What will be the net discount (in per cent) 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:

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

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

### Step-by-Step Solution:

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

2. **Calculate the Remaining Amount after Each Discount**:
- After the first discount (10%):
\[ \text{Remaining} = 100 - 10 = 90 \]
- After the second discount (20% on the remaining amount):
\[ \text{Remaining} = 90 - (20\% \text{ of } 90) = 90 - 18 = 72 \]
- After the third discount (30% on the remaining amount):
\[ \text{Remaining} = 72 - (30\% \text{ of } 72) = 72 - 21.6 = 50.4 \]

3. **Calculate the Net Discount**:
- The original price is 100, and the final price after all discounts is 50.4.
- Therefore, the net discount can be calculated as:
\[ \text{Net Discount} = 100 - 50.4 = 49.6 \]

4. **Convert to Percentage**:
- The net discount percentage is:
\[ \text{Net Discount Percentage} = \frac{\text{Net Discount}}{\text{Original Price}} \times 100 = \frac{49.6}{100} \times 100 = 49.6\% \]

### Final Answer:
The net discount after giving three successive discounts of 10%, 20%, and 30% is **49.6%**.