If 11 oranges are bought for Rs. 10 and sold 10 oranges for Rs. 11. What is the gain in percentage?

Options

A. 11 `%`
B. 21 `%`
C. 25`%`
D. 28`%`

Answer

To solve the problem of finding the gain percentage when 11 oranges are bought for Rs. 10 and sold for Rs. 11 for 10 oranges, we can follow these steps:

### Step 1: Determine the Cost Price (CP) and Selling Price (SP)
- **Cost Price (CP)**: The cost of 11 oranges is Rs. 10.
- **Selling Price (SP)**: The selling price for 10 oranges is Rs. 11.

### Step 2: Calculate the Cost Price for 110 Oranges
To simplify calculations, we can scale the quantities:
- If we buy 110 oranges, we can find the total cost:
\[ \text{CP for 110 oranges} = \left(\frac{10}{11}\right) \times 110 = 100 \text{ Rs.} \]

### Step 3: Calculate the Selling Price for 110 Oranges
Now, let's calculate the selling price for 110 oranges:
- If we sell 110 oranges, we can find the total selling price:
\[ \text{SP for 110 oranges} = \left(\frac{11}{10}\right) \times 110 = 121 \text{ Rs.} \]

### Step 4: Calculate the Profit
Now, we can find the profit made by selling the oranges:
\[ \text{Profit} = \text{SP} - \text{CP} = 121 \text{ Rs.} - 100 \text{ Rs.} = 21 \text{ Rs.} \]

### Step 5: Calculate the Gain Percentage
Finally, we can calculate the gain percentage using the formula:
\[ \text{Gain Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 = \left(\frac{21}{100}\right) \times 100 = 21\% \]

### Conclusion
The gain percentage is **21%**.

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