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 articles is ₹ 30,000 find the difference between their cost prices :

Options

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

Answer

To solve the problem step by step, we will denote the cost prices of the two articles as \( CP_1 \) and \( CP_2 \).

### Step 1: Define the Cost Prices
Let:
- \( CP_1 \) = Cost Price of the first article
- \( CP_2 \) = Cost Price of the second article

### Step 2: Calculate Selling Prices
The first article is sold at a loss of 10%, so its selling price \( SP_1 \) is:
\[ SP_1 = CP_1 - 0.10 \times CP_1 = 0.90 \times CP_1 \]

The second article is sold at a profit of 15%, so its selling price \( SP_2 \) is:
\[ SP_2 = CP_2 + 0.15 \times CP_2 = 1.15 \times CP_2 \]

### Step 3: Total Selling Price
According to the problem, the total selling price of both articles is ₹30,000:
\[ SP_1 + SP_2 = 30000 \]
Substituting the expressions for \( SP_1 \) and \( SP_2 \):
\[ 0.90 \times CP_1 + 1.15 \times CP_2 = 30000 \]

### Step 4: No Loss No Gain Condition
Since there is no loss or gain overall, the loss on the first article is equal to the profit on the second article:
\[ 0.10 \times CP_1 = 0.15 \times CP_2 \]
Rearranging gives:
\[ CP_1 = \frac{0.15}{0.10} \times CP_2 = 1.5 \times CP_2 \]

### Step 5: Substitute \( CP_1 \) in the Selling Price Equation
Now, substitute \( CP_1 \) in the total selling price equation:
\[ 0.90 \times (1.5 \times CP_2) + 1.15 \times CP_2 = 30000 \]
This simplifies to:
\[ 1.35 \times CP_2 + 1.15 \times CP_2 = 30000 \]
\[ 2.50 \times CP_2 = 30000 \]

### Step 6: Solve for \( CP_2 \)
Now, divide both sides by 2.50:
\[ CP_2 = \frac{30000}{2.50} = 12000 \]

### Step 7: Find \( CP_1 \)
Using \( CP_1 = 1.5 \times CP_2 \):
\[ CP_1 = 1.5 \times 12000 = 18000 \]

### Step 8: Calculate the Difference Between Cost Prices
Now, we can find the difference between the cost prices:
\[ \text{Difference} = CP_1 - CP_2 = 18000 - 12000 = 6000 \]

### Final Answer
The difference between the cost prices of the two articles is ₹6000.

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