An article is marked `66 2/3%` above the cost price and the loss incurred on selling that article is `25%` of the discount given on it. Find the discount percentage.

Options

A. `48 1/3%`
B. `53 1/3%`
C. `58 1/3%`
D. `63 1/3%`

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Understand the given information
- The article is marked at `66 2/3%` above the cost price (CP).
- The loss incurred on selling the article is `25%` of the discount given on it.

### Step 2: Convert the percentage into a fraction
The percentage `66 2/3%` can be converted to a fraction:
- `66 2/3% = 66.67% = 200/3%`

### Step 3: Assume a cost price
Let's assume the cost price (CP) of the article is `300` rupees. This is chosen for simplicity in calculations.

### Step 4: Calculate the marked price (MP)
The marked price (MP) can be calculated as follows:
- MP = CP + (66 2/3% of CP)
- MP = 300 + (200/3% of 300)
- MP = 300 + (200/3 * 300/100)
- MP = 300 + 200 = 500 rupees

### Step 5: Let the discount percentage be D%
Let the discount percentage be denoted as `D%`. The discount in rupees can be calculated as:
- Discount = (D/100) * MP = (D/100) * 500 = 5D

### Step 6: Calculate the selling price (SP)
The selling price (SP) can be calculated as:
- SP = MP - Discount
- SP = 500 - 5D

### Step 7: Calculate the loss
The loss incurred is given as `25%` of the discount. Therefore:
- Loss = 25% of Discount = (25/100) * (5D) = (5D/4)

### Step 8: Set up the equation for loss
The loss can also be expressed as:
- Loss = CP - SP
- Loss = 300 - (500 - 5D)
- Loss = 300 - 500 + 5D = 5D - 200

### Step 9: Equate the two expressions for loss
Now we can set the two expressions for loss equal to each other:
- (5D/4) = (5D - 200)

### Step 10: Solve for D
Multiply both sides by 4 to eliminate the fraction:
- 5D = 4(5D - 200)
- 5D = 20D - 800
- Rearranging gives: 20D - 5D = 800
- 15D = 800
- D = 800 / 15
- D = 53.33 (or `53 1/3%`)

### Final Answer
The discount percentage is `53 1/3%`.

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