Marked price of an article is Rs 4200. It was sold at a discount of 16.66%. If there was a loss of 9.09%, then what was the cost price (in Rs) of the article?

Options

A. A)3500
B. B)3750
C. C)4000
D. D)3850

Answer

To solve the problem step by step, we will first identify the given values and then calculate the required cost price (CP) of the article.

### Step 1: Identify the Marked Price (MP) and Discount
- The marked price (MP) of the article is given as Rs 4200.
- The discount is given as 16.66%.

**Hint:** Remember that a discount of 16.66% can be expressed as a fraction.

### Step 2: Calculate the Selling Price (SP)
- A discount of 16.66% means the selling price (SP) can be calculated using the formula:
\[ SP = MP - (Discount \times MP) \]
- First, convert the percentage into a fraction:
\[ 16.66\% = \frac{1}{6} \]
- Therefore, the discount amount is:
\[ Discount = \frac{1}{6} \times 4200 = 700 \]
- Now, calculate the selling price:
\[ SP = 4200 - 700 = 3500 \]

**Hint:** To find the selling price, subtract the discount from the marked price.

### Step 3: Understand the Loss Percentage
- The problem states that there is a loss of 9.09%.
- This loss percentage can also be expressed as a fraction:
\[ 9.09\% = \frac{1}{11} \]

**Hint:** When there is a loss, the selling price is less than the cost price.

### Step 4: Establish the Relationship Between CP and SP
- If there is a loss of 9.09%, it means:
\[ CP - SP = Loss \]
- The relationship can be expressed as:
\[ CP : SP = 11 : 10 \]
- This means if the selling price is 10 parts, the cost price is 11 parts.

**Hint:** Use the ratio of CP to SP to express CP in terms of SP.

### Step 5: Set Up the Ratios
- We already found SP = 3500. Now we can set up the ratio:
\[ \frac{CP}{SP} = \frac{11}{10} \]
- Thus, we can express CP as:
\[ CP = SP \times \frac{11}{10} = 3500 \times \frac{11}{10} \]

**Hint:** Multiply the selling price by the ratio to find the cost price.

### Step 6: Calculate the Cost Price (CP)
- Now calculate the cost price:
\[ CP = 3500 \times 1.1 = 3850 \]

**Hint:** Ensure to multiply correctly to find the cost price.

### Conclusion
- The cost price of the article is Rs 3850.

### Final Answer
- The cost price (CP) of the article is **Rs 3850**.