$I$ have $100$ books of English. $I$ sold some of these at a profit of $12 \%$ and the rest at $8 \%$ loss. On the whole,$I$ got a profit of $11 \%$. How many books were sold at $12 \%$ profit by me?

$60\, kg$ of an alloy $A$ is mixed with $100\, kg$ of alloy $B.$ If alloy $A$ has lead and tin in the ratio $3:2$ and alloy $B$ has tin and copper in the ratio $1:4,$ the amount of tin in the new alloy is (in $kg$)

In what ratio must water be mixed with milk to gain $16 \frac{2}{3} \%$ on selling the mixture at cost price?

In a mixture of $25\, L$,the ratio of acid to water is $4: 1$. Another $3\, L$ of water is added to the mixture. The ratio of acid to water in the new mixture is

$A$ $20\, \text{litre}$ mixture of milk and water contains milk and water in the ratio $3:2$. $10\, \text{litres}$ of the mixture is removed and replaced with pure milk,and the operation is repeated once more. At the end of the two removals and replacements,what is the ratio of milk and water in the resultant mixture?

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?