A trader sells two articles, one at a loss of 10% and another at a profit of 15% but finally there is no loss or gain. If the total sale price of these two article is Rs. 30,000, find the difference between their cost prices :

Options

A. Rs. 5000
B. Rs. 6000
C. Rs. 7500
D. none of these

Answer

To solve the problem step by step, let's denote the cost price of the first article as \( x \) and the cost price of the second article as \( y \).

### Step 1: Set up the equations based on the problem statement.
We know that the total sale price of both articles is Rs. 30,000. Therefore, we can write the equation:
\[ x + y = 30,000 \quad (1) \]

### Step 2: Determine the sale prices based on profit and loss.
The first article is sold at a loss of 10%, so the sale price of the first article can be expressed as:
\[ \text{Sale Price of Article 1} = x - 0.1x = 0.9x \]

The second article is sold at a profit of 15%, so the sale price of the second article can be expressed as:
\[ \text{Sale Price of Article 2} = y + 0.15y = 1.15y \]

### Step 3: Set up the equation for total sale price.
The total sale price of both articles is given by:
\[ 0.9x + 1.15y = 30,000 \quad (2) \]

### Step 4: Solve the equations simultaneously.
From equation (1), we can express \( y \) in terms of \( x \):
\[ y = 30,000 - x \quad (3) \]

Now, substitute equation (3) into equation (2):
\[ 0.9x + 1.15(30,000 - x) = 30,000 \]

### Step 5: Simplify and solve for \( x \).
Expanding the equation:
\[ 0.9x + 34,500 - 1.15x = 30,000 \]
Combining like terms:
\[ -0.25x + 34,500 = 30,000 \]
Subtracting 34,500 from both sides:
\[ -0.25x = 30,000 - 34,500 \]
\[ -0.25x = -4,500 \]
Dividing both sides by -0.25:
\[ x = \frac{-4,500}{-0.25} = 18,000 \]

### Step 6: Find \( y \) using the value of \( x \).
Substituting \( x \) back into equation (3):
\[ y = 30,000 - 18,000 = 12,000 \]

### Step 7: Calculate the difference between the cost prices.
The difference between the cost prices \( x \) and \( y \) is:
\[ x - y = 18,000 - 12,000 = 6,000 \]

### Conclusion:
The difference between the cost prices of the two articles is Rs. 6,000.

---