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