In what ratio must sugar at $Rs. 2$ per $kg$ be mixed with sugar at $Rs. 3.50$ per $kg$ so that the mixture is worth $Rs. 2.50$ per $kg$?

Chocolates at $Rs. 12.00$ per dozen are mixed with chocolates at $Rs. 10.00$ per dozen in the ratio $3:5$. Find the price per dozen of the mixture (in $Rs.$).

$A$ 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?

The acid and water in two vessels $A$ and $B$ are in the ratio $4:3$ and $2:3$. In what ratio should the liquids in both the vessels be mixed to obtain a new mixture in vessel $C$ containing half acid and half water?

$A$ and $B$ are two alloys of gold and copper prepared by mixing metals in the ratio $5:3$ and $5:11,$ respectively. Equal quantities of these alloys are melted to form a third alloy $C.$ The ratio of gold and copper in the alloy $C$ is

Varun's expenditures and savings are in the ratio of $4:1$. His income increases by $20\%$. If his savings increase by $12\%$, by how much percentage should his expenditure increase?