Some articles were bought at $6$ articles for $Rs. 5$ and sold at $5$ articles for $Rs. 6$. The gain percent is: (in $\%$)

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 $Rs. 500$?

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 $\%$)?

$A$ man purchased $150$ pens at the rate of $Rs. 12$ per pen. He sold $50$ pens at a gain of $10 \%$. The percentage gain at which he must sell the remaining pens so as to gain $15 \%$ on the whole outlay is........$\%$

Anil bought an item with $12 \frac{1}{2} \%$ discount on the labelled price. He sold the item with $17 \frac{1}{2} \%$ profit on the labelled price. What was his percent profit on the price he bought?

$A$ shopkeeper sold an article at the rate of $Rs. 35$ per article and earned a profit of $40\%$. At what price should each article have been sold to earn a profit of $60\%$?