A dairy shop has a container filled with \(30\) L of pure milk. First, \(3\) L of milk is removed and replaced with \(3\) L of water. The same process is then repeated \(2\) more times. What is the ratio of milk to water in the container at the end?

A chemistry lab has a solution containing ethanol, methanol, and water in the ratio \(1:4:15\) by volume. The composition of the solution is changed by adding ethanol, methanol, and water such that the amount of ethanol per unit volume of methanol increases by \(15\) percentage points, and the amount of water per unit volume of ethanol decreases by two-thirds. If the volume of the altered solution is \(340\) cubic units, what is the volume of methanol in the altered solution?

A dairy has two vessels of milk with different prices per litre. The first vessel contains \(220\) litres and the second vessel contains \(180\) litres. Equal quantities of milk are removed simultaneously from both vessels. The milk removed from the first vessel is poured into the second vessel, and the milk removed from the second vessel is poured into the first vessel. After this exchange, the price per litre of milk in both vessels becomes the same. How many litres of milk were poured from one vessel into the other?

Solution A contains equal quantities of alcohol and water. It is heated until \(50%\) of the water in Solution A evaporates. Then Solution B, whose volume is equal to the remaining volume of water in Solution A, is added to Solution A. In the resulting solution, the volume of alcohol is \(12\) litres. If Solution B contains alcohol and water in the ratio \(2:3\), how many more litres of water should be added to make the water concentration \(50%\)?

A metal trader has one alloy made of copper and aluminium, containing \(40%\) copper. Another alloy is made of copper and zinc, with copper and zinc in the ratio \(2:7\). These two alloys are mixed such that in the final alloy, the quantity of aluminium is more than the quantity of zinc. If copper forms \(x%\) of the final alloy, what is the approximate range of values that \(x\) can take?

A container has milk and water in the ratio \(2:3\). First, \(15\) litres of water are added to the container, and then \(15\) litres of the well-mixed solution are drawn out. This operation is performed a total of \(3\) times. If the final ratio of milk to water is \(25:231\), find the volume of the original solution.

In a chemistry lab, \(2\) units of an \(a%\) alcohol solution are mixed with \(3\) units of a \(b%\) alcohol solution to obtain a \(40%\) alcohol solution. If \(a > b\) and both \(a\) and \(b\) are integers, how many integer values can \(a\) take?

A container has a mixture of milk and water in the ratio \(2:3\). First, \(15\) litres of the mixture are removed and replaced with \(15\) litres of pure milk. The same operation is performed one more time. After this, the ratio of milk to water becomes \(7:5\). What was the volume of the original mixture?

Two copper alloys in a metal workshop have different percentages of copper. The first alloy weighs \(6\) kg and the second alloy weighs \(12\) kg. A piece of equal weight is removed from each alloy. The piece removed from the first alloy is mixed with the second alloy, and the piece removed from the second alloy is mixed with the first alloy. After this exchange, the two new alloys have the same percentage of copper. What was the weight of each piece removed?

Two tanks in an oil warehouse contain edible oil of different prices per litre. Tank A contains \(140\) litres and Tank B contains \(60\) litres. Equal quantities of oil are drawn from both tanks at the same time. The oil drawn from Tank A is poured into Tank B, and the oil drawn from Tank B is poured into Tank A. After this exchange, the price per litre of oil becomes the same in both tanks. What equal quantity of oil was drawn from each tank?

A metal workshop prepares an alloy using copper, iron, and zinc priced at Rs. \(32\), Rs. \(17\), and Rs. \(36\) per kg respectively. These three metals are mixed in the ratio \(x:y:z\), where \(x\), \(y\), and \(z\) are in geometric progression and \(x < y < z\). If the price of the alloy is Rs. \(30\) per kg, what would be the price per kg of the alloy if the same metals are mixed in the ratio \(x:z:y\)?

