What will be the net discount (in percent) after giving three successive discounts of 10%, 20% and 30%?

Options

A. 50.4
B. 49.6
C. 45.3
D. 48.4

Answer

To find the net discount after giving three successive discounts of 10%, 20%, and 30%, we can use the formula for successive discounts. The formula is:

\[ \text{Net Discount} = 100 - \left( (100 - A) \times (100 - B) \times (100 - C) \right) / 100^2 \]

Where A, B, and C are the percentages of the successive discounts.

### Step-by-Step Solution:

1. **Identify the Discounts**:
- Let A = 10%
- Let B = 20%
- Let C = 30%

2. **Convert Discounts to Decimal**:
- \(100 - A = 100 - 10 = 90\)
- \(100 - B = 100 - 20 = 80\)
- \(100 - C = 100 - 30 = 70\)

3. **Calculate the Product**:
- Now, we calculate the product of these values:
\[ (100 - A)(100 - B)(100 - C) = 90 \times 80 \times 70 \]

4. **Perform the Multiplication**:
- First, calculate \(90 \times 80 = 7200\)
- Then, calculate \(7200 \times 70 = 504000\)

5. **Calculate the Net Value**:
- Now, we need to divide this product by \(100^2\):
\[ \frac{504000}{10000} = 50.4 \]

6. **Calculate the Net Discount**:
- Finally, we find the net discount:
\[ \text{Net Discount} = 100 - 50.4 = 49.6 \]

Thus, the net discount after giving three successive discounts of 10%, 20%, and 30% is **49.6%**.