What will be the net discount (in percentage) after two successive discounts of 40% and 20%?

Options

A. 60
B. 68
C. 52
D. 42

Answer

To find the net discount after two successive discounts of 40% and 20%, we can use the formula for calculating the net discount when two percentages are applied successively.

### Step-by-Step Solution:

1. **Identify the Discounts:**
- Let the first discount be \( A = 40\% \)
- Let the second discount be \( B = 20\% \)

2. **Use the Formula for Net Discount:**
The formula for calculating the net discount \( D \) when two successive discounts \( A \) and \( B \) are applied is:
\[ D = A + B - \frac{A \times B}{100} \]

3. **Substitute the Values:**
Substitute \( A \) and \( B \) into the formula:
\[ D = 40 + 20 - \frac{40 \times 20}{100} \]

4. **Calculate the Product of Discounts:**
Calculate \( \frac{40 \times 20}{100} \):
\[ \frac{40 \times 20}{100} = \frac{800}{100} = 8 \]

5. **Complete the Calculation:**
Now substitute back into the equation:
\[ D = 40 + 20 - 8 \]
\[ D = 60 - 8 = 52 \]

6. **Final Result:**
The net discount after two successive discounts of 40% and 20% is:
\[ \text{Net Discount} = 52\% \]