$A$ mixture of a certain quantity of milk with $16$ litres of water is worth $90$ $P$ per litre. If pure milk is worth $Rs. 1.08$ per litre,how much milk is there in the mixture? (in Litres)

$300$ $grams$ of sugar solution contains $40 \%$ sugar. How much sugar should be added to make the concentration $50 \%$ in the solution? (in $grams$)

$A$ dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains $25 \%$. The percentage of water in the mixture is: (in $\%$)

In what proportion must sugar of $Rs. 17$ per $kg$ be mixed with sugar of $Rs. 29$ per $kg$ to make a mixture of $Rs. 20$ per $kg$?

Two vessels contain milk and water in the ratio $3:2$ and $7:3$. Find the ratio in which the contents of the two vessels have to be mixed to get a new mixture in which the ratio of milk and water is $2:1$.

$A$ vessel of $160 \text{ litres}$ is filled with milk and water. $70 \%$ of milk and $30 \%$ of water is taken out of the vessel. After this task,it is found that the vessel is now filled by $55 \%$ of its original total quantity. What is the original quantity of milk and water in the vessel respectively?