An article is marked up 37% above its cost price. If a profit of 15% is earned by selling the article, then find the discount%?

Options

A. `16.05%`
B. `17.25%`
C. `15.41%`
D. `16.98%`

Answer

To solve the problem step by step, we will use the given information about the markup and profit percentages to find the discount percentage.

### Step 1: Understand the given information
- The article is marked up 37% above its cost price (CP).
- A profit of 15% is earned by selling the article.

### Step 2: Define the variables
Let the cost price (CP) of the article be \( x \).

### Step 3: Calculate the marked price (MP)
The marked price (MP) is calculated as follows:
\[ MP = CP + (37\% \text{ of } CP) = x + 0.37x = 1.37x \]

### Step 4: Calculate the selling price (SP)
The selling price (SP) when a profit of 15% is earned is given by:
\[ SP = CP + (15\% \text{ of } CP) = x + 0.15x = 1.15x \]

### Step 5: Set up the relationship between MP, SP, and discount
We know that:
\[ MP = SP + \text{Discount} \]
Let the discount percentage be \( d\% \). The discount can be expressed as:
\[ \text{Discount} = MP - SP = 1.37x - 1.15x = 0.22x \]

### Step 6: Express the discount in terms of MP
The discount percentage can be calculated as:
\[ d\% = \left( \frac{\text{Discount}}{MP} \right) \times 100 \]
Substituting the values we have:
\[ d\% = \left( \frac{0.22x}{1.37x} \right) \times 100 \]

### Step 7: Simplify the expression
The \( x \) cancels out:
\[ d\% = \left( \frac{0.22}{1.37} \right) \times 100 \]

### Step 8: Calculate the discount percentage
Now, calculate:
\[ d\% = \left( \frac{0.22}{1.37} \right) \times 100 \approx 16.05\% \]

### Final Answer
The discount percentage is approximately **16.05%**.

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