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

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:

$Rs. 21$ is the true discount on $Rs. 371$ for a certain time at a certain rate of interest. If the rate of interest is kept the same,the true discount on the same sum for double that time will be (in $Rs.$)

The marked price of an article is $50 \%$ more than its cost price. If $20 \%$ discount is given,then what will be the profit percentage (in $\%$)?

The present worth of $Rs. 220.50$ due in $2$ years reckoning compound interest at $5 \%$ per annum is (in $Rs.$):