While selling a shirt,a shopkeeper gives a discount of $7 \%$. If he gives a discount of $9 \%$,he earns $Rs. 15$ less in profit. The marked price of the shirt is (in $Rs.$):

$Rs. 20$ is the true discount on $Rs. 260$ due after a certain time. What will be the true discount on the same amount due after half of the earlier time,the rate of interest being the same? (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 $Rs.$)

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

The simple interest and the true discount on a certain sum for a given time and at a given rate are $Rs.\, 85$ and $Rs.\, 80$ respectively. The sum is (in $Rs.$)

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