$A$ 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.

Due to a $20\%$ rise in the price of sugar,a bachelor is able to buy $1.5\, kg$ less for $Rs.\, 135$. What is the increased price of sugar per $kg$ in $Rs.$?

$A$ man buys $300$ dozen of bananas for $Rs. 3,600$. He sold $1/3$ of the stock at a loss of $10\%$ and the remaining $2/3$ of the stock at a gain of $10\%$. Find his overall percent profit or loss.

$A$ vendor bought toffees at $6$ for a rupee. How many for a rupee must he sell to gain $20 \%$?

$A$ single discount,equivalent to a successive discount of $40 \%$ and $30 \%$ is in $\%$?

Sanjay purchased a chair marked at $Rs. 800$ at $2$ successive discounts of $10 \%$ and $15 \%$ respectively. He spent $Rs. 28$ on transportation and sold the chair for $Rs. 800$. How much is his gain percentage (in $\%$)?