A man sold an article for र 322, gaining l/6th of his outlay. Find the cost price of the article.

Options

A. र 300
B. र 376
C. र 175
D. र 276

Answer

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

### Step-by-Step Solution:

1. **Identify Given Information:**
- Selling Price (SP) = Rs. 322
- Profit = \( \frac{1}{6} \) of Cost Price (CP)

2. **Set Up the Profit Formula:**
- Profit can be expressed as:
\[ \text{Profit} = \text{SP} - \text{CP} \]
- From the problem, we know:
\[ \text{Profit} = \frac{1}{6} \times \text{CP} \]

3. **Equate the Two Expressions for Profit:**
- We can set the two expressions for profit equal to each other:
\[ \frac{1}{6} \times \text{CP} = \text{SP} - \text{CP} \]
- Substitute SP with 322:
\[ \frac{1}{6} \times \text{CP} = 322 - \text{CP} \]

4. **Rearrange the Equation:**
- Move CP to one side:
\[ \frac{1}{6} \times \text{CP} + \text{CP} = 322 \]
- This can be rewritten as:
\[ \frac{1}{6} \times \text{CP} + \frac{6}{6} \times \text{CP} = 322 \]
- Combine the terms:
\[ \frac{7}{6} \times \text{CP} = 322 \]

5. **Solve for CP:**
- To find CP, multiply both sides by \( \frac{6}{7} \):
\[ \text{CP} = 322 \times \frac{6}{7} \]
- Calculate \( 322 \times 6 \):
\[ 322 \times 6 = 1932 \]
- Now divide by 7:
\[ \text{CP} = \frac{1932}{7} = 276 \]

6. **Conclusion:**
- The cost price of the article is Rs. 276.

### Final Answer:
The cost price of the article is Rs. 276.