A vessel have 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 litre of mixture is replaced with pure milk so that the container will have milk and water in equal proportion. Find the value of x?

Initial mixture: milk = (2/5) × 60 = 24 L, water = (3/5) × 60 = 36 L. After removing x litres: milk = 24(1 - x/60), water = 36(1 - x/60). Adding x litres of milk: new milk = 24(1 - x/60) + x = 24 + x - 24x/60 = 24 + 36x/60. New water = 36(1 - x/60) = 36 - 36x/60. Setting equal: 24 + 36x/60 = 36 - 36x/60 gives 72x/60 = 12, so x = 10.