 = 2.5 litres of milk, and this is replaced by 4 litres of milk). The amount of water becomes 7.5 - 43/8 = 6.5 litres (because 4 litres of the mixture contains 43/8 = 1.5 litres of water, and this is removed).

Therefore, the ratio of milk to water in the new mixture is 14.5 : 6.5, which simplifies to approximately 2.23 : 1. This is closest to the ratio 2 : 1, so the answer is A.

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