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

How many $kg$ of salt at $42$ $P$ per $kg$ must a man mix with $25 \, kg$ of salt at $24$ $P$ per $kg$,so that he may,on selling the mixture at $40$ $P$ per $kg$,gain $25 \%$ on the outlay?

Two vessels $A$ and $B$ contain milk and water mixed in the ratio $8: 5$ and $5: 2,$ respectively. The ratio in which these two mixtures should be mixed to get a new mixture containing $69 \frac{3}{13} \%$ milk is

$A$ mixture of $48$ litre of milk and water contains $10 \%$ of water. How much water must be added to make $20 \%$ water in the new mixture?

$A$ tub contains a mixture of two liquids $P$ and $Q$ in the ratio of $4:1$. When $10 \, L$ of the mixture is taken out and $10 \, L$ of liquid $Q$ is poured into the tub,the ratio becomes $2:3$. How many litres of liquid $P$ were contained in the tub initially?

$60\, kg$ of an alloy $A$ is mixed with $100\, kg$ of alloy $B.$ If alloy $A$ has lead and tin in the ratio $3:2$ and alloy $B$ has tin and copper in the ratio $1:4,$ the amount of tin in the new alloy is (in $kg$)