Raju sold two fans for Rs. 990 each. On selling one fan, he had a gain of 10% and on selling other fan, he had a loss of 10%. Find his gain or loss percent in the whole transaction :

Question

Accepted Answer

To determine Raju's overall gain or loss percentage from selling the two fans, we need to analyze the transactions individually and then combine the results.

1. **First Fan:**
   - Selling Price (SP) = Rs. 990
   - Gain = 10%
   - Let the Cost Price (CP) be Rs. x.
   - Using the gain formula: SP = CP + Gain
     $$
     990 = x + 0.10x = 1.10x
     $$
     $$
     x = \frac{990}{1.10} = 900
     $$
   - Therefore, the cost price of the first fan is Rs. 900.

2. **Second Fan:**
   - Selling Price (SP) = Rs. 990
   - Loss = 10%
   - Let the Cost Price (CP) be Rs. y.
   - Using the loss formula: SP = CP - Loss
     $$
     990 = y - 0.10y = 0.90y
     $$
     $$
     y = \frac{990}{0.90} = 1100
     $$
   - Therefore, the cost price of the second fan is Rs. 1100.

3. **Overall Transaction:**
   - Total Cost Price (CP) = Rs. 900 + Rs. 1100 = Rs. 2000
   - Total Selling Price (SP) = Rs. 990 + Rs. 990 = Rs. 1980

4. **Calculate Gain or Loss:**
   - Loss = Total CP - Total SP = Rs. 2000 - Rs. 1980 = Rs. 20
   - Loss Percentage = $\frac{\text{Loss}}{\text{Total CP}} \times 100$
     $$
     \text{Loss Percentage} = \frac{20}{2000} \times 100 = 1\%
     $$

Therefore, Raju incurred a 1% loss in the whole transaction, which supports Option 1 as the correct answer.

**Explanation of Incorrect Options:**

- **Option 2 (1% profit):** This is incorrect because the calculations clearly show a loss, not a profit. The total selling price is less than the total cost price, resulting in a loss.
  
- **Option 3 (2% loss):** This is incorrect because the calculated loss percentage is 1%, not 2%. The loss of Rs. 20 on a total cost price of Rs. 2000 results in a 1% loss.

- **Option 4 (2% loss):** This is a repetition of Option 3 and is incorrect for the same reason. The actual loss percentage is 1%, not 2%.

Thus, the correct answer is Option 1, which indicates a 1% loss.