What will be the net discount (in percentage) after two successive discounts of 50% and 50% ?

Options

A. 85
B. 75
C. 100
D. 95

Answer

To find the net discount after two successive discounts of 50% each, we can use the formula for calculating the net discount percentage when two discounts are applied successively.

### Step-by-Step Solution:

1. **Identify the Discounts**:
Let D1 = 50% (first discount) and D2 = 50% (second discount).

2. **Use the Net Discount Formula**:
The formula for calculating the net discount percentage when two successive discounts are applied is:
\[ \text{Net Discount} = D1 + D2 - \left(\frac{D1 \times D2}{100}\right) \]

3. **Substitute the Values**:
Substitute D1 and D2 into the formula:
\[ \text{Net Discount} = 50 + 50 - \left(\frac{50 \times 50}{100}\right) \]

4. **Calculate the Product**:
Calculate \(50 \times 50\):
\[ 50 \times 50 = 2500 \]

5. **Divide by 100**:
Now divide by 100:
\[ \frac{2500}{100} = 25 \]

6. **Final Calculation**:
Substitute this value back into the net discount formula:
\[ \text{Net Discount} = 50 + 50 - 25 \]
\[ \text{Net Discount} = 100 - 25 = 75 \]

7. **Conclusion**:
Therefore, the net discount after two successive discounts of 50% each is:
\[ \text{Net Discount} = 75\% \]

### Final Answer:
The net discount after two successive discounts of 50% is **75%**.