Find the single discount which is equivalent to two successive discounts of 20% and 5%.

Answer

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

### Step 1: Understand the Discounts
We have two successive discounts:
1. First discount = 20%
2. Second discount = 5%

### Step 2: Calculate the Selling Price After the First Discount
Let's assume the marked price (MP) is 100 (for simplicity).

- First discount amount = 20% of 100
\[ \text{First discount} = \frac{20}{100} \times 100 = 20 \]
- Selling price after the first discount (SP1) = Marked Price - First Discount
\[ SP1 = 100 - 20 = 80 \]

### Step 3: Calculate the Selling Price After the Second Discount
Now apply the second discount of 5% on the new selling price (SP1).

- Second discount amount = 5% of 80
\[ \text{Second discount} = \frac{5}{100} \times 80 = 4 \]
- Selling price after the second discount (SP2) = SP1 - Second Discount
\[ SP2 = 80 - 4 = 76 \]

### Step 4: Calculate the Total Discount
Now, we need to find the total discount from the original marked price.

- Total discount = Marked Price - Selling Price after both discounts
\[ \text{Total discount} = 100 - 76 = 24 \]

### Step 5: Calculate the Equivalent Single Discount Percentage
To find the equivalent single discount percentage, we use the formula:
\[ \text{Equivalent Discount Percentage} = \left( \frac{\text{Total Discount}}{\text{Marked Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Equivalent Discount Percentage} = \left( \frac{24}{100} \right) \times 100 = 24\% \]

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

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