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

Question

Accepted Answer

To determine the gain percentage when 11 oranges are bought for Rs. 10 and sold 10 oranges for Rs. 11, we need to calculate the cost price (CP) and selling price (SP) for a single orange and then find the gain percentage.

1. **Calculate the Cost Price (CP) per Orange:**
   - 11 oranges are bought for Rs. 10.
   - Therefore, the cost price of 1 orange = Rs. 10 / 11.

2. **Calculate the Selling Price (SP) per Orange:**
   - 10 oranges are sold for Rs. 11.
   - Therefore, the selling price of 1 orange = Rs. 11 / 10.

3. **Calculate the Gain:**
   - Gain per orange = Selling Price per orange - Cost Price per orange
   - Gain per orange = (Rs. 11 / 10) - (Rs. 10 / 11)

4. **Calculate the Gain Percentage:**
   - Gain percentage = (Gain per orange / Cost Price per orange) × 100
   - Gain percentage = [(Rs. 11 / 10) - (Rs. 10 / 11)] / (Rs. 10 / 11) × 100

To simplify the calculation:
   - Gain per orange = (11/10) - (10/11) = (121 - 100) / 110 = 21/110
   - Gain percentage = (21/110) / (10/11) × 100
   - Gain percentage = (21/110) × (11/10) × 100
   - Gain percentage = 21%

Therefore, the gain percentage is 21%, which corresponds to Option 2.

**Explanation for Incorrect Options:**

- **Option 1 (11%):** This option is incorrect because the calculated gain percentage is 21%, not 11%. The calculation shows that the gain per orange is higher than what would result in an 11% gain.

- **Option 3 (25%):** This option is incorrect because the gain percentage calculation results in 21%, not 25%. The gain per orange does not support a 25% gain when the actual calculation is performed.

- **Option 4 (28%):** This option is incorrect because the gain percentage is calculated to be 21%, not 28%. The mathematical computation clearly shows a 21% gain, making 28% an overestimation.

In conclusion, the correct gain percentage is 21%, which is why Option 2 is the correct answer.