Successive discounts of 30%, 20% and 5% amount to a single discount of .

Options

A. 0.46
B. 0.462
C. 0.532
D. 0.47

Answer

To solve the problem of finding the single discount equivalent to successive discounts of 30%, 20%, and 5%, we can follow these steps:

### Step 1: Understand the Discounts
We have three successive discounts:
- First discount: 30%
- Second discount: 20%
- Third discount: 5%

### Step 2: Convert Discounts to Decimal
Convert each percentage discount into a decimal fraction:
- 30% = 0.30
- 20% = 0.20
- 5% = 0.05

### Step 3: Calculate the Selling Price After Each Discount
Assume the marked price (MP) is 100 (for simplicity):
1. After the first discount of 30%:
\[ \text{Selling Price (SP)} = \text{MP} - \text{Discount} = 100 - (30\% \text{ of } 100) = 100 - 30 = 70 \]

2. After the second discount of 20% on the new SP (70):
\[ \text{SP} = 70 - (20\% \text{ of } 70) = 70 - 14 = 56 \]

3. After the third discount of 5% on the new SP (56):
\[ \text{SP} = 56 - (5\% \text{ of } 56) = 56 - 2.8 = 53.2 \]

### Step 4: Calculate the Total Discount
The total discount given from the original marked price of 100 to the final selling price of 53.2 is:
\[ \text{Total Discount} = \text{MP} - \text{Final SP} = 100 - 53.2 = 46.8 \]

### Step 5: Calculate the Single Equivalent Discount
To find the single equivalent discount percentage:
\[ \text{Single Discount} = \frac{\text{Total Discount}}{\text{MP}} = \frac{46.8}{100} = 0.468 \]

### Step 6: Round the Answer
Rounding 0.468 to two decimal places gives us 0.47.

### Final Answer
The single discount equivalent to successive discounts of 30%, 20%, and 5% is **0.47**.

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