In what proportion must a grocer mix sugar at ₹ $12$ per $kg$ and ₹ $7$ per $kg$ so as to make a mixture worth ₹ $8$ per $kg$?

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

$A$ mixture of $30 \ L$ contains milk and water in the ratio of $7:3$. How much water should be added to it so that the ratio of milk and water becomes $3:7$? (in $L$)

$A$ dishonest trader professes to sell his article at cost price but he uses $900 \, g$ weight instead of $1 \, kg$. What is the percentage gain of the trader in this trade?

$A$ sum of ₹ $390$ was divided among $450$ boys and girls. Each girl gets $50$ paise and each boy gets one rupee. How many girls are there among them?

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?