What is the net discount (in percentage) for successive discounts of 20% and 30% ?

Options

A. 44
B. 56
C. 50
D. 54

Answer

To find the net discount for successive discounts of 20% and 30%, we can follow these steps:

### Step 1: Define the Discounts
Let:
- \( D_1 = 20\% \) (the first discount)
- \( D_2 = 30\% \) (the second discount)

### Step 2: Use the Net Discount Formula
The formula for calculating the net discount when two successive discounts are applied is:
\[ \text{Net Discount} = D_1 + D_2 - \left(\frac{D_1 \times D_2}{100}\right) \]

### Step 3: Substitute the Values
Substituting \( D_1 \) and \( D_2 \) into the formula:
\[ \text{Net Discount} = 20 + 30 - \left(\frac{20 \times 30}{100}\right) \]

### Step 4: Calculate the Product of Discounts
Calculate \( \frac{20 \times 30}{100} \):
\[ \frac{20 \times 30}{100} = \frac{600}{100} = 6 \]

### Step 5: Calculate the Net Discount
Now substitute this value back into the equation:
\[ \text{Net Discount} = 20 + 30 - 6 = 50 - 6 = 44\% \]

### Final Answer
The net discount for successive discounts of 20% and 30% is \( 44\% \).

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