In what ratio must water be added to spirit to gain $10 \%$ by selling it at the cost price?

$A$ $20\, \text{litre}$ mixture of milk and water contains milk and water in the ratio $3:2$. $10\, \text{litres}$ of the mixture is removed and replaced with pure milk,and the operation is repeated once more. At the end of the two removals and replacements,what is the ratio of milk and water in the resultant mixture?

In what ratio must a person mix three kinds of tea costing $Rs. 60$ per $kg$,$Rs. 75$ per $kg$,and $Rs. 100$ per $kg$ so that the resultant mixture when sold at $Rs. 96$ per $kg$ yields a profit of $20\%$?

Pencils at $Rs. 4.20$ per dozen are mixed with pencils at $Rs. 5.40$ per dozen in the ratio $3:5$. Find the price per dozen of the mixture (in $Rs.$).

$A$ sum of $Rs. 41$ was divided among $50$ children. Each boy gets $90$ paise and each girl $65$ paise. The number of boys is?

$A$ container contains $50 \, \text{litres}$ of milk. From this container $5 \, \text{litres}$ of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container? (in $\text{litres}$)