$A$ can contains a mixture of two liquids $A$ and $B$ in the ratio $7:5$. When $9$ litres of the mixture are drawn off and the can is filled with $B$,the ratio of $A$ and $B$ becomes $7:9$. The quantity of liquid $A$ contained by the can initially was:

In what ratio must water be mixed with milk to gain $16 \frac{2}{3} \%$ on selling the mixture at cost price?

$A$ man has $40 \ kg$ of tea,a part of which he sells at $5 \%$ loss and the rest at the cost price. In this business,he incurs a total loss of $3 \%$. Find the quantity of tea which he sells at the cost price (in $kg$).

$18 \text{ litre}$ of pure water was added to a vessel containing $80 \text{ litre}$ of pure milk. $49 \text{ litre}$ of the resultant mixture was then sold,and some more quantity of pure milk and pure water was added to the vessel in the respective ratio of $2:1$. If the resultant respective ratio of milk and water in the vessel was $4:1$,what was the quantity of pure milk added in the vessel? (in $\text{litre}$)

How much water must be added to a vessel which contains $80$ litres of milk at a cost price of ₹ $3.5/litre$ so that the cost of the milk reduces to ₹ $2/litre$? (in litres)

In a mixture of milk and water of volume $30$ $L$,the ratio of milk and water is $8:7$. How much water should be added to the mixture to make the ratio $4:5$? (in $L$)