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

$A$ watch dealer pays $10 \%$ customs duty on a watch which costs $Rs.\, 500$ abroad. He desires to make a profit of $20 \%$ after giving a discount of $25 \%$ to the buyer. The marked price should be (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 $\%$).

What is the rate of interest when the $P.W.$ of $Rs. 1245$ due in $15$ months is $Rs. 1200$? (in $\%$)

At a given rate,the simple interest and the true discount on a certain sum,for a given time,are $Rs. 24$ and $Rs. 22$ respectively. The sum is (in $Rs.$)

The price of a bicycle is marked by a trader at $Rs.\, 1000$. He sold the bicycle allowing successive discounts of $20 \%, 10 \%$ and $5 \%$. If the trader gained $14 \%$,then the cost price of the bicycle (in $rupees$) is: