$A$ 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?

$A$ $20\, \text{litre}$ 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?

$A$ tub contains a mixture of two liquids $P$ and $Q$ in the ratio of $4:1$. When $10 \, L$ of the mixture is taken out and $10 \, L$ of liquid $Q$ is poured into the tub,the ratio becomes $2:3$. How many litres of liquid $P$ were contained in the tub initially?

Vessels $A$ and $B$ contain acid and water in the ratios $4:3$ and $5:3$ respectively. In what ratio must these mixtures be mixed to obtain a new mixture in vessel $C$ containing acid and water in the ratio $3:2$?

$I$ 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?

$A$ mixture of $80$ litre of milk and water contains $10 \%$ water. How much water must be added to make $20 \%$ water in the new mixture? (in $litre$)