Question
A vessel contains 72 litres of a milk-water mixture in
the ratio 5 : 4. Some quantity of the mixture is removed and replaced with pure water. After this operation, the ratio of milk to water becomes 5 : 7. How many litres of mixture were removed?Solution
ATQ, Initial milk = (5/9) × 72 = 40 litres Initial water = (4/9) × 72 = 32 litres Let x litres of mixture be removed. Milk removed = (40/72)x = 5x/9 Water removed = (32/72)x = 4x/9 After replacement with x litres of water: Milk left = 40 - 5x/9 Water = 32 - 4x/9 + x = 32 + 5x/9 Given new ratio = 5 : 7 (40 - 5x/9) / (32 + 5x/9) = 5 / 7 7(40 - 5x/9) = 5(32 + 5x/9) 280 - 35x/9 = 160 + 25x/9 120 = 60x/9 x = 18 Hence, the correct answer is 18 litres.
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