Let's assume we start with 100 units of the initial milk sample. Since it has 50% water, there are 50 units of water and 50 units of milk. When 1/3rd of this sample is taken (which is 100/3 units), it contains (1/3) * 50 units of water and (1/3) * 50 units of milk. This portion is then mixed with an equal amount of pure milk. Let's say the amount taken was 'x' units. So, x units of the initial mixture (containing x/2 water and x/2 milk) are mixed with x units of pure milk. The total volume of the new mixture is 2x. The total amount of water in the new mixture is x/2. The percentage of water in the new mixture is (water / total volume) * 100 = (x/2 / 2x) * 100 = (1/4) * 100 = 25%.