A vessel contained a certain amount of milk and water. When 20 liters of water were added to it, the new mixture had 40% milk. When 10 liters of milk were further added to this new mixture, the final mixture had 50% milk. The ratio of water to milk in the original mixture was?
Show answer & explanation
Correct answer: B
Explanation
Given:
After adding 20 liters of water, the milk in the mixture = 40%
After adding 10 liters of milk, the milk in the mixture = 50%
Let the original mixture = x liters
And the milk in it = m liters
First case:
m / (x + 20) = 40/100
m = 0.4(x + 20)
m = 0.4x + 8 ......(1)
Second case:
(m + 10) / (x + 30) = 50/100
m + 10 = 0.5(x + 30)
m + 10 = 0.5x + 15
m = 0.5x + 5 ......(2)
Equating (1) and (2):
0.4x + 8 = 0.5x + 5
3 = 0.1x
x = 30
m = 0.4(30 + 20)= 20
Water = 30 − 20 = 10
Original ratio
Water : Milk = 10 : 20 = 1 : 2