Two successive discounts of $a \%$ and $b \%$ on the marked price of an article are equivalent to a single discount of:

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 $B.G.$ (Banker's Gain) on a sum due $3 \text{ years}$ at $10 \%$ per annum is $Rs. 180$. The $B.D.$ (Banker's Discount) is (in $Rs.$):

The discounts offered on a shirt of $Rs. 500$ and a pair of trousers of $Rs. 1000$ are $20\%$ and $40\%$ respectively. If Ajay bought $3$ shirts and $3$ pairs of trousers,what was the effective discount (in $\%$) he received?

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 $Rs. 6000$?

The true discount on a bill of $Rs. 2550$ due after $3$ months is $Rs. 50$. Find the banker's discount (in $Rs.$).