By selling $90$ pens for $Rs. 80$,a man loses $20\%$. What should be the selling price (in $Rs.$) of $90$ pens for $20\%$ profit?

$A$ retailer offers the following discount schemes for buyers on an article:
$I.$ Two successive discounts of $10 \%$
$II.$ $A$ discount of $12 \%$ followed by a discount of $8 \%$
$III.$ Successive discounts of $15 \%$ and $5 \%$
$IV.$ $A$ discount of $20 \%$
The selling price will be minimum under the scheme:

$A$ trader mixes $26 \text{ kg}$ of rice at $Rs. 20$ per $\text{kg}$ with $30 \text{ kg}$ of rice of another variety at $Rs. 36$ per $\text{kg}$ and sells the mixture at $Rs. 30$ per $\text{kg}$. His profit percent is:

$A$ man invests $Rs. 21,000$ in shares of a company. He sells one-third of the total shares at a profit of $10\%$. However,he has to sell the remaining shares at a $5\%$ loss. Find his overall profit or loss percentage.

Aditya purchased a book with a $20 \%$ discount on the marked price. How much $Rs.$ did he pay if the marked price of the book was $Rs. 500$?

$A$ man buys a cycle for $Rs. 1400$ and sells it at a loss of $15 \%$. What is the selling price of the cycle? (in $Rs.$)