A trade suffered a loss of 15% by selling ans article Had the sold it for Rs 100 More , he would have made a profit of 5% .find the article cost price.

Answer

To find the cost price of the article, let's break down the problem step by step.

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

### Step 2: Calculate the selling price at a loss of 15%
If the trader suffers a loss of 15%, the selling price (SP) can be calculated as:
\[ SP = CP - \text{Loss} \]
The loss is 15% of the cost price:
\[ \text{Loss} = 15\% \text{ of } x = \frac{15}{100} \times x = 0.15x \]
Thus, the selling price becomes:
\[ SP = x - 0.15x = 0.85x \]

### Step 3: Calculate the selling price for a profit of 5%
If he had sold the article for Rs. 100 more, he would have made a profit of 5%. The selling price at a profit of 5% is:
\[ SP' = CP + \text{Profit} \]
The profit is 5% of the cost price:
\[ \text{Profit} = 5\% \text{ of } x = \frac{5}{100} \times x = 0.05x \]
Thus, the selling price with profit becomes:
\[ SP' = x + 0.05x = 1.05x \]

### Step 4: Set up the equation
According to the problem, selling the article for Rs. 100 more than the selling price at a loss gives:
\[ SP' = SP + 100 \]
Substituting the values we calculated:
\[ 1.05x = 0.85x + 100 \]

### Step 5: Solve for x
Now, we can solve for x:
\[ 1.05x - 0.85x = 100 \]
\[ 0.20x = 100 \]
\[ x = \frac{100}{0.20} \]
\[ x = 500 \]

### Conclusion
The cost price of the article is Rs. 500.

---