A trademan sold an article at 20% loss. If the selling price of the article had been Rs.100 more the trademan would have grained 5% cost price of the article was
एक व्यापारी ने किसी वस्तु को 20% की हानि पर बेचा। यदि वस्तु का विक्रय मूल्य रू0 100 अधिक होता हो उस पर 5% का लाभ हुआ होता । वस्तु का क्रय मूल्य था

Options

A. Rs. 200
B. Rs. 125
C. Rs. 400
D. Rs. 250

Explanation

To solve the problem, we need to find the cost price (CP) of the article based on the information provided about the selling price (SP) and the profit/loss percentages. Let's break it down step by step.

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

### Step 2: Calculate Selling Price at 20% Loss
When the article is sold at a 20% loss, the selling price can be calculated as:
\[ SP = CP - (20\% \text{ of } CP) = x - 0.2x = 0.8x \]

### Step 3: Calculate Selling Price for 5% Profit
If the selling price had been Rs. 100 more, the selling price would be:
\[ SP_{new} = SP + 100 = 0.8x + 100 \]
With this new selling price, the trader would have made a 5% profit, which can be expressed as:
\[ SP_{new} = CP + (5\% \text{ of } CP) = x + 0.05x = 1.05x \]

### Step 4: Set Up the Equation
Now we can set the two expressions for the new selling price equal to each other:
\[ 0.8x + 100 = 1.05x \]

### Step 5: Solve for \( x \)
Rearranging the equation:
\[ 100 = 1.05x - 0.8x \]
\[ 100 = 0.25x \]
Now, solve for \( x \):
\[ x = \frac{100}{0.25} = 400 \]

### Conclusion
The cost price of the article is Rs. 400.