$A$ jar contained a mixture of two liquids $A$ and $B$ in the ratio $3 : 2.$ When $5$ litres of the mixture was taken out and $5$ litres of liquid $B$ was poured in the jar,this ratio became $2 : 3.$ The quantity of liquid $A$ contained in the jar initially was (in litres).

$A$ sum of ₹ $390$ was divided among $450$ boys and girls. Each girl gets $50$ paise and each boy gets one rupee. How many girls are there among them?

Chocolates at $Rs. 12.00$ per dozen are mixed with chocolates at $Rs. 10.00$ per dozen in the ratio $3:5$. Find the price per dozen of the mixture (in $Rs.$).

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)

$A$ merchant mixes three varieties of rice costing $Rs. 20$ per $kg$,$Rs. 24$ per $kg$,and $Rs. 30$ per $kg$ and sells the mixture at a profit of $20\%$ at $Rs. 30$ per $kg$. How many $kgs$ of the second variety will be in the mixture if $2$ $kgs$ of the third variety is there in the mixture?

$A$ 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?