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 $B.G.$ on a certain sum due in $5 \text{ years}$ is $\frac{3}{23}$ of $B.D.$ Here,the rate of interest is (in $\%$):

If a shopkeeper allows a $20 \%$ discount on his advertised price and makes a profit of $25 \%$ on his outlay,what is the advertised price (in $Rs.$) on which he gains $Rs. 6000$?

An article is marked $40 \%$ above the cost price and a discount of $30 \%$ is allowed. What is the gain or loss percentage?

The marked price of an item is $Rs. 900$. On the purchase of $2$ items,the discount is $16\%$,and on the purchase of $5$ items,the discount is $44\%$. If Raksha buys $7$ items,what is the effective discount percentage?

$A$ shopkeeper marks up his wares by $60 \%$ and offers a $10 \%$ discount. What will be the selling price (in $Rs.$) if the cost price is $Rs.\, 7500$?