A single discount equivalent to a discount series of 5%, 10%, 15% and 20% is:

Options

A. A)`43.86%`
B. B)`42.86%`
C. C)`40.86%`
D. D)`41.86%`

Answer

To find the single discount equivalent to a series of discounts of 5%, 10%, 15%, and 20%, we can use the successive discount method. Here’s a step-by-step solution:

### Step 1: Understand the Discounts
We have four successive discounts:
- First discount: 5%
- Second discount: 10%
- Third discount: 15%
- Fourth discount: 20%

### Step 2: Set a Mark Price
Let’s assume the marked price (MP) is 100 (this makes calculations easier).

### Step 3: Calculate Selling Price After Each Discount
1. **After 5% discount:**
- Selling Price (SP) = MP - (5% of MP) = 100 - (5/100 * 100) = 100 - 5 = 95

2. **After 10% discount:**
- SP = 95 - (10% of 95) = 95 - (10/100 * 95) = 95 - 9.5 = 85.5

3. **After 15% discount:**
- SP = 85.5 - (15% of 85.5) = 85.5 - (15/100 * 85.5) = 85.5 - 12.825 = 72.675

4. **After 20% discount:**
- SP = 72.675 - (20% of 72.675) = 72.675 - (20/100 * 72.675) = 72.675 - 14.535 = 58.14

### Step 4: Calculate Total Discount
Now, we can find the total discount given from the original marked price:
- Total Discount = MP - Final SP = 100 - 58.14 = 41.86

### Step 5: Calculate Equivalent Single Discount Percentage
To find the equivalent single discount percentage:
- Equivalent Discount Percentage = (Total Discount / MP) * 100
- Equivalent Discount Percentage = (41.86 / 100) * 100 = 41.86%

### Conclusion
The single discount equivalent to the series of discounts of 5%, 10%, 15%, and 20% is **41.86%**.

---