An article is marked at a price which is 1.2 times its cost price. After allowing certain dis-count, the profit reduces to 10%. The discount percen is :

Options

A. `8 1/3`
B. 9
C. 10
D. `8 2/3`

Answer

To solve the problem step by step, we need to find the discount percentage on the marked price (MP) of an article given its cost price (CP) and the profit percentage after discount.

### Step 1: Define the Cost Price
Let the cost price (CP) of the article be \(100\).

### Step 2: Calculate the Marked Price
The marked price (MP) is given as 1.2 times the cost price. Therefore, we can calculate it as:
\[ MP = 1.2 \times CP = 1.2 \times 100 = 120 \]

### Step 3: Determine the Selling Price for 10% Profit
The selling price (SP) is determined by the profit percentage. A profit of 10% on the cost price means:
\[ SP = CP + \text{Profit} = CP + \left(\frac{10}{100} \times CP\right) = 100 + 10 = 110 \]

### Step 4: Calculate the Discount
The discount can be calculated by subtracting the selling price from the marked price:
\[ \text{Discount} = MP - SP = 120 - 110 = 10 \]

### Step 5: Calculate the Discount Percentage
To find the discount percentage, we use the formula:
\[ \text{Discount Percentage} = \left(\frac{\text{Discount}}{MP}\right) \times 100 \]
Substituting the values we have:
\[ \text{Discount Percentage} = \left(\frac{10}{120}\right) \times 100 = \frac{1000}{120} = \frac{25}{3} \approx 8.33\% \]

### Step 6: Convert to Mixed Fraction
To convert \( \frac{25}{3} \) to a mixed fraction:
\[ \frac{25}{3} = 8 \frac{1}{3} \]

### Final Answer
The discount percentage is \( 8 \frac{1}{3} \% \).