A man bought a number of oranges at 11 for a rupee and an equal number at 9 for a rupee. He mixed the two and sold at 10 for a rupee. Find the profit or loss percentage

Options

A. 1% loss
B. 2% loss
C. 2% loss
D. 2% profit

Answer

To solve the problem step by step, we will calculate the cost price (CP) of the oranges, the selling price (SP), and then find the profit or loss percentage.

### Step 1: Determine the Cost Price of Oranges
1. **Calculate the cost of oranges bought at different rates:**
- The man buys 11 oranges for Rs. 1.
- The man buys 9 oranges for Rs. 1.

To make the quantities equal, we can find a common multiple of 11 and 9. The least common multiple (LCM) of 11 and 9 is 99.

2. **Calculate the number of oranges bought:**
- For the first type (11 oranges for Rs. 1):
- He buys \( \frac{99}{11} = 9 \) sets of 11 oranges.
- Total oranges = \( 9 \times 11 = 99 \)
- Total cost = \( 9 \times 1 = Rs. 9 \)

- For the second type (9 oranges for Rs. 1):
- He buys \( \frac{99}{9} = 11 \) sets of 9 oranges.
- Total oranges = \( 11 \times 9 = 99 \)
- Total cost = \( 11 \times 1 = Rs. 11 \)

3. **Calculate the total cost price (CP):**
- Total CP = Cost of first type + Cost of second type
- Total CP = \( 9 + 11 = Rs. 20 \)

### Step 2: Determine the Selling Price of Oranges
1. **Calculate the selling price (SP):**
- He sells the mixed oranges at 10 for Rs. 1.
- Total number of oranges = 99 (from the first type) + 99 (from the second type) = 198 oranges.
- Selling price for 198 oranges = \( \frac{198}{10} = Rs. 19.8 \)

### Step 3: Calculate Profit or Loss
1. **Determine profit or loss:**
- Total CP = Rs. 20
- Total SP = Rs. 19.8
- Since SP < CP, there is a loss.

2. **Calculate the loss:**
- Loss = CP - SP = \( 20 - 19.8 = Rs. 0.2 \)

### Step 4: Calculate Loss Percentage
1. **Calculate the loss percentage:**
- Loss Percentage = \( \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \)
- Loss Percentage = \( \left( \frac{0.2}{20} \right) \times 100 = 1\% \)

### Final Answer
The loss percentage is **1%**.

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