Vessels $A$ and $B$ contain acid and water in the ratios $4:3$ and $5:3$ respectively. In what ratio must these mixtures be mixed to obtain a new mixture in vessel $C$ containing acid and water in the ratio $3:2$?

Two casks of $48$ $litres$ and $42$ $litres$ are filled with mixtures of wine and water,the proportions in the two casks being respectively $13:7$ and $18:17$. If the contents of the two casks are mixed,and $20$ $litres$ of water is added to the whole,what will be the proportion of wine to water in the resultant 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?

Three boxes of capacity $24\, kg$,$36\, kg$,and $84\, kg$ are completely filled with three varieties of wheat $A$,$B$,and $C$ respectively. All three boxes were emptied,the three types of wheat were thoroughly mixed,and the mixture was put back into the three boxes. How many $kg$ of type $A$ wheat would be there in the third box?

In a zoo,there are rabbits and pigeons. If the heads are counted,there are $200$ and if legs are counted,there are $580$. How many pigeons are there?

In what ratio must a person mix three kinds of wheat costing $Rs. 1.20$,$Rs. 1.44$ and $Rs. 1.74$ per $kg$ so that the mixture may be worth $Rs. 1.41$ per $kg$?