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

In what ratio should coffee powder costing ₹ $2500$ per $kg$ be mixed with coffee powder costing ₹ $1500$ per $kg$ so that the cost of the mixture is ₹ $2250$ per $kg$?

$A$ 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 $\text{kg}$)

How many $kg$ of sugar costing ₹ $5.50$ per $kg$ must be mixed with $60 \ kg$ of sugar costing ₹ $4.80$ per $kg$ so that the mixture is worth ₹ $5.25$ per $kg$?

How many $Kg$ of tea,worth ₹ $25$ per $Kg$,must be blended with $30 \ Kg$ of tea worth ₹ $30$ per $Kg$,so that by selling the blended variety at ₹ $30$ per $Kg$ there should be a gain of $10 \%$?

$8$ 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 the water is $16$:$65$. How much wine did the cask hold originally? (in litres)