A man sells two pipes at Rs. 12 each. He gains 20% on one and loses 20% on the other. find 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 pipe based on the given selling price and profit/loss percentages, and then determine the overall gain or loss percentage.

### Step 1: Calculate the Cost Price of the First Pipe
- **Given**: Selling Price (SP) of the first pipe = Rs. 12, Profit Percentage = 20%
- **Formula**:
\[ \text{SP} = \left( \frac{100 + \text{Profit Percentage}}{100} \right) \times \text{CP} \]
- **Substituting the values**:
\[ 12 = \left( \frac{100 + 20}{100} \right) \times \text{CP1} \]
\[ 12 = \left( \frac{120}{100} \right) \times \text{CP1} \]
\[ 12 = 1.2 \times \text{CP1} \]
- **Solving for CP1**:
\[ \text{CP1} = \frac{12}{1.2} = 10 \text{ Rs.} \]

### Step 2: Calculate the Cost Price of the Second Pipe
- **Given**: Selling Price (SP) of the second pipe = Rs. 12, Loss Percentage = 20%
- **Formula**:
\[ \text{SP} = \left( \frac{100 - \text{Loss Percentage}}{100} \right) \times \text{CP} \]
- **Substituting the values**:
\[ 12 = \left( \frac{100 - 20}{100} \right) \times \text{CP2} \]
\[ 12 = \left( \frac{80}{100} \right) \times \text{CP2} \]
\[ 12 = 0.8 \times \text{CP2} \]
- **Solving for CP2**:
\[ \text{CP2} = \frac{12}{0.8} = 15 \text{ Rs.} \]

### Step 3: Calculate Total Cost Price and Total Selling Price
- **Total Cost Price (CP)**:
\[ \text{Total CP} = \text{CP1} + \text{CP2} = 10 + 15 = 25 \text{ Rs.} \]
- **Total Selling Price (SP)**:
\[ \text{Total SP} = 12 + 12 = 24 \text{ Rs.} \]

### Step 4: Determine Gain or Loss
- **Loss**:
\[ \text{Loss} = \text{Total CP} - \text{Total SP} = 25 - 24 = 1 \text{ Rs.} \]

### Step 5: Calculate Loss Percentage
- **Loss Percentage**:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 \]
\[ \text{Loss Percentage} = \left( \frac{1}{25} \right) \times 100 = 4\% \]

### Final Answer
The man incurs a loss of **4%** in the whole transaction.

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