A man sells two pipes for Rs 12 each. On one he gains 20% and on the other he loses 20%. Find the profit or loss in the whole transaction.

Options

A. no loss no gain
B. Profit of Rs 1
C. loss of Rs 1
D. Profit of Rs 3

Answer

To solve the problem of finding the overall profit or loss when a man sells two pipes, one at a gain of 20% and the other at a loss of 20%, we can follow these steps:

### Step 1: Determine the Selling Price (SP) of each pipe
The selling price of each pipe is given as Rs 12.

### Step 2: Calculate the Cost Price (CP) of the first pipe
Let the cost price of the first pipe be \( CP_1 \).
Since there is a gain of 20%, we can use the formula:
\[ SP = CP + \text{Profit} \]
Where Profit = 20% of \( CP_1 \):
\[ SP = CP_1 + 0.20 \times CP_1 = 1.20 \times CP_1 \]
Substituting the selling price:
\[ 12 = 1.20 \times CP_1 \]
To find \( CP_1 \):
\[ CP_1 = \frac{12}{1.20} = 10 \]

### Step 3: Calculate the Cost Price (CP) of the second pipe
Let the cost price of the second pipe be \( CP_2 \).
Since there is a loss of 20%, we can use the formula:
\[ SP = CP - \text{Loss} \]
Where Loss = 20% of \( CP_2 \):
\[ SP = CP_2 - 0.20 \times CP_2 = 0.80 \times CP_2 \]
Substituting the selling price:
\[ 12 = 0.80 \times CP_2 \]
To find \( CP_2 \):
\[ CP_2 = \frac{12}{0.80} = 15 \]

### Step 4: Calculate the total Cost Price (CP) and Selling Price (SP)
Total Cost Price:
\[ \text{Total CP} = CP_1 + CP_2 = 10 + 15 = 25 \]

Total Selling Price:
\[ \text{Total SP} = 12 + 12 = 24 \]

### Step 5: Determine the overall profit or loss
To find the overall profit or loss, we subtract the total cost price from the total selling price:
\[ \text{Profit or Loss} = \text{Total SP} - \text{Total CP} = 24 - 25 = -1 \]
This indicates a loss of Rs 1.

### Conclusion
The man incurs a loss of Rs 1 in the whole transaction.

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