I: A container has 60 litres of a mixture of milk and water in the ratio 7 : 3. II: Some quantity of this mixture is removed and replaced by pure water. After this operation, the ratio of milk to water in the container becomes 7 : 5. How many litres of the mixture were removed (and replaced by water)?

ATQ, Initial mixture: 60 litres. Milk = (7/10) × 60 = 42 litres Water = (3/10) × 60 = 18 litres Let x litres of mixture be removed and replaced by x litres of pure water. When x litres of mixture are removed, milk and water removed are in the same 7:3 ratio: Milk removed = (7/10)x Water removed = (3/10)x After removal: Milk left = 42 − (7/10)x Water left = 18 − (3/10)x Then x litres of pure water added: Final milk = 42 − (7/10)x Final water = 18 − (3/10)x + x = 18 + (7/10)x Final ratio of milk : water = 7 : 5 Cross-multiply: 210 − (35/10)x = 126 + (49/10)x Move terms: 210 − 126 = (35/10)x + (49/10)x 84 = (84/10)x x = 84 × (10/84) = 10 So, 10 litres of mixture were removed.