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

$A$ cloth merchant has announced a $25 \%$ rebate in prices. If one needs to have a rebate of $Rs. 40$,then how many metres of cloth costing $Rs. 32$ per metre should he purchase?

$Rs. 21$ is the true discount on $Rs. 371$ for a certain time at a certain rate of interest. If the rate of interest is kept the same,the true discount on the same sum for double that time will be (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 $Rs.$)

The $B.G.$ on a certain sum due in $5 \text{ years}$ is $\frac{3}{23}$ of $B.D.$ Here,the rate of interest is (in $\%$):

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 $Rs.$).