$A$ bill for $Rs. 8000$ is drawn on September $19$ for $6$ months. It is discounted on January $8$ at $10\%$. Find the banker's discount,true discount,banker's gain,and the money that the holder of the bill receives (in $Rs.$).

If $Rs. 21$ is the true discount on $Rs. 371$ for a certain time,what is the true discount on the same amount for double that time,the rate being the same in both the cases? (in $Rs.$)

The price of a shirt after $15\%$ discount is $Rs.\,119$. What was the marked price of the shirt before the discount? (in $Rs.$)

If the true discount on $Rs. 161$ due for $2$ years and $6$ months is $Rs. 21$, then find the rate of interest (in $\%$).

After giving $20 \%$ discount on an article there is a profit of $20 \%$. What will be the profit percent when no discount is given (in $\%$)?

$A$ has to pay $Rs. 220$ to $B$ after $1$ year. $B$ asks $A$ to pay $Rs. 110$ in cash and defers the payment of the remaining $Rs. 110$ for $2$ years. $A$ agrees to it. Counting the rate of interest at $10\%$ per annum in this new mode of payment,which of the following is true?