$A$ 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?

$8$ litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in the cask to that of water is $16:65$. How much wine did the cask hold originally? (in litres)

$A$ trader has $50 \text{ kg}$ of rice,a part of which he sells at $10 \%$ profit and the rest at $5 \%$ loss. He gains $7 \%$ on the whole. What is the quantity sold at $10 \%$ gain and $5 \%$ loss? (in $\text{kg}$)

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?

$A$ 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 $ltr$)?

$A$ 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 $1:1$?