After selling $5 \%$ of a quantity of sugar,$5 \text{ kg}$ of sugar remains. Find the total quantity of sugar in $\text{kg}$.

$A$ man gains $20 \%$ by selling an article for a certain price. If he sells it at double the price,what will be the percentage of profit (in $\%$)?

$A$ dishonest dealer professes to sell his goods at cost price but uses a weight of $960 \, g$ instead of a $1 \, kg$ weight. Find his gain $\%$. (in $\%$)

Mohan buys a watch for $Rs. 350$ and sells it for $Rs. 392$. Find out his percentage of profit.

Half of $100$ items were sold at a profit of $20 \%$ and the remaining were sold at a profit of $40 \%$. If all the items were sold at a profit of $25 \%$,the total profit would have been $Rs. 100$ less than the previous profit. What was the cost price (in $Rs.$) of each item?

$A$ trader buys $500 \, kg$ of cotton for $Rs. 9,000$. $10 \%$ of this cotton is spoiled due to rain. At what rate $(Rs./ kg)$ should he sell the rest to earn $10 \%$ profit?