To solve the problem step by step, we will first analyze the situation and then calculate the overall profit or loss percentage.
### Step 1: Understand the Selling Prices
Ajay sold two motorbikes for Rs 40,000 each.
- Selling Price (SP) of Motorbike 1 = Rs 40,000
- Selling Price (SP) of Motorbike 2 = Rs 40,000
### Step 2: Calculate the Cost Price for Each Motorbike
1. **Motorbike 1**: Sold at a 20% profit.
- Let the Cost Price (CP) of Motorbike 1 be \( CP_1 \).
- Selling Price = Cost Price + Profit
- Profit = 20% of \( CP_1 \) = \( \frac{20}{100} \times CP_1 = 0.2 \times CP_1 \)
- Therefore, \( SP_1 = CP_1 + 0.2 \times CP_1 = 1.2 \times CP_1 \)
- Setting the selling price equal to Rs 40,000:
\[
1.2 \times CP_1 = 40,000
\]
- Solving for \( CP_1 \):
\[
CP_1 = \frac{40,000}{1.2} = 33,333.33
\]
2. **Motorbike 2**: Sold at a 20% loss.
- Let the Cost Price (CP) of Motorbike 2 be \( CP_2 \).
- Selling Price = Cost Price - Loss
- Loss = 20% of \( CP_2 \) = \( \frac{20}{100} \times CP_2 = 0.2 \times CP_2 \)
- Therefore, \( SP_2 = CP_2 - 0.2 \times CP_2 = 0.8 \times CP_2 \)
- Setting the selling price equal to Rs 40,000:
\[
0.8 \times CP_2 = 40,000
\]
- Solving for \( CP_2 \):
\[
CP_2 = \frac{40,000}{0.8} = 50,000
\]
### Step 3: Calculate Total Cost Price and Total Selling Price
- Total Cost Price (CP) = \( CP_1 + CP_2 \)
\[
CP = 33,333.33 + 50,000 = 83,333.33
\]
- Total Selling Price (SP) = \( SP_1 + SP_2 \)
\[
SP = 40,000 + 40,000 = 80,000
\]
### Step 4: Calculate Overall Profit or Loss
- Since the total selling price is less than the total cost price, we have a loss.
- Loss = Total Cost Price - Total Selling Price
\[
Loss = 83,333.33 - 80,000 = 3,333.33
\]
### Step 5: Calculate the Loss Percentage
- Loss Percentage = \( \left( \frac{Loss}{Total CP} \right) \times 100 \)
\[
Loss \% = \left( \frac{3,333.33}{83,333.33} \right) \times 100 \approx 4\%
\]
### Final Answer
Ajay incurred a loss of approximately **4%** in the whole transaction.
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