To find the equivalent single discount for two successive discounts, you can use the following formula:
The Formula
If the successive discounts are $x\%$ and $y\%$, the single equivalent discount is:
$$\text{Single Discount} = \left( x + y - \frac{x \times y}{100} \right)\%$$
Step-by-Step Calculation
Identify the values: $x = 20$ and $y = 10$.
Apply the formula:
$$\text{Single Discount} = \left( 20 + 10 - \frac{20 \times 10}{100} \right)$$
Simplify:
$$\text{Single Discount} = 30 - \frac{200}{100}$$
$$\text{Single Discount} = 30 - 2 = 28\%$$
Alternative Method (Base 100)
Assume the marked price is ₹100.
Apply the first discount of 20%: $100 - 20 = \text{₹80}$.
Apply the second discount of 10% on the new price: $80 - (10\% \text{ of } 80) = 80 - 8 = \text{₹72}$.
The total reduction from the original price is: $100 - 72 = 28$.
The equivalent single discount for successive discounts of 20% and 10% is 28%.
Important Questions from Discount and MP
- Two successive discounts of 25% and 10% on a deal are equivalent to a single discount of:
- A shopkeeper offers the following three schemes. Which scheme has the maximum discount percent?
I. Two successive discounts of 15% and 20%.
II. Buy 4 get 2 free.
III. Buy 6 get 4 free - A shopkeeper is given a 10% trade discount and a 5% scheme discount (free units). On purchasing 100 units priced at ₹50 each, what is the trade discount amount?
- Rahul buys a box of pens (listed price of ₹900) with a trade discount of 30%. What is the net price?
- A shopkeeper marked the price of a table as ₹1,400 and offered two successive discounts, one of which is 12%. If a customer pays ₹1,133.44 for the table, then what was the second discount percentage offered?
