A dealer marks his goods 20% above their cost price. He then allows some discount on marked price so that he makes a profit of 10%. The rate of discount is

Options

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

Answer

To solve the problem step by step, follow these instructions:

### Step 1: Understand the Cost Price and Marked Price
Let the cost price (CP) of the goods be \(100\) rupees.

### Step 2: Calculate the Marked Price
The dealer marks his goods 20% above the cost price. Therefore, the marked price (MP) can be calculated as:
\[ MP = CP + (20\% \text{ of } CP) = 100 + (0.20 \times 100) = 100 + 20 = 120 \text{ rupees} \]

### Step 3: Calculate the Selling Price for Desired Profit
The dealer wants to make a profit of 10%. Therefore, the selling price (SP) can be calculated as:
\[ SP = CP + (10\% \text{ of } CP) = 100 + (0.10 \times 100) = 100 + 10 = 110 \text{ rupees} \]

### Step 4: Determine the Discount
To find the discount, we need to calculate how much discount is required to go from the marked price to the selling price:
\[ \text{Discount} = MP - SP = 120 - 110 = 10 \text{ rupees} \]

### Step 5: Calculate the Rate of Discount
The rate of discount can be calculated as a percentage of the marked price:
\[ \text{Rate of Discount} = \left(\frac{\text{Discount}}{MP}\right) \times 100 = \left(\frac{10}{120}\right) \times 100 = \frac{1000}{120} = \frac{25}{3} \approx 8.33\% \]

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

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