The profit earned on selling an article at ₹720 is half of the loss incurred on selling the same article at ₹ 360. What is the cost price of the article .

Options

A. ₹ 540
B. ₹ 600
C. ₹ 480
D. ₹ 420

Answer

To find the cost price of the article, we can set up the problem using the information given about profit and loss.

### Step-by-Step Solution:

1. **Define Variables:**
Let the cost price of the article be \( CP \).
Let the profit when selling at ₹720 be \( P \).
Let the loss when selling at ₹360 be \( L \).

2. **Set Up Equations:**
From the problem, we know:
- Selling Price 1 (SP1) = ₹720
- Selling Price 2 (SP2) = ₹360
- The profit earned on selling at ₹720 is half of the loss incurred on selling at ₹360.

This can be expressed as:
\[ P = \frac{1}{2} L \]

3. **Express Profit and Loss in Terms of Cost Price:**
- Profit when selling at ₹720:
\[ P = SP1 - CP = 720 - CP \]
- Loss when selling at ₹360:
\[ L = CP - SP2 = CP - 360 \]

4. **Substitute the Expressions into the Profit-Loss Relationship:**
Substitute \( P \) and \( L \) into the equation \( P = \frac{1}{2} L \):
\[ 720 - CP = \frac{1}{2} (CP - 360) \]

5. **Clear the Fraction:**
Multiply both sides by 2 to eliminate the fraction:
\[ 2(720 - CP) = CP - 360 \]
This simplifies to:
\[ 1440 - 2CP = CP - 360 \]

6. **Rearrange the Equation:**
Combine like terms:
\[ 1440 + 360 = CP + 2CP \]
\[ 1800 = 3CP \]

7. **Solve for Cost Price:**
Divide both sides by 3:
\[ CP = \frac{1800}{3} = 600 \]

### Conclusion:
The cost price of the article is ₹600.