An article is purchased for Rs 450 and sold for Rs 500. Find the gain percentage?

Answer

To find the gain percentage when an article is purchased for Rs. 450 and sold for Rs. 500, we can follow these steps:

### Step 1: Identify the Cost Price (CP) and Selling Price (SP)
- **Cost Price (CP)** = Rs. 450
- **Selling Price (SP)** = Rs. 500

### Step 2: Calculate the Profit
Profit can be calculated using the formula:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
Substituting the values:
\[ \text{Profit} = 500 - 450 = 50 \]

### Step 3: Calculate the Gain Percentage
The gain percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Gain Percentage} = \left( \frac{50}{450} \right) \times 100 \]

### Step 4: Simplify the Calculation
Now, simplify the fraction:
\[ \frac{50}{450} = \frac{5}{45} = \frac{1}{9} \]
Now multiply by 100:
\[ \text{Gain Percentage} = \left( \frac{1}{9} \right) \times 100 = \frac{100}{9} \]

### Step 5: Final Answer
Thus, the gain percentage is:
\[ \text{Gain Percentage} \approx 11.11\% \]