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 per cent?

Options

A. `16(2)/(3)`
B. `33(1)/(3)`
C. 50
D. 100

Answer

To solve the problem step by step, we need to find the cost price (CP) of the article first, and then calculate the profit percentage based on the selling price (SP) of Rs. 910.

### Step 1: Define the variables
Let the cost price of the article be \( CP \).

### Step 2: Calculate profit and loss
According to the problem:
- Selling price when profit is made: \( SP_1 = Rs. 540 \)
- Selling price when loss is incurred: \( SP_2 = Rs. 370 \)

The profit when sold for Rs. 540 can be expressed as:
\[ \text{Profit} = SP_1 - CP = 540 - CP \]

The loss when sold for Rs. 370 can be expressed as:
\[ \text{Loss} = CP - SP_2 = CP - 370 \]

### Step 3: Set up the equation
According to the problem, the profit obtained on selling for Rs. 540 is equal to the loss incurred on selling for Rs. 370:
\[ 540 - CP = CP - 370 \]

### Step 4: Solve for CP
Now, we can solve the equation:
1. Rearranging gives:
\[ 540 + 370 = 2CP \]
\[ 910 = 2CP \]
2. Dividing both sides by 2:
\[ CP = \frac{910}{2} = 455 \]

### Step 5: Calculate the profit when selling for Rs. 910
Now that we have the cost price, we can find the profit when the article is sold for Rs. 910:
\[ \text{Profit} = SP - CP = 910 - 455 = 455 \]

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

### Final Answer
The profit percentage when the article is sold for Rs. 910 is **100%**.

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