How many kilograms of sugar costing $Rs. 9$ per $kg$ must be mixed with $27\, kg$ of sugar costing $Rs. 7$ per $kg$ so that there may be a gain of $10\%$ by selling the mixture at $Rs. 9.24$ per $kg$?

$A$ mixture of milk and water measures $60 \, ltr$. It contains $20 \%$ water. How many litres of water should be added to it so that water may be $25 \% $ (in $ltr$)?

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

$A$ merchant has $1000 \ kg$ of sugar,part of which he sells at $8 \%$ profit and the rest at $18 \%$ profit. If he gains $14 \%$ on the whole,then the quantity sold at $18 \%$ profit is.......$kg$.

Two liquids are mixed in the ratio of $3: 2$ and the mixture is sold at $Rs. 11$ per litre at a $10 \%$ profit. If the $1$st liquid costs $Rs. 2$ more per litre than the second,what is the cost per litre of the second liquid (in $.80$)? (in $Rs.$)

Vessels $A$ and $B$ contain mixtures of milk and water in the ratios $4:5$ and $5:1$ respectively. In what ratio should quantities of mixture be taken from $A$ and $B$ to form a mixture in which milk to water is in the ratio $5:4$?