By selling an article for Rs 382.50 a man loses 15%. Find its cost price.

Answer

To find the cost price of the article given that it was sold for Rs 382.50 with a loss of 15%, we can follow these steps:

### Step 1: Understand the relationship between Selling Price (SP), Cost Price (CP), and Loss Percentage
The formula to find the Cost Price when there is a loss is:
\[ CP = \frac{SP}{(100 - \text{Loss Percentage})} \times 100 \]

### Step 2: Identify the values
From the question:
- Selling Price (SP) = Rs 382.50
- Loss Percentage = 15%

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the formula:
\[ CP = \frac{382.50}{(100 - 15)} \times 100 \]

### Step 4: Calculate the denominator
Calculate \(100 - 15\):
\[ 100 - 15 = 85 \]

### Step 5: Substitute the denominator back into the formula
Now we can rewrite the formula:
\[ CP = \frac{382.50}{85} \times 100 \]

### Step 6: Calculate the division
Now, calculate \( \frac{382.50}{85} \):
\[ \frac{382.50}{85} = 4.5 \]

### Step 7: Multiply by 100
Now multiply by 100 to find the Cost Price:
\[ CP = 4.5 \times 100 = 450 \]

### Final Answer
The Cost Price (CP) of the article is Rs 450.

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