The present worth of a sum of money due for $146 \text{ days}$ at $5 \%$ is $Rs. 400$. The sum due is (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 $\%$).

The simple interest and the true discount on a certain sum for a given time and at a given rate are $Rs.\, 85$ and $Rs.\, 80$ respectively. The sum is (in $Rs.$)

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

The banker's discount on a certain sum of money is $Rs. 84$ and the true discount on the same sum for the same time is $Rs. 70$. The sum due is (in $Rs.$)

The present worth of $Rs. 920$ due at the end of $3$ years at $5\%$ simple interest per annum is (in $Rs.$)