A dealer sold an article at 6% loss. Had he sold it for ₹ 64 more, he would have made a profit of 10%. Then the cost of the article is

एक विक्रेता ने किसी वस्तु को 6% की हानि पर बेचा। यदि उसने उस वस्तु को Rs 64 अधिक में बेचा होता तो उसे 10% का लाभ होता। वस्तु की लागत कितनी है ?

Options

A. Rs 400
B. Rs 200
C. Rs 164
D. Rs 464

Explanation

To find the cost of the article, let's break down the problem step by step.

### Step 1: Define the Variables
Let the cost price (CP) of the article be represented as \( x \).

### Step 2: Calculate Selling Price at 6% Loss
If the dealer sells the article at a 6% loss, the selling price (SP) can be calculated as:
\[ \text{SP at 6% loss} = x - 0.06x = 0.94x \]

### Step 3: Calculate Selling Price for 10% Profit
If the dealer had sold the article for ₹64 more, he would have made a profit of 10%. The selling price for a 10% profit is:
\[ \text{SP at 10% profit} = x + 0.10x = 1.10x \]

### Step 4: Set Up the Equation
According to the problem, the difference between the selling price at 10% profit and the selling price at 6% loss is ₹64. Therefore, we can set up the equation:
\[ 1.10x - 0.94x = 64 \]

### Step 5: Simplify the Equation
Now, simplify the left side of the equation:
\[ (1.10 - 0.94)x = 64 \]
\[ 0.16x = 64 \]

### Step 6: Solve for x
To find \( x \), divide both sides by 0.16:
\[ x = \frac{64}{0.16} \]
\[ x = 400 \]

### Conclusion
The cost of the article is ₹400.

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