A tank contains a mixture of milk and water in the ratio 7 : 5. When 24 litres of this mixture are drawn out and replaced by pure water, the ratio of milk to water becomes 7 : 11. What was the initial quantity of the mixture in the tank?

Solution

Let initial quantity of mixture = V litres. Milk = 7V/12, Water = 5V/12. When 24 L mixture is removed, milk and water removed are in 7:5: Milk removed = (7/12) × 24 = 14 L Water removed = (5/12) × 24 = 10 L Remaining: Milk = 7V/12 − 14 Water = 5V/12 − 10 Then 24 L of pure water is added: New water = 5V/12 − 10 + 24 = 5V/12 + 14 New ratio milk : water = 7 : 11: (7V/12 − 14) / (5V/12 + 14) = 7 / 11 Cross-multiply: 11(7V/12 − 14) = 7(5V/12 + 14) (77V/12 − 154) = (35V/12 + 98) 77V/12 − 35V/12 = 98 + 154 42V/12 = 252 (7V/2) = 252 V = 252 × 2 / 7 = 72 So initial quantity = 72 litres.