Question
In a container, the ratio of milk to water is 5:3. If
30% of the mixture is removed and replaced by the same quantity of milk and 24 ml of water is added afterwards, the new ratio of milk to water becomes 11:5. What was the volume of the mixture removed?Solution
ATQ,
Let the quantities of milk and water be 5x ml and 3x ml respectively Amount of mixture taken out = 0.3 × (5x + 3x) = 2.4x According to question, (0.7 × 5x + 2.4x)/(0.7 × 3x + 24) = 11/5 (3.5x + 2.4x)/(2.1x + 24) = 11/5 5.9x/(2.1x + 24) = 11/5 Cross-multiplying: 5 × 5.9x = 11 × (2.1x + 24) 29.5x = 23.1x + 264 6.4x = 264 x = 41.25 Amount of mixture taken out = 2.4 × 41.25 = 99 ml
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