An article of cost price Rs. 8,000 is marked at Rs. 11,200. After allowing a discount of x% a profit of 12% is made. The value of x is

Options

A. `21%`
B. `20%`
C. `22%`
D. `23%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the given values
- Cost Price (CP) = Rs. 8000
- Marked Price (MP) = Rs. 11200
- Profit Percentage = 12%

### Step 2: Calculate the Selling Price (SP)
To find the Selling Price when a profit of 12% is made, we use the formula:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]
Profit can be calculated as:
\[ \text{Profit} = \frac{\text{Profit Percentage}}{100} \times \text{Cost Price (CP)} \]
Calculating the profit:
\[ \text{Profit} = \frac{12}{100} \times 8000 = 960 \]
Now, substituting back to find SP:
\[ \text{SP} = 8000 + 960 = 8960 \]

### Step 3: Calculate the Discount
The discount can be calculated using the formula:
\[ \text{Discount} = \text{Marked Price (MP)} - \text{Selling Price (SP)} \]
Substituting the values:
\[ \text{Discount} = 11200 - 8960 = 2240 \]

### Step 4: Calculate the Discount Percentage (x%)
The discount percentage can be calculated using the formula:
\[ \text{Discount Percentage (x)} = \left( \frac{\text{Discount}}{\text{Marked Price (MP)}} \right) \times 100 \]
Substituting the values:
\[ x = \left( \frac{2240}{11200} \right) \times 100 \]
Calculating the percentage:
\[ x = \left( \frac{2240 \div 112}{11200 \div 112} \right) \times 100 = \left( \frac{20}{100} \right) \times 100 = 20 \]

### Final Answer
The value of x is **20%**.

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