$A$ man bought apples at the rate of $8$ for $Rs. 34$ and sold them at the rate of $12$ for $Rs. 57$. How many apples should be sold to earn a net profit of $Rs. 45$?

$A$ and $B$ jointly made a profit of $Rs. 1650$ and they decided to share it such that $\frac{1}{3}$ of $A$'s profit is equal to $\frac{2}{5}$ of $B$'s profit. Then the profit of $B$ is (in $Rs.$)

The list price of a book is $Rs. 100$. $A$ dealer sells three such books for $Rs. 274.50$ after allowing a discount at a certain rate. Find the rate of discount in $\%$.

$A$ man buys a table and a chair for $Rs. 500$. He sells the table at a loss of $10\%$ and the chair at a gain of $10\%$. He still gains $Rs. 10$ on the whole. The cost price of the chair in rupees is

$A$ fair price shopkeeper takes $10 \%$ profit on his goods. He lost $20 \%$ of his goods due to theft. What is his loss percentage (in $\%$)?

If an item is sold for $Rs. 924$,there is a profit of $10\%$. What is the cost price?