A trader sold an article at `12%` loss. Had he sold the article for ₹109.20 more, he would have earned a profit of `30%`. What would be .the selling price of the article if the article is sold at `40%` profit?

Options

A. ₹364
B. ₹392
C. ₹350
D. ₹332

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define the Cost Price
Let the cost price (CP) of the article be \(100X\).

### Step 2: Calculate Selling Price at 12% Loss
If the trader sells the article at a 12% loss, the selling price (SP) can be calculated as:
\[ SP = CP - (12\% \text{ of } CP) = 100X - 12X = 88X \]

### Step 3: Calculate Selling Price for 30% Profit
If the trader had sold the article for ₹109.20 more, he would have made a 30% profit. The selling price at 30% profit is:
\[ SP = CP + (30\% \text{ of } CP) = 100X + 30X = 130X \]

### Step 4: Set Up the Equation
According to the problem, if he sells it for ₹109.20 more than the selling price at a 12% loss, it equals the selling price at a 30% profit:
\[ 88X + 109.20 = 130X \]

### Step 5: Solve for X
Rearranging the equation:
\[ 109.20 = 130X - 88X \]
\[ 109.20 = 42X \]
Now, divide both sides by 42 to find \(X\):
\[ X = \frac{109.20}{42} = 2.6 \]

### Step 6: Calculate the Cost Price
Now, substituting \(X\) back to find the cost price:
\[ CP = 100X = 100 \times 2.6 = 260 \]

### Step 7: Calculate Selling Price at 40% Profit
To find the selling price when the article is sold at a 40% profit:
\[ SP = CP + (40\% \text{ of } CP) = 100X + 40X = 140X \]
Substituting \(X\):
\[ SP = 140 \times 2.6 = 364 \]

### Final Answer
The selling price of the article if sold at a 40% profit is **₹364**.

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