Three successive discounts of 20%, 30% and 20% are given, what will be the net discount (in percentage)?

Options

A. `43.76`
B. `55.2`
C. 70
D. `83.2`

Answer

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

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

### Step 2: Convert Discounts to Fractions
Convert the percentages to fractions:
- 20% = 20/100 = 1/5
- 30% = 30/100 = 3/10
- 20% = 20/100 = 1/5

### Step 3: Calculate the Selling Price after Each Discount
Assume the marked price (MP) of an item is 100 (this makes calculations easier).

1. **First Discount (20%)**:
- Selling Price after first discount = MP × (1 - 0.20) = 100 × (4/5) = 80

2. **Second Discount (30%)**:
- Selling Price after second discount = Previous SP × (1 - 0.30) = 80 × (7/10) = 56

3. **Third Discount (20%)**:
- Selling Price after third discount = Previous SP × (1 - 0.20) = 56 × (4/5) = 44.8

### Step 4: Calculate the Net Discount
Now, we can find the net discount:
- Net Discount = MP - Final Selling Price = 100 - 44.8 = 55.2

### Step 5: Calculate the Net Discount Percentage
To find the net discount percentage:
- Net Discount Percentage = (Net Discount / MP) × 100 = (55.2 / 100) × 100 = 55.2%

### Final Answer
The net discount percentage after applying the three successive discounts is **55.2%**.

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