Profit obtained on selling an article for Rs 540 is equal to the loss incurred on selling the article for Rs.370. If selling price is Rs.910. Then what is the profit percentage ?

Options

A. a)16`/3`
B. b)33`1/3`
C. c)50
D. d)100

Answer

To solve the problem step by step, let's denote the cost price (CP) of the article as \( x \).

### Step 1: Understand the given information
- Selling Price (SP) when profit is made: Rs 540
- Selling Price (SP) when loss is incurred: Rs 370
- Selling Price (SP) for profit percentage calculation: Rs 910

### Step 2: Set up the equations based on profit and loss
1. **Profit when sold for Rs 540**:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = 540 - x \]

2. **Loss when sold for Rs 370**:
\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} = x - 370 \]

### Step 3: Equate profit and loss
According to the problem, the profit obtained on selling for Rs 540 is equal to the loss incurred on selling for Rs 370:
\[ 540 - x = x - 370 \]

### Step 4: Solve for \( x \)
Rearranging the equation:
\[ 540 + 370 = 2x \]
\[ 910 = 2x \]
\[ x = \frac{910}{2} = 455 \]

So, the cost price (CP) of the article is Rs 455.

### Step 5: Calculate the profit when sold for Rs 910
Now, we need to find the profit when the article is sold for Rs 910:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = 910 - 455 = 455 \]

### Step 6: Calculate the profit percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{455}{455} \right) \times 100 = 100\% \]

### Final Answer
The profit percentage is **100%**.

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