An article is sold for 500 and hence a loss is incurred. Had the article been sold for 700 the shopkeeper would have gained three times the former loss. What is the cost price of the article?

Options

A. Rs. 525
B. Rs. 550
C. Rs. 600
D. Rs. 650

Answer

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

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

### Step 2: Determine the loss incurred when sold for Rs 500
The loss incurred when the article is sold for Rs 500 can be expressed as:
\[ \text{Loss} (L) = \text{Cost Price} - \text{Selling Price} = X - 500 \]

### Step 3: Determine the gain if sold for Rs 700
If the article is sold for Rs 700, the gain can be expressed as:
\[ \text{Gain} = \text{Selling Price} - \text{Cost Price} = 700 - X \]

### Step 4: Set up the equation based on the problem statement
According to the problem, if the article is sold for Rs 700, the gain would be three times the former loss. Therefore, we can write:
\[ 700 - X = 3 \times (X - 500) \]

### Step 5: Simplify the equation
Now, let's simplify the equation:
\[ 700 - X = 3X - 1500 \]

### Step 6: Rearrange the equation
Rearranging gives:
\[ 700 + 1500 = 3X + X \]
\[ 2200 = 4X \]

### Step 7: Solve for \( X \)
Now, divide both sides by 4:
\[ X = \frac{2200}{4} = 550 \]

### Step 8: Conclusion
The cost price of the article is Rs 550.

---