The true discount on a certain bill due for nine months at $4 \%$ simple interest is $Rs.\, 150$. Find the amount of the bill (in $Rs.$).

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?

If two successive discounts of $50 \%$ and $10 \%$ are offered,what is the net discount (in $\%$) ?

Ticket for an adult is $Rs. 1500$ and that of a child is $Rs. 800$. One child goes free with two adults. If a group has $25$ adults and $12$ children,what is the discount the group gets? (in $\%$)

Ramesh marks his goods $30 \%$ above cost price. If he sells the item for $Rs. 910$ after allowing a discount of $15 \%$,find his cost price (in $Rs.$).