A Mixture of milk and water in a vessel has milk and water in the ratio 3: 1. 64 liters of mixture is taken out and replaced completely with milk such that the ratio of milk and water now becomes 4: 1. What will be the quantity of water left in the mixture if 20 liters of mixture is again taken out from the vessel?

Let total volume = T. Initial milk:water = 3:1, so milk = 3T/4, water = T/4. Removing 64L removes 48L milk and 16L water. Adding 64L milk gives milk = 3T/4 + 16, water = T/4 - 16. New ratio (3T/4 + 16)/(T/4 - 16) = 4/1. Solving: T = 320L. Water after first operation = 320/4 - 16 = 64L. After removing 20L (which contains 20 * 1/5 = 4L water), remaining water = 64 - 4 = 60L.