Questions :
A 108-liter mixture contains milk and water in the ratio 7 : 2. If 27 liters of this mixture are removed and replaced with 9 liters of pure milk, what is the new ratio of milk to water in the mixture?
Options :
- 2 : 1
- 4 : 1
- 7 : 1
- 9 : 2
correct answer : b)
Explanation :
Milk in the mixture = (7/9) × 108 = 84 liters
Water in the mixture = (2/9) × 108 = 24 liters
Milk removed = (7/9) × 27 = 21 liters
Water removed = (2/9) × 27 = 6 liters
Remaining milk = 84 − 21 = 63 liters
Remaining water = 24 − 6 = 18 liters
After adding 9 liters of pure milk:
New milk quantity = 63 + 9 = 72 liters
Water quantity = 18 liters
New ratio of milk to water = 72 : 18 = 4 : 1
Therefore, the new ratio of milk to water is 4 : 1.
Hence, the correct answer is option (b) 4 : 1. The options 2 : 1, 7 : 1, and 9 : 2 are incorrect because they do not match the ratio obtained after removing part of the mixture and adding pure milk.