If the profit on selling an article for Rs 425 is the same as the loss on selling it for Rs 355 then the cost price of the article is

Options

A. a)Rs 410
B. b)Rs 380
C. c)Rs 400
D. d)Rs 390

Answer

To find the cost price (CP) of the article given that the profit from selling it for Rs 425 is equal to the loss from selling it for Rs 355, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables**:
Let the cost price (CP) of the article be \( X \).

2. **Identify Selling Prices**:
- Selling Price (SP) when there is a profit: \( SP_1 = 425 \)
- Selling Price (SP) when there is a loss: \( SP_2 = 355 \)

3. **Write Profit and Loss Equations**:
- Profit when selling at Rs 425:
\[ \text{Profit} = SP_1 - CP = 425 - X \]
- Loss when selling at Rs 355:
\[ \text{Loss} = CP - SP_2 = X - 355 \]

4. **Set Profit Equal to Loss**:
According to the problem, the profit is equal to the loss:
\[ 425 - X = X - 355 \]

5. **Solve for X**:
Rearranging the equation:
\[ 425 + 355 = X + X \]
\[ 780 = 2X \]
Dividing both sides by 2:
\[ X = \frac{780}{2} = 390 \]

6. **Conclusion**:
The cost price of the article is \( \text{Rs } 390 \).

### Final Answer:
The cost price of the article is Rs 390.

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