An article is sold for Rs 500 and hence a merchant loses some amount. Had the article been sold for Rs 700, the merchant would have gained three times the former loss. The cost price of the article is:

Options

A. Rs 525
B. Rs 500
C. Rs 600
D. Rs 650

Answer

To solve the problem step by step, we will use algebra to find the cost price of the article.

### Step-by-Step Solution:

1. **Define Variables:**
Let the cost price of the article be \( C \).

2. **Selling Prices:**
- The selling price when the article is sold for Rs 500 is \( SP_1 = 500 \).
- The selling price when the article is sold for Rs 700 is \( SP_2 = 700 \).

3. **Loss Calculation:**
When the article is sold for Rs 500, the merchant incurs a loss. Let the loss be \( X \).
According to the formula for selling price:
\[ SP_1 = C - X \]
Substituting the values:
\[ 500 = C - X \quad \text{(Equation 1)} \]

4. **Gain Calculation:**
If the article is sold for Rs 700, the merchant gains three times the former loss. Thus, the gain is \( 3X \).
The formula for selling price in this case is:
\[ SP_2 = C + \text{Gain} \]
Substituting the values:
\[ 700 = C + 3X \quad \text{(Equation 2)} \]

5. **Setting Up the Equations:**
Now we have two equations:
- From Equation 1: \( C - X = 500 \)
- From Equation 2: \( C + 3X = 700 \)

6. **Solving the Equations:**
We can rearrange Equation 1 to express \( C \):
\[ C = 500 + X \quad \text{(Equation 3)} \]
Now substitute Equation 3 into Equation 2:
\[ 700 = (500 + X) + 3X \]
Simplifying this gives:
\[ 700 = 500 + 4X \]
Subtracting 500 from both sides:
\[ 200 = 4X \]
Dividing both sides by 4:
\[ X = 50 \]

7. **Finding the Cost Price:**
Now substitute the value of \( X \) back into Equation 3:
\[ C = 500 + 50 = 550 \]

8. **Conclusion:**
Therefore, the cost price of the article is:
\[ \boxed{550} \]