Question
A vessel contains a mixture of milk and water in the ratio 3:1. When 12 litres of this mixture are taken out and replaced with pure water, the ratio of milk to water becomes 9:7. What is the initial quantity of the mixture in the vessel?
Solution
Let initial quantity = V litres. Milk = 3V/4, Water = V/4. When 12 L mixture is removed, milk and water removed are: Milk removed = (3/4)×12 = 9 L Water removed = (1/4)×12 = 3 L Remaining: Milk = 3V/4 − 9 Water = V/4 − 3 Then 12 L pure water is added: New water = V/4 − 3 + 12 = V/4 + 9 New ratio milk : water = 9 : 7: (3V/4 − 9) / (V/4 + 9) = 9 / 7 Cross-multiply: 7(3V/4 − 9) = 9(V/4 + 9) 21V/4 − 63 = 9V/4 + 81 21V/4 − 9V/4 = 81 + 63 12V/4 = 144 3V = 144 V = 48 litres.
More Mixture Questions
- A chemist prepared 50 grams of a medicine by mixing two ingredients P and 'Q, Rate of 'P' is ₹150 per 10 gm and that of 'Q' is ₹ 500 per 100 gm. 'P' and 'Q...
- A mixture consists of 50% water and 50% milk. 10 liters of the mixture is replaced with the same quantity of milk. If the final ratio of milk to water is 6...
- A vessel contains milk and water in the ratio 3:2. When 30 litres of water is added, the ratio becomes 3:4. Find the total quantity of the final solution.
- A vessel contains 300 litres of milk. Each time, x litres of the mixture are replaced with water, and this is done three times. If finally the vessel has 9...
- An alloy contains 50% iron, 30% zinc, and 20% aluminum. How much iron should be added to 30 kg of the alloy so that the new alloy contains 60% iron?
- If 50L of liquid containing 20% spirit is added with 15L of water, then what would be the percentage of spirit in the resulting mixture?
- A mixture of honey and lemon juice is in the ratio 4:1. If 40% of the mixture is replaced with lemon juice, what will be the new ratio of honey to lemon ju...
- A mixture of milk and water contains (x + 25) litres of milk, which is (x + 55) litres less than the quantity of water. If the total quantity of water in t...
- 136 litres of mixture ‘A’ (milk + water) contains 32 litres more water than milk. If 25% of mixture ‘A’, 70 litres of milk and 80 litres of water are added...
- 84 ml of mixture ‘P’ contains milk and water in the ratio of 7:5, respectively is mixed with 27 ml of mixture ‘Q’ containing milk and water in the ratio of...
