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A mixture contains milk and water in the ratio 4 : 5. If 30 liters of water is added to the mixture, the ratio becomes 1 : 2. Find the initial quantity of milk in the mixture?
1. 20 liters
2. 40 liters
3. 50 liters
4. 60 liters

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Correct Answer - Option 2 : 40 liters

Given:

Initial ratio of milk and water in the given mixture = 4 : 5

Adding 30 liters of water in the mixture then ratio of milk and water = 1 : 2

Calculation:

Let the initial amount of mixture be p liters

Initial amount of milk in the mixture = 4/9 × p liters

⇒ 4p/9 liters

Initial amount of water in the mixture = 5/9 × p liters

⇒ 5p/9 liters

Now, 30 liters of water is added

Final amount of water = 30 + 5p/9 liters

Ratio of milk and water after adding 30 liters of water = (4p/9)/(30 + 5p/9)

⇒ (4p/9)/(30 + 5p/9) = 1/2

⇒ 2 × (4p/9) = 30 + 5p/9

⇒ 8p/9 = (270 + 5p)/9

⇒ 8p = 270 + 5p

⇒ 3p = 270

⇒ p = 270/3 

⇒ p = 90 liters

Initial amount of milk in the given mixture = 4/9 × 90 liters

⇒ 40 liters

∴ The initial quantity of milk in the mixture is 40 liters

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