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.
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  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 $Q$?
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  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?
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  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?
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  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 $8:5$?
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  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.
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  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?
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  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.
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  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?
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  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 $A:B::11:4$?
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