How many kg of sugar costing ₹ $11.70/kg$ must be mixed with $24$ $kg$ of sugar costing ₹ $8.1/kg$ so that there may be a gain of $15 \%$ by selling the mixture at ₹ $9/kg$? (in $kg$)

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 $30 \%$?

$A$ barrel contains a mixture of wine and water in the ratio $3:1$. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel becomes $1:1$?

$20$ litres of a mixture contains $20 \%$ alcohol and the rest is water. If $4$ litres of water are added to it,what will be the percentage of alcohol in the new mixture?

$60 \ kg$ of a certain variety of rice at $Rs. 32$ per $kg$ is mixed with $48 \ kg$ of another variety of rice,and the mixture is sold at the average price of $Rs. 28$ per $kg$. If there is no profit or loss due to the new sale price,the price of the second variety of rice in $Rs.$ per $kg$ is:

The ratio of milk and water in mixtures of four containers are $5:3$,$2:1$,$3:2$,and $7:4$,respectively. In which container is the quantity of milk,relative to water,the minimum?