A container contains a mixture of water and milk in the ratio of 7 : 5. When 9 litres of mixture is drawn out and the remaining part of the container is filled with 9 litres milk, the ratio of water to milk becomes 7 : 9. How many litres of water does the container have initially? (in litres)

Initial water:milk = 7:5. Let initial quantity be 12x (water = 7x, milk = 5x). When 9 litres drawn, ratio remains 7:5, so water drawn = (7/12)*9 = 5.25 L, milk drawn = (3/12)*9 = 3.75 L. Remaining: water = 7x - 5.25, milk = 5x - 3.75. After adding 9 L milk: new water = 7x - 5.25, new milk = 5x - 3.75 + 9 = 5x + 5.25. New ratio (7x - 5.25):(5x + 5.25) = 7:9. Cross-multiplying: 9(7x - 5.25) = 7(5x + 5.25). 63x - 47.25 = 35x + 36.75. 28x = 84. x = 3. Initial water = 7x = 21 litres.