A vessel contains 60 litres of a milk-water mixture in the ratio 2:1. From this mixture, 10 litres are taken out and then replaced with 10 litres of pure water. After this operation, what will be the new ratio of milk to water in the vessel?
Show answer & explanation
Correct answer: B
Explanation
Given:
Total mixture = 60 liters
Milk : Water = 2 : 1
Mixture taken out = 10 liters
Pure water added = 10 liters
Total ratio = 2 + 1 = 3
Milk = (2/3) × 60 = 40 liters
Water = (1/3) × 60 = 20 liters
Of the 10 liters taken out
Milk = (2/3) × 10 = 20/3 liters
Water = (1/3) × 10 = 10/3 liters
Remaining milk = 40 − 20/3 = 100/3 liters
Remaining water = 20 − 10/3 = 50/3 liters
After adding 10 liters of pure water
Water = 50/3 + 10 = 80/3 liters
New ratio = Milk : Water
= (100/3) : (80/3)
= 100 : 80
= 5 : 4
Milk : Water = 5 : 4