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 330 gm mixture contains two components 'P' and 'Q' such that the quantity of 'P' is 20% more than that of 'Q'. After adding 'K' gm of 'P', the ratio of '...
- In a solution, the quantity of syrup is (x+10) L and water is 70 L. If 5 L syrup and 5 L water are added, the ratio of syrup and water becomes 7:5. Find x%...
- A man buys two varieties of sugar weighing 50 kg and 80 kg at ₹60 and ₹70 per kg respectively. He mixes the two varieties and sells the entire mixture at ₹...
- An alloy of copper and tin contains 60% of copper. If 10 kg of more tin is added to the alloy, the copper content gets reduced to 50%. Find the quantity of...
- A jar contains a mixture of mango juice and water in the ratio of 5:2. 84 litres of the mixture was taken out and 34 litres of water was added to it. If th...
- Container 'P' has 180 litres of a water–soda mixture in the ratio 3:2. 25% of this mixture is shifted to container 'Q', which already contains 19 litres of...
- A 480 ml mixture consists of milk and honey in a 5:7 ratio. If ‘p’ ml of both milk and honey is added to the mixture, the new ratio of milk to honey become...
- A mixture contains milk and water in the ratio of 3:1, respectively. If 280 ml of mixture is taken out and 90 ml of milk and 70 ml of water is added into t...
- In mixture 'X,' there are (4a + 20) liters of Juice and the remaining 20% consists of Soda.When mixture 'X' is combined with mixture 'Y,' which contains (a...
- 120 ml of mixture A containing milk and water in the ratio of 2:1 respectively is mixed with another 120 ml of mixture B containing milk and water in the r...
