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 $2:1$.

In what ratio should wheat at ₹ $32$ per $kg$ be mixed with wheat at ₹ $24$ per $kg$ so that on selling the mixture at ₹ $39$ per $kg$,there is a profit of $30 \%$?

$I$ have $100$ books of English. $I$ sold some of these at a profit of $12 \%$ and the rest at $8 \%$ loss. On the whole,$I$ got a profit of $11 \%$. How many books were sold at $12 \%$ profit by me?

$A$ mixture contains wine and water in the ratio $3:2$ and another mixture contains them in the ratio $4:5$. How many litres of the latter must be mixed with $3 \, L$ of the former so that the resulting mixture may contain equal quantities of the wine and water? (in $L$)

Gold is $21$ times as heavy as water and copper is $11$ times as heavy as water. In what ratio should these metals be mixed so that the mixture may be $17$ times as heavy as water?

$80 \text{ litre}$ mixture of milk and water contains $10 \%$ milk. How much milk (in $\text{litre}$) must be added to make water percentage in the mixture $80 \% ?$