On selling an article for Rs 3450, the gain is 20% more than the loss incurred on selling it for Rs 3120. If the article is sold for Rs 3858.6, then the profit percentage is

Options

A. 21
B. 18
C. 16.66
D. 20

Answer

To solve the problem step by step, we need to establish the relationships between the selling prices, cost price, gain, and loss.

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

### Step 2: Calculate Loss on Selling at Rs. 3120
When the article is sold for Rs. 3120, the loss incurred can be calculated as:
Loss = Cost Price - Selling Price
Loss = X - 3120

### Step 3: Calculate Gain on Selling at Rs. 3450
When the article is sold for Rs. 3450, the gain can be calculated as:
Gain = Selling Price - Cost Price
Gain = 3450 - X

### Step 4: Set Up the Relationship Between Gain and Loss
According to the problem, the gain is 20% more than the loss incurred when sold for Rs. 3120. This can be expressed as:
Gain = Loss + 20% of Loss
Gain = Loss + 0.2 * Loss
Gain = 1.2 * Loss

Substituting the expressions for gain and loss:
3450 - X = 1.2 * (X - 3120)

### Step 5: Solve the Equation
Now, we will solve the equation:
3450 - X = 1.2X - 3744

Combine like terms:
3450 + 3744 = 1.2X + X
7194 = 2.2X

Now, divide both sides by 2.2 to find X:
X = 7194 / 2.2
X = 3270

### Step 6: Calculate Profit When Sold for Rs. 3858.6
Now that we have the cost price, we can calculate the profit when the article is sold for Rs. 3858.6:
Profit = Selling Price - Cost Price
Profit = 3858.6 - 3270
Profit = 588.6

### Step 7: Calculate Profit Percentage
Profit Percentage can be calculated using the formula:
Profit Percentage = (Profit / Cost Price) * 100
Profit Percentage = (588.6 / 3270) * 100
Profit Percentage ≈ 17.98%

### Final Answer
The profit percentage when the article is sold for Rs. 3858.6 is approximately **17.98%**.

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