Two articles are sold for Rs. 10,005 each. On one, the seller gains 15% and on the other, he loses 13%. What is his overall gain or loss percent, correct to two decimal places?

Options

A. `0.94%` gain
B. `1.42%` gain
C. `1.42%` loss
D. `0.94%` loss

Answer

To solve the problem step by step, we will calculate the cost price (CP) of each article based on the selling price (SP) and the gain or loss percentage, and then find the overall gain or loss percentage.

### Step 1: Calculate the Cost Price of the First Article
Given:
- Selling Price (SP) of the first article = Rs. 10,005
- Gain Percentage = 15%

Using the formula for Selling Price:
\[ SP = CP + (Gain \% \times CP) \]
We can express this as:
\[ SP = CP \times \left(1 + \frac{Gain \%}{100}\right) \]
Substituting the values:
\[ 10,005 = CP \times \left(1 + \frac{15}{100}\right) \]
\[ 10,005 = CP \times \left(1 + 0.15\right) \]
\[ 10,005 = CP \times 1.15 \]
Now, solving for CP:
\[ CP = \frac{10,005}{1.15} \]
Calculating:
\[ CP = \frac{10,005}{1.15} \approx 8,700 \]

### Step 2: Calculate the Cost Price of the Second Article
Given:
- Selling Price (SP) of the second article = Rs. 10,005
- Loss Percentage = 13%

Using the formula for Selling Price:
\[ SP = CP - (Loss \% \times CP) \]
We can express this as:
\[ SP = CP \times \left(1 - \frac{Loss \%}{100}\right) \]
Substituting the values:
\[ 10,005 = CP \times \left(1 - \frac{13}{100}\right) \]
\[ 10,005 = CP \times \left(1 - 0.13\right) \]
\[ 10,005 = CP \times 0.87 \]
Now, solving for CP:
\[ CP = \frac{10,005}{0.87} \]
Calculating:
\[ CP = \frac{10,005}{0.87} \approx 11,500 \]

### Step 3: Calculate Total Cost Price and Total Selling Price
Now we can find the total cost price (CP) and total selling price (SP) for both articles:
- Total CP = CP of first article + CP of second article
\[ Total \, CP = 8,700 + 11,500 = 20,200 \]

- Total SP = SP of first article + SP of second article
\[ Total \, SP = 10,005 + 10,005 = 20,010 \]

### Step 4: Calculate Overall Gain or Loss
Now we can calculate the overall gain or loss:
- Net Loss = Total CP - Total SP
\[ Net \, Loss = 20,200 - 20,010 = 190 \]

### Step 5: Calculate Loss Percentage
To find the loss percentage:
\[ Loss \% = \left(\frac{Net \, Loss}{Total \, CP}\right) \times 100 \]
Substituting the values:
\[ Loss \% = \left(\frac{190}{20,200}\right) \times 100 \]
Calculating:
\[ Loss \% \approx 0.94\% \]

### Final Answer
The overall loss percentage is approximately **0.94%**.