In $50\, g$ alloy of gold and silver,the gold is $80\%$ by weight. How much gold should be mixed to this alloy,so that the weight of gold would become $95\%$? (in $g$)

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

Acid and water are mixed in a vessel $A$ in the ratio of $5:2$ and in the vessel $B$ in the ratio $8:5$. In what proportion should quantities be taken out from the two vessels so as to form a mixture in which the acid and water will be in the ratio of $9:4$?

$A$ 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 $\text{kg}$)

Rama mixes $20 \%$ of kerosene to his petrol and then he sells the whole mixture at the price of petrol. If the cost price of the kerosene is $40 \%$ of the $CP$ of petrol,what is the net profit percentage (in $\%$)?

$200$ litres of mixture contains $15 \%$ water and the rest is milk. The amount of milk that must be added so that the resulting mixture contains $87.5 \%$ milk is..........$Litre$