A trader sells two cycles at Rs. 1188 each and gains 10% on the first and loses 10% on the second. What is the profit or loss percent on the whole ?

Question

Accepted Answer

To determine the overall profit or loss percentage when a trader sells two cycles at Rs. 1188 each, with a 10% gain on the first cycle and a 10% loss on the second cycle, we need to calculate the cost price of each cycle and then find the net effect.

1. **Calculating the Cost Price of the First Cycle:**
   - Selling Price (SP) of the first cycle = Rs. 1188
   - Gain = 10%
   - Let the Cost Price (CP) of the first cycle be Rs. x.
   - Using the formula for gain: SP = CP + (Gain% of CP)
   - 1188 = x + (10/100)x
   - 1188 = 1.1x
   - x = 1188 / 1.1
   - x = Rs. 1080

2. **Calculating the Cost Price of the Second Cycle:**
   - Selling Price (SP) of the second cycle = Rs. 1188
   - Loss = 10%
   - Let the Cost Price (CP) of the second cycle be Rs. y.
   - Using the formula for loss: SP = CP - (Loss% of CP)
   - 1188 = y - (10/100)y
   - 1188 = 0.9y
   - y = 1188 / 0.9
   - y = Rs. 1320

3. **Calculating the Total Cost Price and Total Selling Price:**
   - Total CP = CP of first cycle + CP of second cycle = Rs. 1080 + Rs. 1320 = Rs. 2400
   - Total SP = SP of first cycle + SP of second cycle = Rs. 1188 + Rs. 1188 = Rs. 2376

4. **Calculating the Overall Profit or Loss:**
   - Loss = Total CP - Total SP = Rs. 2400 - Rs. 2376 = Rs. 24
   - Loss Percentage = (Loss / Total CP) * 100 = (24 / 2400) * 100 = 1%

Therefore, the trader incurs a 1% loss on the whole transaction, which supports Option 1 as the correct answer.

**Explanation for Incorrect Options:**

- **Option 2 (1% gain):** This is incorrect because the calculations show a loss, not a gain. 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 difference between the total cost price and total selling price results in a 1% loss.

- **Option 4 (No loss no gain):** This is incorrect because there is a clear loss of Rs. 24, which translates to a 1% loss. The total selling price is less than the total cost price, indicating a loss.

In conclusion, the correct answer is Option 1, which indicates a 1% loss on the whole transaction.