$A$ 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 $1:1$?

Gold is $19$ times as heavy as water and copper is $9$ times. In what ratio should these metals be mixed so that the mixture may be $15$ times as heavy as water?

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 $2:1$.

There are two vessels $A$ and $B.$ Vessel $A$ contains $40$ $litres$ of pure milk and vessel $B$ contains $22$ $litres$ of pure water. From vessel $A,$ $8$ $litres$ of milk is taken out and poured into vessel $B.$ Then,$6$ $litres$ of the mixture (milk and water) is taken out from vessel $B$ and poured into vessel $A.$ What is the ratio of the quantity of pure milk in vessel $A$ to the quantity of pure water in vessel $B\,?$

$A$ drum contains $80$ $litres$ of ethanol. $20$ $litres$ of this liquid is removed and replaced with water. $20$ $litres$ of this mixture is again removed and replaced with water. How much water (in $litres$) is present in this drum now?

Find the ratio in which rice at ₹ $7.20/kg$ should be mixed with rice at ₹ $5.70/kg$ to produce a mixture worth ₹ $6.30/kg$.