The true discount on a bill of $Rs. 5450$ due in $9$ months is $Rs. 450$. Find the rate of interest (in $\%$).

When a discount of $Rs. 42$ is allowed on the marked price of an article,the new reduced price becomes $86 \%$ of the original marked price. Find the marked price (in $Rs.$).

$Rs.\, 20$ is the true discount on $Rs.\, 210$ due after a certain time. What will be the true discount on the same sum due after half of the former time,the rate of interest being the same? (in $Rs.$)

At $20 \%$ discount,the selling price of an article is $Rs. 2400$. What is the selling price (in $Rs.$) if the discount is $32.5 \%$?

The selling price of an article is $Rs.\, 816$ if the discount on it is $15 \%$. What would be the selling price of the article $($ in $Rs.\,)$ if the discount on it is $25 \%$?

The price of a chair is $Rs.\, 500$. It has been sold at two successive discounts of $10\%$ each. What is its selling price? (in $Rs.$)