A man sold two houses for ? 96000 each. In the sale of the first house, he incurred 20% profit and in the sale of the second,he incurred 20% loss,what is the gain or loss percentage in total?

Options

A. 6% gain
B. 6% loss
C. 4% gain
D. 4% loss

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Selling Price (SP)
The selling price of each house is given as ₹96,000.

### Step 2: Calculate the Cost Price (CP) of the First House
The first house is sold at a profit of 20%.
Let the cost price of the first house be CP1.

Using the formula for profit:
\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]
We can express profit as:
\[ \text{Profit} = \frac{20}{100} \times \text{CP1} = 0.2 \times \text{CP1} \]
Thus, we can write:
\[ 96,000 = \text{CP1} + 0.2 \times \text{CP1} \]
This simplifies to:
\[ 96,000 = 1.2 \times \text{CP1} \]
Now, solving for CP1:
\[ \text{CP1} = \frac{96,000}{1.2} = 80,000 \]

### Step 3: Calculate the Cost Price (CP) of the Second House
The second house is sold at a loss of 20%.
Let the cost price of the second house be CP2.

Using the formula for loss:
\[ \text{Selling Price} = \text{Cost Price} - \text{Loss} \]
We can express loss as:
\[ \text{Loss} = \frac{20}{100} \times \text{CP2} = 0.2 \times \text{CP2} \]
Thus, we can write:
\[ 96,000 = \text{CP2} - 0.2 \times \text{CP2} \]
This simplifies to:
\[ 96,000 = 0.8 \times \text{CP2} \]
Now, solving for CP2:
\[ \text{CP2} = \frac{96,000}{0.8} = 120,000 \]

### Step 4: Calculate Total Cost Price (CP) and Total Selling Price (SP)
Now, we can find the total cost price and total selling price:
- Total CP = CP1 + CP2 = 80,000 + 120,000 = 200,000
- Total SP = Selling Price of both houses = 96,000 + 96,000 = 192,000

### Step 5: Calculate Overall Gain or Loss
To find out if there is a gain or loss, we compare total SP and total CP:
\[ \text{Total Loss} = \text{Total CP} - \text{Total SP} = 200,000 - 192,000 = 8,000 \]

### Step 6: Calculate Loss Percentage
The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{8,000}{200,000} \right) \times 100 = 4\% \]

### Final Answer
The overall loss percentage is **4%**.

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