The banker's discount on a sum of money for $1 \frac{1}{2}$ years is $Rs.\, 837$ and the true discount on the same sum for $2$ years is $Rs.\, 900$. The rate percent is:

The selling price of a radio was $Rs. 255$ when $15 \%$ discount was allowed. Then the marked price of the radio was (in $Rs.$)

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

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 $\%$)

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 marked price of an article is $20 \%$ more than its cost price. If $5 \%$ discount is given on the marked price,what is the profit percent (in $\%$)?