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

If $21 \%$ of an electricity bill is discounted,$Rs. 1817$ is still to be paid. How much was the original bill amount? (in $Rs.$)

$A$ sells a car priced at $Rs. 36,000$. He gives a discount of $8\%$ on the first $Rs. 20,000$ and $5\%$ on the remaining $Rs. 16,000$. $B$ also sells a car of the same make,priced at $Rs. 36,000$. He gives a discount of $7\%$ on the total price. Calculate the actual prices charged by $A$ and $B$ for the cars (in $Rs.$).

If $60 \%$ discount is offered on the marked price and selling price becomes equal to cost price,then what was the percentage mark up?

The difference between the simple interest and the true discount on a certain sum of money for $2$ years at $15 \%$ per annum at simple interest is $Rs. 45$. Find the sum (in $Rs.$).

The discount on $Rs. 5229$ due in $1$ $year$ $9$ $months$ reckoning compound interest at $5 \%$ is (in $Rs.$)