$A$ 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 $\%$)

$A$ shopkeeper sold an article offering a discount of $24 \%$ and earned a profit of $23.5 \%$. What would have been the percentage of profit earned if no discount had been offered?

$A$ man bought $15$ mangoes for a rupee. How many mangoes were sold for a rupee so that there is a loss of $25 \% ?$

$A$ shopkeeper buys a toy at $Rs. 100$ and sells it at $Rs. 125$. Another shopkeeper buys the same toy at $Rs. 125$ but sells it at $Rs. 100$. What are the respective profit and loss percentages for the two shopkeepers?

$A$ 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?

$A$ man sells an article at a loss of $5 \%$. If he had bought it at $20 \%$ more and sold it for $Rs. 115$ less,he would have made a loss of $40 \%$. Find the cost price of the article.