A 7:5 mixture of milk and water is contained in a vessel. The ratio of milk to water becomes 7:9, when 9 liters of the mixture is removed and the same volume of water is added to the vessel. How much milk was there in the vessel at the beginning?
Show answer & explanation
Correct answer: C
Explanation
Given:
Milk : Water = 7 : 5
Mixture drawn off = 9 liters
New ratio = 7 : 9
Formula:
Milk and water are drawn off in the same ratio from the drawn off mixture.
Assume total mixture = 12x
Milk = 7x
Water = 5x
Milk drawn off = (7/12) × 9 = 5.25
Water drawn off = (5/12) × 9 = 3.75
Milk remaining = 7x − 5.25
Water remaining = 5x − 3.75
9 liters of water added
New water = 5x − 3.75 + 9 = 5x + 5.25
New ratio
(7x − 5.25) / (5x + 5.25) = 7 / 9
9(7x − 5.25) = 7(5x + 5.25) 5.25)
63x − 47.25 = 35x + 36.75
28x = 84
x = 3
Initial milk = 7x = 21
Initial milk = 21 liters