Correct Answer - Option 3 : 65 liters
Given:
The initial ratio of milk to water is = 5 : 4
Calculation:
Let the quantity of milk and water be 5x and 4x respectively.
Initial concentration the of mixture = 5x + 4x = 9x
The initial quantity of milk = 5x
The initial quantity of water = 4x
According to the question,
[5x - {20 × (5/9)}]/[4x - {20 × (4/9)} + 10] = 5/6
⇒ (45x - 100)/(36x + 10) = 5/6
⇒ 270x - 600 = 180x + 50
⇒ 90x = 650
⇒ x = 650/90
x = 65/9
The initial concentration of the mixture = 9 × (65/9)
⇒ The initial concentration of the mixture = 65 liters
∴ The initial concentration of the mixture is 65 liters.