When Sulekha sells and article for Rs870, she earns a profit (in Rs) which is equal to twice the loss (in Rs) she incurs on selling it for Rs 450. To earn a profit of 15% , she should sell the article for (in Rs) .

Options

A. 667
B. 690
C. 676.5
D. 678.5

Answer

To solve the problem step by step, let's break it down:

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

### Step 2: Calculate Profit and Loss
When Sulekha sells the article for Rs 870, the profit she makes is:
\[ \text{Profit} = 870 - x \]

When she sells the article for Rs 450, the loss she incurs is:
\[ \text{Loss} = x - 450 \]

### Step 3: Set Up the Equation
According to the problem, the profit when selling for Rs 870 is equal to twice the loss when selling for Rs 450. Therefore, we can set up the equation:
\[ 870 - x = 2(x - 450) \]

### Step 4: Simplify the Equation
Expanding the equation:
\[ 870 - x = 2x - 900 \]
Rearranging gives:
\[ 870 + 900 = 2x + x \]
\[ 1770 = 3x \]

### Step 5: Solve for Cost Price
Now, divide both sides by 3:
\[ x = \frac{1770}{3} = 590 \]

### Step 6: Calculate the Selling Price for 15% Profit
To find the selling price (SP) for a profit of 15%, we use the formula:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where profit is 15% of CP:
\[ \text{Profit} = 0.15 \times 590 = 88.5 \]
Thus,
\[ \text{SP} = 590 + 88.5 = 678.5 \]

### Final Answer
Sulekha should sell the article for Rs 678.5 to earn a profit of 15%.

---