# In a mixture, the ratio of milk and water is 5 ∶ 4. If 20 liters of mixture is taken out and 10 liters of water is added to the mixture, such that the

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In a mixture, the ratio of milk and water is 5 ∶ 4. If 20 liters of mixture is taken out and 10 liters of water is added to the mixture, such that the ratio of milk and water becomes 5 ∶ 6. What is the initial concentration of the mixture at the beginning?

1. 45 liters
2. 54 liters
3. 65 liters
4. 78 liters

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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.