Successive discounts of 20%, 10% and 15% are equivalent to a single discount of:

Options

A. `42.2%`
B. ` 43.5%`
C. ` 38.8%`
D. ` 44.5%`

Answer

To find the equivalent single discount for successive discounts of 20%, 10%, and 15%, we can follow these steps:

### Step 1: Understand the discounts
We have three successive discounts:
- First discount (D1): 20%
- Second discount (D2): 10%
- Third discount (D3): 15%

### Step 2: Assume an initial price
Let's assume the initial price of the article is Rs. 100. This makes calculations easier.

### Step 3: Calculate the price after the first discount (D1)
The first discount is 20% of Rs. 100.
- Amount after D1 = Initial Price × (1 - D1)
- Amount after D1 = 100 × (1 - 0.20) = 100 × 0.80 = Rs. 80

### Step 4: Calculate the price after the second discount (D2)
The second discount is 10% on the new price (Rs. 80).
- Amount after D2 = Amount after D1 × (1 - D2)
- Amount after D2 = 80 × (1 - 0.10) = 80 × 0.90 = Rs. 72

### Step 5: Calculate the price after the third discount (D3)
The third discount is 15% on the new price (Rs. 72).
- Amount after D3 = Amount after D2 × (1 - D3)
- Amount after D3 = 72 × (1 - 0.15) = 72 × 0.85 = Rs. 61.20

### Step 6: Calculate the total discount
Now, we find the total discount given from the original price of Rs. 100 to the final price of Rs. 61.20.
- Total discount = Initial Price - Final Price
- Total discount = 100 - 61.20 = Rs. 38.80

### Step 7: Calculate the equivalent single discount percentage
To find the equivalent single discount percentage, we use the formula:
- Equivalent Single Discount (%) = (Total Discount / Initial Price) × 100
- Equivalent Single Discount (%) = (38.80 / 100) × 100 = 38.80%

### Final Answer
The equivalent single discount for successive discounts of 20%, 10%, and 15% is **38.80%**.

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