$A$ shopkeeper sold an item at $10 \%$ loss after giving a discount equal to half the marked price. The cost price of the item is ......... of the marked price.

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 $\%$.

$A$ sold a pen to $B$ at a profit of $20\%,$ $B$ sold the same pen to $C$ for $Rs.\,75$ thereby making a profit of $25 \% .$ Find the price at which $A$ bought the pen? (in $Rs.$)

$A$ man sells two articles,each for $Rs. 640$. He earns $20\%$ profit on the first and $40\%$ profit on the second. Find his overall percent profit.

Nutan bought $30$ dozens of oranges for her juice stall in the school fair. She paid $Rs. 8$ per dozen of oranges. She also had to pay $Rs. 500$ as the stall fee to the school authorities. She calculated that each glass of juice would need $3$ oranges. How much should she charge per glass of juice so as to make $20 \%$ profit in $Rs$?

$A$ shopkeeper professes to sell his goods at cost price but uses a $930 \text{ g}$ weight instead of $1 \text{ kg}$ weight. What will be the profit percentage of the shopkeeper (in $\%$)?