Three students A, B, and C are conducting a mixing activity with alcohol solutions. Whenever there is a contest between any two of them, the student having the solution with the higher alcohol percentage pours \(200\) ml of his solution into the student's container having the lower alcohol percentage. The contests happen in this order: A and B, then B and C, then C and A, and this cycle continues. If a student runs out of solution, the remaining two continue with the same rule. If two students have the same alcohol percentage, the younger one pours \(200\) ml into the elder one's container. Initially, all three have \(600\) ml of solution. A's solution has \(60%\) alcohol, B's has \(48%\) alcohol, and C's has \(50%\) alcohol. Each contest takes \(3\) minutes. A fourth student D leaves immediately after the activity begins, returns after \(1\) hour, and drinks from the student who has the highest alcohol percentage at that time. What is the alcohol concentration of the solution that D drinks?

A container is completely filled with fruit juice. \(8\) litres of juice are drawn out and replaced with water. The same operation is repeated \(3\) more times. After all the operations, the ratio of juice left in the container to water is \(16:65\). How many litres of juice did the container originally hold?

A bakery chef prepares \(15\) cups of dessert sauce containing \(40%\) melted chocolate and \(60%\) raspberry puree. However, the correct recipe requires the sauce to contain \(50%\) melted chocolate and \(50%\) raspberry puree. How many cups of the sauce should be removed and replaced with pure melted chocolate to make the sauce contain \(50%\) of each?

A vessel is completely filled with water. \(8\) litres of water are drawn out and replaced with pure milk. Again, \(8\) litres of the mixture are drawn out and replaced with pure milk. If the vessel now contains water and milk in the ratio \(9:40\), find the capacity of the vessel.

A container has \(3\) litres of pure grape juice. From the container, \(1\) litre is removed and then \(2\) litres of water are added. This operation is repeated several times. After \(19\) such operations, what is the quantity of grape juice left in the mixture?

A milk vendor starts the day with \(1000\) litres of pure milk. After selling every \(500\) litres, he adds water equal to the quantity of mixture remaining with him. He can continue this dilution only as long as the ratio of milk to water does not fall below \(1:7\). If the next addition of water would make the ratio fall below \(1:7\), he stops adding water and sells the remaining mixture as it is. Each customer buys exactly \(2\) litres of milk from him. What is the total number of customers to whom he sells diluted milk?

In a laboratory, three containers A, B, and C have equal volumes of different mixtures of liquid oxygen and liquid nitrogen. The concentration by volume of liquid oxygen in containers A, B, and C is \(20%\), \(40%\), and \(80%\) respectively. First, one-fifth of the contents of A are poured into B. Then, two-fifths of the contents of B are poured into C. The final concentration of liquid oxygen in container C is approximately:

How many litres of water should be added to \(24\) litres of an acid-water solution so that the concentration of acid decreases from \(60\%\) to \(45\%\)?

Two containers of capacities \(3\) litres and \(5\) litres are filled with mixtures of milk and water. In the smaller container, \(25\%\) of the mixture is milk, while in the larger container, \(25\%\) of the mixture is water. The contents of both containers are poured into a \(9\)-litre vessel. The remaining space is then filled with water. What is the percentage of milk in the final mixture?

A dairy owner purchases pure milk at Rs. \(5\) per litre. After mixing it with water, he sells the mixture at Rs. \(6\) per litre and earns a profit of \(33\frac{1}{3}\%\). Assuming water is freely available, what is the ratio of water to milk in the mixture?

A container is completely filled with \(10\) litres of wine. First, \(2\) litres of wine are removed and replaced with water. Then, \(4\) litres of the resulting mixture are removed and replaced with water. Next, \(6\) litres of the mixture are replaced with water, followed by a fourth replacement of \(8\) litres. At the end of the fourth operation, what is the ratio of wine to water in the container?

A vessel is completely filled with alcohol. Some alcohol is transferred into another empty vessel of the same capacity. The second vessel is then filled to the brim by adding water. Next, enough of this mixture is poured back into the first vessel to fill it completely. After that, \(6\frac{2}{3}\) litres of the mixture from the first vessel is transferred into the second vessel. At this stage, both vessels contain the same quantity of alcohol. How much alcohol was originally transferred from the first vessel to the second?