The ratio of milk and water in $66$ $litres$ of adulterated milk is $5:1$. Water is added to it to make the ratio $5:3$. The quantity of water added is (in $litres$):

There are $3$ tubs which contain mixtures of milk and water in the ratios of $5:2, 4:3,$ and $3:1$ respectively. If the mixtures are poured into a single tub,find the ratio of milk to water.

$A$ barrel contains a mixture of wine and water in the ratio $3:1$. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel becomes $1:1$?

How many kg of sugar costing ₹ $11.70/kg$ must be mixed with $24$ $kg$ of sugar costing ₹ $8.1/kg$ so that there may be a gain of $15 \%$ by selling the mixture at ₹ $9/kg$? (in $kg$)

$A$ 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?

$A$ mixture contains $80 \%$ acid and the rest water. What part of the mixture should be removed and replaced by the same amount of water to make the ratio of acid to water $4:3$?