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 $g$)

In the first alloy,zinc and copper are in the ratio $1:2.$ In the second alloy,the same elements are in the ratio $2:3.$ If these two alloys are mixed to form a new alloy in which the two elements are in the ratio $5:8,$ the ratio of these two alloys in the new alloy is

Two casks of $48$ $litres$ and $42$ $litres$ are filled with mixtures of wine and water,the proportions in the two casks being respectively $13:7$ and $18:17$. If the contents of the two casks are mixed,and $20$ $litres$ of water is added to the whole,what will be the proportion of wine to water in the resultant mixture?

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 water be mixed with milk to gain $16 \%$ on selling the mixture at cost price?

$18 \text{ litre}$ of pure water was added to a vessel containing $80 \text{ litre}$ of pure milk. $49 \text{ litre}$ of the resultant mixture was then sold,and some more quantity of pure milk and pure water was added to the vessel in the respective ratio of $2:1$. If the resultant respective ratio of milk and water in the vessel was $4:1$,what was the quantity of pure milk added in the vessel? (in $\text{litre}$)