What is the discount percentage equivalent to three successive discounts of 12%, 10% and 5%?

Options

A. 24.76
B. 26.64
C. 27
D. 26

Answer

To find the equivalent discount percentage for three successive discounts of 12%, 10%, and 5%, we can follow these steps:

### Step 1: Convert the Discounts to Decimal Form
Convert each percentage discount to its decimal form:
- 12% = 0.12
- 10% = 0.10
- 5% = 0.05

### Step 2: Calculate the Selling Price After Each Discount
Assume the marked price (MP) is 100 (this simplifies calculations). We will calculate the selling price (SP) after each discount.

1. **After the first discount (12%)**:
\[ SP_1 = MP - (12\% \text{ of } MP) = 100 - (0.12 \times 100) = 100 - 12 = 88 \]

2. **After the second discount (10%)**:
\[ SP_2 = SP_1 - (10\% \text{ of } SP_1) = 88 - (0.10 \times 88) = 88 - 8.8 = 79.2 \]

3. **After the third discount (5%)**:
\[ SP_3 = SP_2 - (5\% \text{ of } SP_2) = 79.2 - (0.05 \times 79.2) = 79.2 - 3.96 = 75.24 \]

### Step 3: Calculate the Total Discount Given
Now, we can calculate the total discount given from the original marked price:
\[ \text{Total Discount} = MP - SP_3 = 100 - 75.24 = 24.76 \]

### Step 4: Calculate the Equivalent Discount Percentage
To find the equivalent discount percentage, we use the formula:
\[ \text{Equivalent Discount Percentage} = \left( \frac{\text{Total Discount}}{\text{MP}} \right) \times 100 \]
Substituting the values:
\[ \text{Equivalent Discount Percentage} = \left( \frac{24.76}{100} \right) \times 100 = 24.76\% \]

### Conclusion
The equivalent discount percentage for the successive discounts of 12%, 10%, and 5% is **24.76%**.

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