Mixtures and Alligation

Three containers A, B and C have milk and water solutions in them in the ratio 3 : 4 : 5. The ratio of milk to water in the respective containers are 2 : 1, 5 : 3 and 7 : 3. If the contents of container A are mixed with those of container B, and then half of the contents of the new mixture thus formed is mixed with the contents of container C, then which of the following gives the ratio of milk to water in the final mixture?

Three containers – A, B and C contain equal volumes of milk-and-water solution with the respective concentrations of milk in them being 60%, 70% and 𝑎%. When the contents in the three containers are completely mixed, the ratio of milk to water in it becomes 11 : 7. How many litres of the solution in container C should be mixed with 10 L of an 80% milk-and-water solution to obtain a 60% milk-and-water solution?

From a container having pure milk in it, 20% of the milk is first removed and replenished with an equal volume of water and solution A is formed. Then, 40% of solution A is removed and replenished with an equal volume of water and solution B is formed. Finally, 60% of solution B is removed and replenished with an equal volume of water and solution C is formed. Find the ratio of the amount of water in solution A to the amount of milk in solution C.

There are three mixtures – P, Q and R, with each having a mixture of liquids A and B only. The ratios of liquids A and B in mixtures P, Q and R are 5 : 3, 1 : 1 and 5 : 7, respectively. If half of P is mixed with Q, then the ratio of A and B in the mixture becomes 11 : 9, whereas, if half of R is mixed with Q, then the ratio of A and B in the mixture becomes 11 : 13. Find the ratio of the quantity of A in P to the quantity of B in R.

In a bowl containing 60 ml orange juice, 40 ml of water is poured. Thereafter, 100 ml of apple juice is poured to make a fruit punch. Madhu drinks 50 ml of this fruit punch and comments that the proportion of orange juice needs to be higher for better taste. How much orange juice should be poured into the fruit punch that remained, in order to bring up the level of orange juice to 50 percentage?

In a scientific laboratory, a researcher has a 25-litre solution containing 80% water. To meet specific experimental requirements, the researcher needs to adjust the solution to precisely 60% water concentration. How much water in millilitres (ml) should the researcher remove from the solution to achieve this desired concentration?

A mixture in a container consisted of orange juice and water in unknown quantities. When 3 liters of water were added to the mixture, the resulting solution contained 60% orange juice. Later, 9 liters of orange juice were poured into this new solution, and the orange juice content increased to 75%. What was the original ratio of water to orange juice in the container?

A mixture X is made by removing a certain fraction of orange juice from a jar filled with pure orange juice and replacing it with the same amount of water. The same fraction of mixture X is then removed and replaced with water to form a new mixture Y. If the ratio of orange juice to water in mixture Y is 9 : 16, what is the ratio of water in mixture X to that in mixture Y?

The concentration of salt in a solution is defined as the number of grams of salt per 100 cc of solution, expressed as a percentage. Two 1200 cc containers are filled with salt solutions having concentrations of 45% and 25%, respectively. A portion of the solution from the first container is removed and replaced with an equal volume from the second container. If the resulting concentration in the first container becomes 33%, what is the volume, in cc, of solution left in the second container?

At Sunrise Café, a large tank held a special tropical drink made by mixing pineapple juice and soda in unknown proportions. Later, 7 litres of soda were added to the mixture, resulting in a blend that contained 60% pineapple juice. Afterwards, 21 litres of pineapple juice were added, increasing the pineapple juice concentration to 75%. What was the original amount of mixture in the tank?