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 $30 \%$?

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?

$300$ $gm$ of sugar solution contains $40 \%$ sugar. How much sugar (in $gm$) should be added to make the concentration $50 \%$ in the solution?

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 $kg$?

$4 \, kg$ 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 $kg$).

$A$ man has $40 \ kg$ of tea,a part of which he sells at $5 \%$ loss and the rest at the cost price. In this business,he incurs a total loss of $3 \%$. Find the quantity of tea which he sells at the cost price (in $kg$).