2 liters of a liquid having milk and water in the ratio 3: 2 is mixed with 3 liters of a liquid having milk and water in the ratio 2 : 3. Find the ratio of milk to water in the new mixture.

Solution

Let the common ratios be x and y in respective cases. In the mixture of 2 liters, Quantity of milk = 2 × 3x/5x = 1.2 liters Quantity of water = (2 - 1.2) = 0.8 liters In the mixture of 3 liters, Quantity of milk = 3 × 2y/5y = 1.2 liters Quantity of water = (3 - 1.2) = 1.8 liters Hence in the new mixture, Quantity of milk = 1.2 + 1.2 = 2.4 liters Quantity of water = 0.8 + 1.8 = 2.6 liters The ratio of milk to water in the new mixture = 2.4: 2.6 = 12: 13 ∴ The ratio of milk to water in the new mixture is 12: 13.