Giving two successive discounts of 25% is equal to giving one discount of ________%.

Options

A. 43.75
B. 56.25
C. 50
D. 45

Answer

To find the equivalent single discount for two successive discounts of 25%, we can use the formula for successive discounts:

\[ \text{Equivalent Discount} = x + y - \frac{xy}{100} \]

Where:
- \( x \) is the first discount percentage
- \( y \) is the second discount percentage

### Step-by-Step Solution:

1. **Identify the Discounts**:
- Let \( x = 25\% \)
- Let \( y = 25\% \)

2. **Substitute the Values into the Formula**:
\[ \text{Equivalent Discount} = 25 + 25 - \frac{25 \times 25}{100} \]

3. **Calculate the Product of the Discounts**:
\[ \frac{25 \times 25}{100} = \frac{625}{100} = 6.25 \]

4. **Combine the Values**:
\[ \text{Equivalent Discount} = 25 + 25 - 6.25 \]
\[ = 50 - 6.25 = 43.75 \]

5. **Conclusion**:
The equivalent single discount for two successive discounts of 25% is \( 43.75\% \).

### Final Answer:
The answer is \( 43.75\% \).

---