The profit earned after selling an article for ₹878 is the same as loss incuned after selling the article for ₹636. What is the cost price of the article?

Options

A. ₹797
B. ₹787
C. ₹767
D. ₹757

Explanation

To find the cost price of the article, we can use the information given in the question. Let's denote the cost price of the article as CP.

1. **Understanding Profit and Loss**:
- When the article is sold for ₹878, the profit is earned.
- When the article is sold for ₹636, a loss is incurred.
- According to the question, the profit from selling at ₹878 is equal to the loss from selling at ₹636.

2. **Setting Up the Equations**:
- Profit when sold for ₹878:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = 878 - CP \]
- Loss when sold for ₹636:
\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} = CP - 636 \]
- According to the problem, these two amounts are equal:
\[ 878 - CP = CP - 636 \]

3. **Solving the Equation**:
- Rearranging the equation:
\[ 878 + 636 = 2CP \]
- Adding the values:
\[ 1514 = 2CP \]
- Dividing both sides by 2 to find CP:
\[ CP = \frac{1514}{2} = 757 \]

4. **Conclusion**:
- The cost price of the article is ₹757.

### Summary of Steps:
1. Understand the relationship between profit and loss.
2. Set up the equations based on selling prices and cost price.
3. Solve the equation to find the cost price.