Gold is $21$ times as heavy as water and copper is $11$ times as heavy as water. In what ratio should these metals be mixed so that the mixture may be $17$ times as heavy as water?

In what ratio must a person mix three kinds of wheat costing $Rs. 1.20$,$Rs. 1.44$ and $Rs. 1.74$ per $kg$ so that the mixture may be worth $Rs. 1.41$ per $kg$?

$A$ and $B$ are two alloys of gold and copper prepared by mixing metals in the ratio $7:2$ and $7:11$ respectively. If equal quantities of the alloys are melted to form a third alloy $C$,the ratio of gold and copper in $C$ will be

$729 \, ml$ of a mixture contains milk and water in the ratio $7:2$. How much more water is to be added to get a new mixture containing milk and water in the ratio $7:3$? (in $ml$)

$A$ man buys $2$ cows for $Rs. 2700$ and sells one at a loss of $6\%$ and the other at a gain of $7.5\%$. On the whole,he neither gained nor lost. What is the cost price of the $2^{nd}$ cow?

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 $kg$?