A single discount equivalent to three successive discounts of `5%, 10%, 20%` is:

Options

A. `68.4%`
B. `35%`
C. `31.6%`
D. `32%`

Answer

To find a single discount equivalent to three successive discounts of 5%, 10%, and 20%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Successive Discounts**:
When applying successive discounts, the final price is determined by applying each discount one after the other.

2. **Convert Percentages to Decimal**:
- 5% = 0.05
- 10% = 0.10
- 20% = 0.20

3. **Calculate the Price After Each Discount**:
Assume the original price of the item is 100 (this simplifies calculations).
- After the first discount of 5%:
\[ \text{Price after 5% discount} = 100 - (5\% \text{ of } 100) = 100 - 5 = 95 \]
- After the second discount of 10%:
\[ \text{Price after 10% discount} = 95 - (10\% \text{ of } 95) = 95 - 9.5 = 85.5 \]
- After the third discount of 20%:
\[ \text{Price after 20% discount} = 85.5 - (20\% \text{ of } 85.5) = 85.5 - 17.1 = 68.4 \]

4. **Calculate the Total Discount**:
The total discount given from the original price of 100 to the final price of 68.4 is:
\[ \text{Total Discount} = 100 - 68.4 = 31.6 \]

5. **Calculate the Equivalent Single Discount Percentage**:
To find the equivalent single discount percentage:
\[ \text{Single Discount} = \left( \frac{\text{Total Discount}}{\text{Original Price}} \right) \times 100 = \left( \frac{31.6}{100} \right) \times 100 = 31.6\% \]

### Final Answer:
The single discount equivalent to three successive discounts of 5%, 10%, and 20% is **31.6%**.