The marked price of an article is Rs 500. A shopkeeper gives a discount of 5% and still makes a profit of 25%. The cost price of the article is.
एक वस्तु का अंकित मूल्य Rs 500 है। दुकानदार 5% की छूट देता है और फिर भी 25% का लाभ कमाता है। वस्तु का क्रय मूल्य है:

Options

A. Rs 300
B. Rs 376
C. Rs 384
D. Rs 380

Explanation

To find the cost price of the article, we can follow these steps:

### Step 1: Calculate the Selling Price after Discount
The marked price (MP) of the article is Rs 500. The shopkeeper gives a discount of 5%.

To find the selling price (SP) after the discount, we can use the formula:
\[ \text{SP} = \text{MP} - \left(\frac{\text{Discount \%}}{100} \times \text{MP}\right) \]
Substituting the values:
\[ \text{SP} = 500 - \left(\frac{5}{100} \times 500\right) \]
\[ \text{SP} = 500 - 25 = 475 \]

### Step 2: Relate Selling Price to Cost Price
We know that the selling price is also related to the cost price (CP) and profit percentage. The profit percentage is 25%.

The relationship can be expressed as:
\[ \text{SP} = \text{CP} + \left(\frac{\text{Profit \%}}{100} \times \text{CP}\right) \]
This can be rewritten as:
\[ \text{SP} = \text{CP} \left(1 + \frac{25}{100}\right) = \text{CP} \times 1.25 \]

### Step 3: Substitute Selling Price into the Equation
Now, we substitute the selling price we calculated in Step 1 into this equation:
\[ 475 = \text{CP} \times 1.25 \]

### Step 4: Solve for Cost Price
To find the cost price, we rearrange the equation:
\[ \text{CP} = \frac{475}{1.25} \]
Calculating this gives:
\[ \text{CP} = 380 \]

### Conclusion
The cost price of the article is Rs 380.

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