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 two successive discounts of $20 \%$ and $30 \%$ are given,what is the net discount (in $\%$) ?

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 marked price of an item is $Rs. 900$. On the purchase of $2$ items,the discount is $16\%$,and on the purchase of $5$ items,the discount is $44\%$. If Raksha buys $7$ items,what is the effective discount percentage?

Find the present worth $(P.W.)$ and the true discount $(T.D.)$ reckoning $6 \%$ per annum simple interest of $Rs. 176$ due in $20 \text{ months}$ time. (in $Rs.$)

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 $Rs.$).