If the difference between `15%` loss and `15%` gain is ₹ 450, then the cost price is:

Options

A. ₹ 1,500
B. ₹ 2,000
C. ₹ 2,200
D. ₹ 1,200

Answer

To find the cost price given that the difference between a 15% loss and a 15% gain is ₹450, we can follow these steps:

### Step 1: Define the Cost Price
Let the cost price (CP) be represented as ₹100 for simplicity.

### Step 2: Calculate Selling Price for 15% Gain
If there is a 15% gain, the selling price (SP) can be calculated as:
\[ SP_{\text{gain}} = CP + 15\% \text{ of } CP = 100 + 0.15 \times 100 = 100 + 15 = ₹115 \]

### Step 3: Calculate Selling Price for 15% Loss
If there is a 15% loss, the selling price can be calculated as:
\[ SP_{\text{loss}} = CP - 15\% \text{ of } CP = 100 - 0.15 \times 100 = 100 - 15 = ₹85 \]

### Step 4: Find the Difference Between Gain and Loss
Now, we find the difference between the selling price for gain and the selling price for loss:
\[ \text{Difference} = SP_{\text{gain}} - SP_{\text{loss}} = 115 - 85 = ₹30 \]

### Step 5: Set Up the Equation
According to the problem, this difference of ₹30 corresponds to the actual difference of ₹450. Therefore, we can set up the equation:
\[ 30 \text{ (difference)} = 450 \]

### Step 6: Find the Value of 1 Unit
To find the value of 1 unit, we divide ₹450 by 30:
\[ 1 \text{ unit} = \frac{450}{30} = ₹15 \]

### Step 7: Calculate the Cost Price
Since we initially set the cost price as ₹100, we can find the actual cost price by multiplying:
\[ \text{Cost Price} = 100 \times 15 = ₹1500 \]

### Final Answer
Thus, the cost price is ₹1500.

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