An article is marked at a price that is `20%` more than its cost price. After allowing a certain discount on the marked price, the profit reduces to `10%`. The discount percentage is :

Options

A. `12%`
B. `10(1)/(3)%`
C. `7 (1)/(3)%`
D. `8 (1)/(3)%`

Answer

To solve the problem step by step, let's denote the cost price (CP) of the article as \( CP = 100 \) (for simplicity).

### Step 1: Calculate the Marked Price (MP)
The article is marked at a price that is 20% more than its cost price. Therefore, the marked price (MP) can be calculated as:
\[ MP = CP + 20\% \text{ of } CP = 100 + 20 = 120 \]

### Step 2: Determine the Selling Price (SP) for 10% Profit
After allowing a certain discount on the marked price, the profit reduces to 10%. The selling price (SP) can be calculated as:
\[ SP = CP + 10\% \text{ of } CP = 100 + 10 = 110 \]

### Step 3: Relate Selling Price to Marked Price and Discount
Let the discount be \( d \). The selling price is also given by the equation:
\[ SP = MP - d \]
Substituting the values we have:
\[ 110 = 120 - d \]

### Step 4: Solve for the Discount
Rearranging the equation to find \( d \):
\[ d = 120 - 110 = 10 \]

### Step 5: Calculate the Discount Percentage
The discount percentage can be calculated using the formula:
\[ \text{Discount Percentage} = \left( \frac{d}{MP} \right) \times 100 = \left( \frac{10}{120} \right) \times 100 = \frac{1000}{120} = \frac{100}{12} = 8.33\% \]

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