If the true discount on $Rs. 249$ at $5\%$ simple interest $(S.I.)$ is $Rs. 9$,when is the sum due? (in months)

$A$ bill is discounted at $5 \%$ per annum. If banker's discount be allowed, at what rate of interest must the proceeds be invested, so that nothing is lost? (in $\%$)

If $Rs. 10$ is allowed as true discount on a bill of $Rs. 110$ due at the end of a certain time,then the discount allowed on the same amount due at the end of double the time is (in $Rs.$)

The banker's gain on a bill due $1$ $year$ hence at $15 \%$ p.a. is $Rs.\, 9$. The true discount is (in $Rs.$)

$Rs. 20$ is the true discount on $Rs. 260$ due after a certain time. What will be the true discount on the same amount due after half of the earlier time,the rate of interest being the same? (in $Rs.$)

If the banker's discount on a certain sum in $2$ years at a certain rate is $Rs. 150$ and the simple interest on the same sum in $3$ years is $Rs. 240$,find the sum (in $Rs.$) and the rate of interest (in $\%$).