A trader sells an article at Rs. 3200 with `20%` loss. What will be the selling price of article if trader gains `25%` ?

Options

A. A)Rs. 5000
B. B)Rs. 3500
C. C)Rs. 4000
D. D)Rs. 4700

Answer

To solve the problem step by step, we will first find the cost price (CP) of the article based on the selling price (SP) given with a loss, and then we will calculate the new selling price when there is a gain.

### Step 1: Understand the Loss
The trader sells the article at Rs. 3200 with a 20% loss. This means that the selling price (SP) is 80% of the cost price (CP).

### Step 2: Set Up the Equation
Let the cost price (CP) be represented as 100%. Since the trader sells at a 20% loss, the selling price can be represented as:
\[ SP = CP - (20\% \text{ of } CP) = 80\% \text{ of } CP \]
Thus, we can write:
\[ 3200 = 0.8 \times CP \]

### Step 3: Calculate the Cost Price
To find the cost price (CP), we rearrange the equation:
\[ CP = \frac{3200}{0.8} \]
Calculating this gives:
\[ CP = 4000 \]

### Step 4: Calculate the New Selling Price with Gain
Now, we need to find the selling price when the trader gains 25%. This means the new selling price (SP2) will be:
\[ SP2 = CP + (25\% \text{ of } CP) = 125\% \text{ of } CP \]
So we can write:
\[ SP2 = 1.25 \times CP \]

### Step 5: Substitute the Cost Price
Now substituting the value of CP we found:
\[ SP2 = 1.25 \times 4000 \]
Calculating this gives:
\[ SP2 = 5000 \]

### Final Answer
The selling price of the article if the trader gains 25% is Rs. 5000.