If two successive discounts of 25% and 20% respectively are given, then what will be the net discount percentage?

Options

A. `42.5%`
B. `45%`
C. `50%`
D. `40%`

Answer

To find the net discount percentage when two successive discounts of 25% and 20% are applied, we can solve the problem step by step.

### Step-by-Step Solution:

1. **Assume the Original Price**:
Let's assume the original price (SP) of an item is 100 rupees. This makes calculations easier.

**Hint**: Always start with a simple value like 100 when calculating discounts, as it simplifies the math.

2. **Calculate the First Discount**:
The first discount is 25% of 100 rupees.
\[ \text{First Discount} = 25\% \text{ of } 100 = \frac{25}{100} \times 100 = 25 \text{ rupees} \]

**Hint**: To find a percentage of a number, multiply the percentage (as a fraction) by the number.

3. **Calculate the Price After First Discount**:
Subtract the first discount from the original price.
\[ \text{Price after First Discount (SP1)} = 100 - 25 = 75 \text{ rupees} \]

**Hint**: After applying a discount, always subtract the discount amount from the original price to get the new price.

4. **Calculate the Second Discount**:
The second discount is 20% of the new price (75 rupees).
\[ \text{Second Discount} = 20\% \text{ of } 75 = \frac{20}{100} \times 75 = 15 \text{ rupees} \]

**Hint**: Always calculate the second discount based on the price after the first discount.

5. **Calculate the Price After Second Discount**:
Subtract the second discount from the price after the first discount.
\[ \text{Price after Second Discount (SP2)} = 75 - 15 = 60 \text{ rupees} \]

**Hint**: Repeat the subtraction process to find the new price after each discount.

6. **Calculate the Total Discount**:
The total discount given is the difference between the original price and the final price after both discounts.
\[ \text{Total Discount} = 100 - 60 = 40 \text{ rupees} \]

**Hint**: The total discount is simply the original price minus the final price after all discounts.

7. **Calculate the Net Discount Percentage**:
To find the net discount percentage, use the formula:
\[ \text{Net Discount Percentage} = \left(\frac{\text{Total Discount}}{\text{Original Price}}\right) \times 100 \]
\[ \text{Net Discount Percentage} = \left(\frac{40}{100}\right) \times 100 = 40\% \]

**Hint**: The discount percentage is calculated as the total discount divided by the original price, multiplied by 100 to convert it to a percentage.

### Final Answer:
The net discount percentage is **40%**.