If selling price of an article is ₹ 432 and profit is 35%, then what will be the cost price of the article?

Options

A. ₹480.40
B. ₹320
C. ₹583.20
D. ₹368

Answer

To find the cost price (CP) of an article when the selling price (SP) and profit percentage are given, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Selling Price (SP) = ₹432
- Profit Percentage = 35%

2. **Understand the relationship between Selling Price, Cost Price, and Profit**:
- The formula for Selling Price when profit is involved is:
\[ SP = CP + Profit \]
- Profit can also be expressed in terms of Cost Price (CP):
\[ Profit = \frac{Profit\%}{100} \times CP \]

3. **Express Selling Price in terms of Cost Price**:
- From the above, we can rewrite the Selling Price formula as:
\[ SP = CP + \left(\frac{35}{100} \times CP\right) \]
- This simplifies to:
\[ SP = CP \left(1 + \frac{35}{100}\right) \]
- Which can be further simplified to:
\[ SP = CP \left(\frac{135}{100}\right) \]

4. **Substitute the Selling Price into the equation**:
- Now we can substitute the known Selling Price into the equation:
\[ 432 = CP \left(\frac{135}{100}\right) \]

5. **Solve for Cost Price (CP)**:
- To isolate CP, we multiply both sides by \(\frac{100}{135}\):
\[ CP = 432 \times \frac{100}{135} \]
- Calculating this gives:
\[ CP = \frac{43200}{135} \]

6. **Perform the division**:
- Now, we can simplify \(\frac{43200}{135}\):
\[ CP = 320 \]

### Final Answer:
The Cost Price (CP) of the article is ₹320.

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