A single discount equivalent to a discount series of 30%, 20% and 10% is

Options

A. `49.6%`
B. `50.4%`
C. `53.0%`
D. `47.0%`

Explanation

To find the single discount equivalent to a series of discounts of 30%, 20%, and 10%, we can use the formula for calculating the net discount when applying consecutive discounts.

### Step-by-Step Solution:

1. **Identify the Discounts**:
Let the discounts be:
- D1 = 30%
- D2 = 20%
- D3 = 10%

2. **Calculate the Net Discount for the First Two Discounts (D1 and D2)**:
We use the formula:
\[ \text{Net Discount} = D1 + D2 - \frac{D1 \times D2}{100} \]
Substituting the values:
\[ \text{Net Discount} = 30 + 20 - \frac{30 \times 20}{100} \]
\[ = 50 - \frac{600}{100} \]
\[ = 50 - 6 = 44\% \]
So, the net discount after the first two discounts is 44%.

3. **Calculate the Net Discount Including the Third Discount (D3)**:
Now we need to include the third discount (D3 = 10%) using the net discount calculated from the first two discounts (D' = 44%):
\[ \text{Net Discount} = D' + D3 - \frac{D' \times D3}{100} \]
Substituting the values:
\[ \text{Net Discount} = 44 + 10 - \frac{44 \times 10}{100} \]
\[ = 54 - \frac{440}{100} \]
\[ = 54 - 4.4 = 49.6\% \]

4. **Final Result**:
The single discount equivalent to a discount series of 30%, 20%, and 10% is **49.6%**.