# Questions with detailed step by step solutions from Mixture and Allegations

##### Questions in Mixture and Allegations
1. Two vessels containing equal quantity of mixture of milk and water in the ratio $7:3$ and $3:2$ are mixed with $6$ litre of water to form a mixture containing milk and water in the ratio $1:1.$ Find the quantity in each vessel.
2. If two vessels $P$ and $Q$ contain milk and water in the ratio $3:7\,\,\text{and}\,\,13:7.$ Then to form a new mixture where milk and water are in the ratio $8:7.$ What should be the ratio of quantities of $P$ to $Q$?
3. $35$ litres of $27:8$ milk and water solution are removed and replaced with water. This operation is done thrice and the solution now has milk and water in the ratio $8:27.$ What was the total volume of original solution?
4. A cask is filled with a mixture of two liquids $A$ and $B$ in the proportion $A:B::5:3.$ When $16$ gallons of the mixture are drawn off and the cask is filled with liquid $B$ the proportion becomes $A:B::3:5.$ How many gallons does the cask hold?
5. Cask $A$ contains wine and water in the ratio $6:7$ and cask $B$ in the ratio $9:4.$ In what ratio must the contents of the two casks be mixed to give a mixture of wine and water in the ratio $8:5$?
6. A man buys milk at $\text{Rs}.\,5$ a litre and after adding water sells it at $\text{Rs}.\,6$ a litre, thereby making a profit of $33.33\%.$ Find the proportion of water to milk in the mixture.
7. A cask contains a mixture of two liquids $A$ and $B$ in the ratio $7:5.$ When a gallon of the mixture is drawn off and the cask is filled with liquid $B,$ the proportion becomes $A:B::7:9.$ How many gallons does the cask hold?
8. Two jars of capacity $3$ and $5$ litres are filled with mixtures of an alcohol and water. In the smaller jar $25\%$ of the mixture is alcohol and in the larger $25\%$ of the mixture is water. The jars are emptied into a $9$ litre cask and the remaining volume is filled up with water. Find the percentage of alcohol in the cask.
9. The percentage of alcohol in two wine tanks is $20\%$ and $40\%$ respectively and rest is grape juice. If a wine glass is filled to its half by the tank $1$ and $2$ in the ratio $2:3$ and the rest is filled again by pure alcohol, then what is ratio of the grape juice to alcohol in the wine glass?
10. Two casks contain mixtures of liquids $A$ and $B.$ In the first cask $A:B::7:3$ and in the second cask $A:B::3:1.$ In what ratio must the mixture from the two casks be taken to give a mixture in which $A:B::11:4$?