By selling an article at 80% of the marked price, there is a loss of 10%. If the article is sold at the marked price, the profit per cent will be

Options

A. 18.4
B. 20
C. 12.5
D. 15

Answer

To solve the problem step by step, let's break it down clearly:

### Step 1: Understand the given information
- Selling price (SP) is 80% of the marked price (MP).
- There is a loss of 10% when selling at this price.

### Step 2: Define variables
Let:
- Marked Price (MP) = 100 (for simplicity)
- Cost Price (CP) = CP (unknown for now)
- Selling Price (SP) = 80% of MP = 0.8 * 100 = 80

### Step 3: Calculate the Cost Price (CP)
Since there is a loss of 10%, the selling price is 90% of the cost price.
- Therefore, we can write the equation:

\[ SP = CP \times (1 - \text{Loss Percentage}) = CP \times (1 - 0.10) = CP \times 0.90 \]

Substituting the value of SP:

\[ 80 = CP \times 0.90 \]

Now, solve for CP:

\[ CP = \frac{80}{0.90} = \frac{800}{9} \]

### Step 4: Calculate the Profit Percentage if sold at Marked Price
If the article is sold at the marked price (MP = 100), we need to find the profit percentage.

1. Profit = Selling Price at Marked Price - Cost Price
\[ \text{Profit} = MP - CP = 100 - \frac{800}{9} \]

2. To simplify, convert 100 into a fraction with a denominator of 9:
\[ 100 = \frac{900}{9} \]
Thus,
\[ \text{Profit} = \frac{900}{9} - \frac{800}{9} = \frac{100}{9} \]

3. Profit Percentage is calculated as:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{\frac{100}{9}}{\frac{800}{9}}\right) \times 100 \]

4. Simplifying:
\[ = \left(\frac{100}{800}\right) \times 100 = \frac{1}{8} \times 100 = 12.5\% \]

### Final Answer
The profit percentage when the article is sold at the marked price is **12.5%**.

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