A man sells an article at 5% above its cost price. Ifhe had bought it at 5% less than what he had paid for it and sold it at Rs 2 less, he would have gained 10%. The cost price of the article is.

Options

A. Rs 200
B. Rs 300
C. Rs 100
D. Rs 400

Answer

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

### Step 1: Selling Price Calculation
The man sells the article at 5% above its cost price. Therefore, the selling price (SP) can be calculated as:
\[ SP = CP + 0.05 \times CP = 1.05 \times CP \]

### Step 2: Adjusted Cost Price
If he had bought the article at 5% less than what he paid for it, the adjusted cost price would be:
\[ Adjusted \, CP = CP - 0.05 \times CP = 0.95 \times CP \]

### Step 3: Selling Price with 10% Gain
If he sold it for Rs 2 less than the original selling price, and he would have gained 10% on the adjusted cost price, the new selling price can be calculated as:
\[ New \, SP = Adjusted \, CP + 0.10 \times Adjusted \, CP = 1.10 \times Adjusted \, CP \]
Substituting the adjusted cost price:
\[ New \, SP = 1.10 \times (0.95 \times CP) = 1.045 \times CP \]

### Step 4: Relating the New Selling Price to the Original Selling Price
According to the problem, the new selling price is Rs 2 less than the original selling price:
\[ 1.05 \times CP - 2 = 1.045 \times CP \]

### Step 5: Solving for Cost Price
Now, we can solve for \( CP \):
\[ 1.05 \times CP - 1.045 \times CP = 2 \]
\[ (1.05 - 1.045) \times CP = 2 \]
\[ 0.005 \times CP = 2 \]
\[ CP = \frac{2}{0.005} = 400 \]

### Conclusion
The cost price of the article is Rs 400.