In a mixture of wine and water is in the ratio of (5 : 3). If 16 liters of mixtures taken out and replaced with water, so that the ratio of wine and water becomes (3 : 5). Find the initial quantity of wine in the mixture.

Let initial quantities be wine = 5x, water = 3x (total 8x). When 16L is removed, wine removed = 16 × 5/8 = 10L, water removed = 6L. Remaining: wine = 5x - 10, water = 3x - 6. After adding 16L water: wine = 5x - 10, water = 3x + 10. New ratio is 3:5, so (5x-10)/(3x+10) = 3/5. Solving: 5(5x-10) = 3(3x+10), giving 16x = 80, so x = 5. Initial wine = 5 × 5 = 25 liters.