There would be a $10 \%$ loss,if rice is sold at $Rs. 54$ per $kg$. To earn a profit of $20 \%$,the price of rice per $kg$ will be (in $Rs.$)

By selling $80$ ball pens for $₹ 140$,a retailer loses $30 \%$. How many ball pens should he sell for $₹ 104$ so as to make a profit of $30 \%$?

$A$ shopkeeper has to sell $24 \text{ kg}$ of sugar. He sells a part of these at a gain of $20 \%$ and the rest at a loss of $5 \%$. If on the whole he earns a profit of $10 \%$,what is the quantity of sugar (in $\text{kg}$) sold at a loss?

Sita sells a calculator to Gita at a gain of $17 \%$ and Gita sells it to Anu at a loss of $25 \%$. If Anu pays $Rs. 1842.75$ for it,then what did Sita pay for it? (in $Rs.$)

If the cost price of $20$ articles is equal to the selling price of $15$ articles,find the profit percent?

An article is marked for sale at $Rs. 504$. The shopkeeper gives a discount of $5\%$ on the marked price and still earns a profit of $20\%$. What is the cost price of the article? (in $Rs.$)