In what ratio must a grocer mix two varieties of pulses costing $Rs. 15$ and $Rs. 20$ per $kg$ respectively so as to get a mixture worth $Rs. 16.5$ per $kg$?

$A$ mixture of $48$ litre of milk and water contains $10 \%$ of water. How much water must be added to make $20 \%$ water in the new mixture?

The ratio of milk and water in mixtures of four containers are $5:3, 2:1, 3:2$ and $7:4$ respectively. In which container is the quantity of milk,relative to water,minimum?

How much water must be added to a vessel which contains $80$ litres of milk at a cost price of ₹ $3.5/litre$ so that the cost of the milk reduces to ₹ $2/litre$? (in litres)

Gold is $19$ times as heavy as water and copper is $9$ times. In what ratio should these metals be mixed so that the mixture may be $15$ times as heavy as water?

$A$ trader has $50 \ kg$ of sugar,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 $kg$)