A vessel contains 180 liters mixture of milk to water is 5 : 1. 40% of the mixture taken out and x liters of pure milk added in the mixture. If the ratio of milk to water in resultant mixture becomes 7 :1, then find value of x?

Explanation

Information Given: Total mixture = 180 liters Ratio of milk to water = 5 : 1 40% of mixture is taken out x liters of pure milk is added Final ratio of milk to water = 7 : 1 Concept/Formula Used: Milk quantity = (ratio part / total parts) × total mixture Water quantity = (ratio part / total parts) × total mixture Mixture taken out contains milk and water in same ratio Remaining milk and water after removal = initial amount - removed amount After adding pure milk, milk increases but water remains same Final ratio = milk / water Explanation: Total parts = 5 + 1 = 6 Milk initially = (5/6) × 180 = 150 liters Water initially = (1/6) × 180 = 30 liters Mixture taken out = 40% of 180 = 72 liters Milk removed = (5/6) × 72 = 60 liters Water removed = (1/6) × 72 = 12 liters Remaining milk = 150 – 60 = 90 liters Remaining water = 30 – 12 = 18 liters After adding x liters of pure milk, milk = 90 + x liters Water remains 18 liters Final ratio milk to water = (90 + x) / 18 = 7 / 1 Cross multiply: 90 + x = 7 × 18 = 126 x = 126 – 90 = 36 liters