Question
A 40-litre mixture of milk and water has milk and water
in the ratio 3 : 1. 'x' litres of this mixture are removed and replaced with pure water. After this operation, the ratio of milk to water becomes 3 : 2. Find the value of x.Solution
Initial milk = 3/4 × 40 = 30 L Initial water = 1/4 × 40 = 10 L. When x litres of mixture are removed: Milk removed = (3/4)x Water removed = (1/4)x. After removal: Milk = 30 − 3x/4 Water = 10 − x/4. Then x litres of pure water are added: Final milk = 30 − 3x/4 Final water = 10 − x/4 + x = 10 + 3x/4. Given final ratio milk : water = 3 : 2 (30 − 3x/4) / (10 + 3x/4) = 3/2 Cross-multiply: 2(30 − 3x/4) = 3(10 + 3x/4) 60 − 3x/2 = 30 + 9x/4 Multiply both sides by 4: 240 − 6x = 120 + 9x 120 = 15x x = 8. Answer: x = 8 litres.
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