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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 liters2. 40 liters3. 50 liters4. 60 liters |
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Answer» 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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