A 108 liters of milk and water in the ratio 5 : 7. What liters of the mixture should be taken out and replaced with pure milk so that the final mixture contains milk and water in equal proportions?

Initial mixture: 108L with milk:water = 5:7, so milk = 45L, water = 63L. Let x liters be removed and replaced with milk. After removal, remaining milk = 45(1-x/108), water = 63(1-x/108). Adding x liters milk: new milk = 45(1-x/108)+x, water = 63(1-x/108). For equal quantities: 45(1-x/108)+x = 63(1-x/108). Solving: 45-45x/108+x = 63-63x/108, giving x = 18×63/108 = 15.4 liters.