A vessel contains 180 liters of a mixture of milk and water. 75% of the milk and 25% of the water are taken out separately. If 55% of the total mixture is removed from the vessel, find the initial quantity of milk.

ATQ, 75% of milk is removed. 25% of water is removed. Overall, 55% of the total mixture is removed. Now compare the overall removal percentage with milk and water removal percentages. Milk : Water = (Overall percentage − Water percentage) : (Milk percentage − Overall percentage) Milk : Water = (55 − 25) : (75 − 55) Milk : Water = 30 : 20 Now simplify the ratio. 30 : 20 = 3 : 2 So, the initial ratio of milk to water = 3 : 2 Total quantity of mixture = 180 liters. Total ratio parts = 3 + 2 = 5 parts. Milk quantity = 3 parts out of 5 parts. Initial milk quantity = (3/5) × 180 Initial milk quantity = 108 liters