A shopkeeper sold two fans for Rs. 1140 each. One he gains 14%, while on the other he loses 5%. Calculate his gain or loss percent in the whole transaction.

Answer

To solve the problem step-by-step, we will calculate the cost price of each fan based on the selling price and the profit or loss percentage, and then determine the overall gain or loss.

### Step 1: Calculate the Cost Price of the First Fan
- **Selling Price (SP) of the first fan** = Rs. 1140
- **Gain Percentage** = 14%

Using the formula for cost price when there is a gain:
\[ \text{Cost Price (CP)} = \frac{100}{100 + \text{Gain Percentage}} \times \text{SP} \]
Substituting the values:
\[ \text{CP of first fan} = \frac{100}{100 + 14} \times 1140 = \frac{100}{114} \times 1140 \]
Calculating:
\[ \text{CP of first fan} = 1000 \]

### Step 2: Calculate the Cost Price of the Second Fan
- **Selling Price (SP) of the second fan** = Rs. 1140
- **Loss Percentage** = 5%

Using the formula for cost price when there is a loss:
\[ \text{Cost Price (CP)} = \frac{100}{100 - \text{Loss Percentage}} \times \text{SP} \]
Substituting the values:
\[ \text{CP of second fan} = \frac{100}{100 - 5} \times 1140 = \frac{100}{95} \times 1140 \]
Calculating:
\[ \text{CP of second fan} = 1200 \]

### Step 3: Calculate Total Selling Price (SP) and Total Cost Price (CP)
- **Total Selling Price (SP)** = SP of first fan + SP of second fan
\[ \text{Total SP} = 1140 + 1140 = 2280 \]

- **Total Cost Price (CP)** = CP of first fan + CP of second fan
\[ \text{Total CP} = 1000 + 1200 = 2200 \]

### Step 4: Calculate Overall Gain or Loss
- **Gain or Loss** = Total SP - Total CP
\[ \text{Gain or Loss} = 2280 - 2200 = 80 \]

### Step 5: Calculate Gain or Loss Percentage
Using the formula for gain or loss percentage:
\[ \text{Gain or Loss Percentage} = \left(\frac{\text{Gain or Loss}}{\text{Total CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Gain Percentage} = \left(\frac{80}{2200}\right) \times 100 \approx 3.64\% \]

### Final Result
The shopkeeper has a gain of approximately **3.64%** in the whole transaction.

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