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 $kg$?

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?

There are $81 \ L$ of pure milk in a container. One-third of the milk is replaced by water. Again,one-third of the mixture is extracted and an equal amount of water is added. What is the ratio of milk to water in the new mixture?

Three glasses of equal volume contain acid mixed with water. The ratios of acid to water are $2:3$,$3:4$,and $4:5$ respectively. If the contents of these glasses are poured into a large vessel,what is the ratio of acid to water in the large vessel?

$4 \, kg$ of potato at $Rs. \,5$ per $kg$ is mixed with $8 \,kg$ of potato at $Rs. \,6$ per $kg.$ Find the average price of the mixture (in $Rs.$ per $kg$).

In what ratio must oil at $Rs. 62$ per $kg$ be mixed with oil at $Rs. 72$ per $kg$ so that the mixture is worth $Rs. 64.50$ per $kg$?