The marked price of an article is Rs 4450. If a person earns a profit of 15% after allowing a discount of 15%, then the cost price (in Rs) (correct to the nearest integer) of the article is:

Options

A. 3289
B. 3378
C. 3189
D. 3498

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Understand the problem
We are given:
- Marked Price (MP) = Rs 4450
- Discount = 15%
- Profit = 15%

### Step 2: Calculate the Selling Price (SP)
The Selling Price can be calculated after applying the discount on the Marked Price.

\[ \text{Discount} = \frac{15}{100} \times \text{MP} = \frac{15}{100} \times 4450 = 667.5 \]

\[ \text{Selling Price (SP)} = \text{MP} - \text{Discount} = 4450 - 667.5 = 3782.5 \]

### Step 3: Relate Selling Price to Cost Price
Let the Cost Price be \( CP \). Given that the profit is 15%, we can express this as:

\[ SP = CP + \text{Profit} \]

Since profit is 15% of the Cost Price, we can write:

\[ SP = CP + 0.15 \times CP = 1.15 \times CP \]

### Step 4: Substitute the Selling Price
Now we substitute the Selling Price we calculated:

\[ 3782.5 = 1.15 \times CP \]

### Step 5: Solve for Cost Price
To find \( CP \), we rearrange the equation:

\[ CP = \frac{3782.5}{1.15} \]

Calculating this gives:

\[ CP = 3289.13 \]

### Step 6: Round to the nearest integer
The problem asks for the cost price rounded to the nearest integer:

\[ CP \approx 3289 \]

### Final Answer
The cost price of the article is approximately Rs 3289.

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