Let's break down the problem step by step to determine Ankit's gain or loss percentage in the whole transaction where he sold two jeans for ₹990 each, with one making a gain of 10% and the other making a loss of 10%.
### Step-by-Step Solution:
1. Identify the selling prices and percentages:
- Selling price of each jean: ₹990
- Profit percentage on one jean: 10%
- Loss percentage on the other jean: 10%
2. Calculate the cost prices for each jean:
- For the jean sold at a 10% profit:
- Let the cost price be \( C_1 \).
- The selling price after 10% profit is \( C_1 \times (1 + \frac{10}{100}) \).
- Given selling price is ₹990, so we write the equation:
[tex]\[
990 = C_1 \times 1.1
\][/tex]
- Solving for \( C_1 \):
[tex]\[
C_1 = \frac{990}{1.1} = 900
\][/tex]
- For the jean sold at a 10% loss:
- Let the cost price be \( C_2 \).
- The selling price after 10% loss is \( C_2 \times (1 - \frac{10}{100}) \).
- Given selling price is ₹990, so we write the equation:
[tex]\[
990 = C_2 \times 0.9
\][/tex]
- Solving for \( C_2 \):
[tex]\[
C_2 = \frac{990}{0.9} = 1100
\][/tex]
3. Calculate the total cost price and total selling price:
- Total cost price:
[tex]\[
\text{Total Cost Price} = C_1 + C_2 = 900 + 1100 = 2000
\][/tex]
- Total selling price:
[tex]\[
\text{Total Selling Price} = 990 + 990 = 1980
\][/tex]
4. Calculate the overall gain or loss:
- Gain or Loss:
[tex]\[
\text{Net Gain/Loss} = \text{Total Selling Price} - \text{Total Cost Price} = 1980 - 2000 = -20
\][/tex]
- A negative value indicates a loss.
5. Determine the gain or loss percentage:
- Loss percentage:
[tex]\[
\text{Loss Percentage} = \left( \frac{\text{Net Loss}}{\text{Total Cost Price}} \right) \times 100 = \left( \frac{-20}{2000} \right) \times 100 = -1\%
\][/tex]
So, Ankit had an overall loss of 1% in the whole transaction.
