When an article is sold for Rs. 388, there is a loss of 3%. What is the selling price (in Rs.) of the article, if it is sold at a gain of 18%?

Options

A. 444
B. 472
C. 432
D. 460

Answer

To solve the problem step by step, we need to determine the cost price of the article first and then calculate the selling price when it is sold at an 18% gain.

### Step 1: Understand the relationship between selling price, cost price, and loss percentage.
When an article is sold at a loss, the selling price (SP) can be calculated using the formula:
\[ SP = CP \times \left(1 - \frac{Loss\%}{100}\right) \]
Where:
- SP = Selling Price
- CP = Cost Price
- Loss% = Percentage of loss

### Step 2: Set up the equation using the given information.
We know that when the article is sold for Rs. 388, there is a loss of 3%. Therefore, we can write:
\[ 388 = CP \times \left(1 - \frac{3}{100}\right) \]
\[ 388 = CP \times 0.97 \]

### Step 3: Solve for the cost price (CP).
To find the cost price, rearrange the equation:
\[ CP = \frac{388}{0.97} \]
Calculating this gives:
\[ CP = 400 \]

### Step 4: Calculate the selling price at an 18% gain.
Now that we have the cost price, we can find the selling price when there is an 18% gain. The formula for selling price at a gain is:
\[ SP = CP \times \left(1 + \frac{Gain\%}{100}\right) \]
Substituting the values:
\[ SP = 400 \times \left(1 + \frac{18}{100}\right) \]
\[ SP = 400 \times 1.18 \]
Calculating this gives:
\[ SP = 472 \]

### Final Answer:
The selling price of the article, if it is sold at a gain of 18%, is Rs. 472.

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