On selling an article at ₹ 530,the gain is 20% more than the loss incurred on selling it at ₹ 475.In order to gain 20%, the selling price will be

Options

A. ₹ 900
B. ₹ 600
C. ₹ 700
D. ₹ 500

Answer

To solve the problem, we need to find the cost price (CP) of the article first, and then determine the selling price (SP) required to achieve a 20% gain.

### Step-by-Step Solution:

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

2. **Calculate Gain and Loss**:
- When the article is sold at ₹530, the gain can be expressed as:
\[ \text{Gain} = SP - CP = 530 - CP \]
- When the article is sold at ₹475, the loss can be expressed as:
\[ \text{Loss} = CP - SP = CP - 475 \]

3. **Set Up the Equation**:
According to the problem, the gain when sold at ₹530 is 20% more than the loss when sold at ₹475. Therefore, we can write the equation:
\[ 530 - CP = 1.2 \times (CP - 475) \]

4. **Expand and Rearrange the Equation**:
Expanding the right side gives:
\[ 530 - CP = 1.2CP - 570 \]
Now, rearranging the equation to isolate \( CP \):
\[ 530 + 570 = 1.2CP + CP \]
\[ 1100 = 2.2CP \]

5. **Solve for Cost Price**:
Dividing both sides by 2.2:
\[ CP = \frac{1100}{2.2} = 500 \]

6. **Calculate Selling Price for 20% Gain**:
To find the selling price for a 20% gain, we use the formula:
\[ SP = CP + 0.2 \times CP = 1.2 \times CP \]
Substituting the value of \( CP \):
\[ SP = 1.2 \times 500 = 600 \]

### Final Answer:
The selling price in order to gain 20% will be ₹600.