Two successive discounts of 20% and 5% are equivalent to a single discount of

Options

A. 0.25
B. 0.24
C. 0.18
D. 0.15

Answer

To find the equivalent single discount of two successive discounts of 20% and 5%, we can follow these steps:

### Step-by-Step Solution:

1. **Assume a Cost Price**:
Let's assume the cost price (CP) of the article is ₹100. This makes calculations easier.

**Hint**: Always start by assuming a base value for the cost price to simplify percentage calculations.

2. **Calculate the First Discount**:
The first discount is 20%.
- Discount Amount = 20% of ₹100 = (20/100) * 100 = ₹20.
- Selling Price after first discount (SP1) = Cost Price - Discount Amount = ₹100 - ₹20 = ₹80.

**Hint**: To find the selling price after a discount, subtract the discount amount from the original price.

3. **Calculate the Second Discount**:
The second discount is 5%, which is applied to the new selling price (SP1).
- Discount Amount = 5% of ₹80 = (5/100) * 80 = ₹4.
- Selling Price after second discount (SP2) = SP1 - Discount Amount = ₹80 - ₹4 = ₹76.

**Hint**: Always apply the second discount to the new selling price after the first discount.

4. **Calculate Total Discount**:
The total discount given is the sum of both discounts.
- Total Discount = First Discount + Second Discount = ₹20 + ₹4 = ₹24.

**Hint**: To find the total discount, simply add the amounts of all discounts applied.

5. **Calculate the Equivalent Single Discount Percentage**:
The equivalent single discount percentage can be calculated using the formula:
\[ \text{Single Discount Percentage} = \left(\frac{\text{Total Discount}}{\text{Cost Price}}\right) \times 100 \]
- Substituting the values:
\[ \text{Single Discount Percentage} = \left(\frac{24}{100}\right) \times 100 = 24\%. \]

**Hint**: The single discount percentage reflects the total discount as a percentage of the original cost price.

### Final Answer:
The equivalent single discount of two successive discounts of 20% and 5% is **24%**.