Th profit percentage by way of selling an article for ₹180/- is the same as the loss percentage by selling it for ₹120/-, How much is the profit or loss percentage?

Options

A. 12
B. 16
C. 15
D. 20

Answer

To solve the problem, we need to find the profit or loss percentage when an article is sold for ₹180 and ₹120, with the condition that the profit percentage at ₹180 is equal to the loss percentage at ₹120.

### Step-by-Step Solution:

1. **Define Variables:**
Let the Cost Price (CP) of the article be ₹x.

2. **Calculate Profit when Selling Price (SP) is ₹180:**
When the article is sold for ₹180, the profit can be calculated as:
\[ \text{Profit} = \text{SP} - \text{CP} = 180 - x \]
The profit percentage is given by:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 = \left(\frac{180 - x}{x}\right) \times 100 \]

3. **Calculate Loss when Selling Price (SP) is ₹120:**
When the article is sold for ₹120, the loss can be calculated as:
\[ \text{Loss} = \text{CP} - \text{SP} = x - 120 \]
The loss percentage is given by:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{CP}}\right) \times 100 = \left(\frac{x - 120}{x}\right) \times 100 \]

4. **Set Profit Percentage Equal to Loss Percentage:**
According to the problem, the profit percentage at ₹180 is equal to the loss percentage at ₹120:
\[ \left(\frac{180 - x}{x}\right) \times 100 = \left(\frac{x - 120}{x}\right) \times 100 \]

5. **Simplify the Equation:**
We can cancel out the 100 and x (assuming x ≠ 0):
\[ 180 - x = x - 120 \]

6. **Solve for x:**
Rearranging the equation gives:
\[ 180 + 120 = 2x \implies 300 = 2x \implies x = 150 \]
So, the Cost Price (CP) is ₹150.

7. **Calculate Profit:**
Now, we can calculate the profit when selling at ₹180:
\[ \text{Profit} = 180 - 150 = 30 \]

8. **Calculate Profit Percentage:**
The profit percentage is:
\[ \text{Profit Percentage} = \left(\frac{30}{150}\right) \times 100 = 20\% \]

### Conclusion:
The profit percentage is 20%. Since the profit percentage and loss percentage are equal, the loss percentage is also 20%.