$50 \, g$ 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 $g$)

There are two vessels $A$ and $B.$ Vessel $A$ contains $40$ $litres$ of pure milk and vessel $B$ contains $22$ $litres$ of pure water. From vessel $A,$ $8$ $litres$ of milk is taken out and poured into vessel $B.$ Then,$6$ $litres$ of the mixture (milk and water) is taken out from vessel $B$ and poured into vessel $A.$ What is the ratio of the quantity of pure milk in vessel $A$ to the quantity of pure water in vessel $B\,?$

The cost of Type $1$ rice is ₹ $15/kg$ and Type $2$ rice is ₹ $20/kg$. If both Type $1$ and Type $2$ are mixed in the ratio of $2:3$,then the price per $kg$ of the mixed variety of rice is (in ₹):

Vessels $A$ and $B$ contain mixtures of milk and water in the ratios $4:5$ and $5:1$ respectively. In what ratio should quantities of mixture be taken from $A$ and $B$ to form a mixture in which milk to water is in the ratio $5:4$?

In what ratio must a grocer mix two varieties of tea worth ₹ $60$ a $kg$ and ₹ $65$ a $kg$ so that by selling the mixture at ₹ $68.20$ a $kg$ he may gain $10 \%$?

In what ratio must oil at $Rs. 62$ per $kg$ be mixed with oil at $Rs. 72$ per $kg$ so that the mixture is worth $Rs. 64.50$ per $kg$?