$A$ can contains a mixture of two liquids $A$ and $B$ in the ratio $4:7$. When $6 \text{ litres}$ of the mixture are drawn off and the can is filled with liquid $B$,the ratio of $A$ and $B$ becomes $3:7$. How many litres of liquid $A$ were contained in the can initially?

There are $81 \ L$ of pure milk in a container. One-third of the milk is replaced by water. Again,one-third of the mixture is extracted and an equal amount of water is added. What is the ratio of milk to water in the new mixture?

Milk and water are mixed in vessel $A$ in the ratio of $5:2$ and in vessel $B$ in the ratio of $8:5$. In what ratio should quantities be taken from the two vessels so as to form a mixture in which milk and water will be in the ratio of $9:4$?

$50 \, g$ of an alloy of gold and silver contains $80 \%$ gold (by weight). The quantity of gold,that is to be mixed with this alloy,so that it may contain $95 \%$ gold,is (in $g$)

$A$ bottle full of whisky contains $50 \%$ alcohol. $A$ part of this whisky is replaced by another containing $18 \%$ alcohol and the percentage of alcohol was found to be $26 \%$. The quantity of whisky replaced is

$A$ $12 \text{ litres}$ cylinder contains a mixture of oxygen and nitrogen,the volume of oxygen being $40 \%$ of the total volume. $A$ few litres of the mixture is released and an equal amount of nitrogen is added. Then,the same amount of the mixture as before is released and replaced by nitrogen for the $second$ time. As a result,the oxygen content becomes $10 \%$ of the total volume. How many $litres$ of the mixture is released each time?