In what ratio should sugar at ₹ $30$ per $kg$ be mixed with sugar at ₹ $45$ per $kg$ so that on selling the mixture at ₹ $42$ per $kg$ there is a profit of $20 \%$?

$A$ shopkeeper has $50 \ kg$ 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?

How many $kg$ of sugar costing ₹ $5.75$ per $kg$ should be mixed with $75 \, kg$ of cheaper sugar costing ₹ $4.50$ per $kg$,so that the mixture is worth ₹ $5.50$ per $kg$?

$A$ drum contains $80$ $litres$ of ethanol. $20$ $litres$ of this liquid is removed and replaced with water. $20$ $litres$ of this mixture is again removed and replaced with water. How much water (in $litres$) is present in this drum now?

$50 \, g$ of an alloy of gold and silver contains $80 \%$ gold (by weight). The quantity of gold,that is to be mixed with this alloy,so that it may contain $95 \%$ gold,is (in $g$)

In a $729 \ L$ mixture of milk and water,the ratio of milk to water is $7:2.$ To get a new mixture containing milk and water in the ratio $7:3,$ the amount of water to be added is (in $L$)