Mixture and Alligation

The ratio of milk and water in three completely-filled bottles of the same volume is $1 : 1, 2 : 1,$and $3 : 2$. If the three bottles are mixed in a larger vessel, then the ratio of milk and water in larger vessel is _____.

What quantity of a $90\%$ wine solution should be mixed with $40$ ml of a $35\%$ wine solution in order to get a$50\%$ wine solution?

A vessel is filled with $150$ litres of a wine and water solution in the ratio of $2:1.$ First, $15$ litres of wine is taken out and replaced with water. Again, $15$ litres is taken out and replaced with water. How many minimum times should this process be carried out so that the quantity of wine becomes less than $75$ litres in the final mixture?

A vessel is completely filled with $150$ litres of wine. First, $15$ litres of wine is taken out and replaced with water. Again, $15$ litres is taken out and replaced with water. How many minimum times should this process be carried out so that the quantity of wine becomes less than $100$ litres in the final mixture?

A jar containing a mixture of wine and soda has $60\%$ wine. A part of this mixture was replaced by another mixture of wine and soda having $45\%$ soda. The mixture now has $53\%$ wine. Find out what percentage of the jar was replaced.

A cloth merchant bought $3,000$ m of cloth. He sells part of the stock at $3\%$ loss and the remaining at $12\%$ profit. If he made an overall profit of $10\%$, then how many metres of cloth was sold at a loss?

A bartender steals $45$ litres of wine from a cask full of wine and replaces it with water. He repeats the process one more time. What is the volume of the cask if the ratio of wine to water in the final solution is $16 : 9$?

A bartender steals $20$ litres of wine from a cask full of wine and replaces it with water. He repeats the process two more times. What is the volume of the cask if the ratio of wine to water in the final solution is $64: 61$ ?

Two solutions A and B are such that they have milk and water in the ratio $1 : 2$ and $3 : 2$. Solutions A and B are mixed in the ratio $2 : 1$ to produce a solution C. Find the ratio of milk and water in solution C.

The $120$ litres of a solution of milk and water is in the ratio $3 : 2$. $20$ litres of the solution is removed and the same amount of water is added. This process is done once again. Find the amount of milk in the final solution.

To a $60$ litres solution having milk and water in the ratio$3 : 2$. $6$ litres of water is added in the solution. Find the ratio of milk to water in the final solution.

How many litres of soda should be added in $60$ litres of a solution of liquor and soda so that the percentage of liquor drops from $60\%$ to$20\%$?

If $10\%$ of a solution of milk and water is removed from a vessel and replaced with water, the ratio of milk and water becomes $5 : 4$. Find the ratio of milk and water in the original solution.

In a solution which has milk and water in the ratio of $3 : 1$, milk equals to $10\%$ of the total solution is added. What is the ratio of milk and water in the final solution?

A bartender purchased x litres of wine worth $Rs. 140$ per litres and mixed $15$ litres of water in it. He then sold the mixture at the rate of $Rs.160$ per litres, making a profit of $25\%$. Find the total amount of wine in the mixture.

A milkman purchased milk worth $Rs. 60$ per litre  and mixed $20$ litres of water in it. By selling the mixture at the rate of $Rs. 55$ per litre, he makes a profit of $10\%$. Find the total amount of milk in the mixture.

Ali purchased a radio and a tape recorder for $₹2,400$ He sold the radio at a profit of$20\%$ and the tape recorder at a loss of $10\%$. However, overall, he made a profit of $5\%$ on the whole. Find the S.P. of the tape recorder.

Ali purchased a radio and a tape recorder for $\mathrm{Rs}.1,800$. He sold the radio at a profit of $40\%$ and the tape recorder at a profit of $25\%$. However, the overall profit was $30\%$. Find the selling price of the tape recorder.

In what ratio should two qualities of wheat having the rates $Rs.56$ per kg and $Rs. 34$ per kg, respectively, be mixed in order to get a mixture that would have a rate of $Rs. 45$ per kg?

In a class of $600$ students, $80\%$ of the boys passed while $92\%$ of the girls passed the exam. However, only $88\%$ of the students passed the exam. How many boys were there in the class?