A man sold two houses for Rs. `7.81` lakhs each. On one he gained `5%` and on the other he lost `5%`. What per cent is the effect of the sale on the whole?

Options

A. `0.25%` loss
B. `0.25%` gain
C. `0.25%` loss
D. `25%` gain

Answer

To solve the problem, we need to find the overall effect of selling two houses, one at a gain of 5% and the other at a loss of 5%. Here’s a step-by-step breakdown of the solution:

### Step 1: Determine the Selling Price of Each House
The selling price of each house is given as Rs. 7.81 lakhs.

### Step 2: Calculate the Cost Price of Each House
Let’s denote:
- Selling Price (SP) = Rs. 7.81 lakhs
- Gain on the first house = 5%
- Loss on the second house = 5%

For the first house (with a gain of 5%):
- Let the Cost Price (CP) of the first house be \( CP_1 \).
- Using the formula for selling price with gain:
\[ SP = CP_1 + \left( \frac{5}{100} \times CP_1 \right) \]
\[ 7.81 = CP_1 \left( 1 + \frac{5}{100} \right) \]
\[ 7.81 = CP_1 \times 1.05 \]
\[ CP_1 = \frac{7.81}{1.05} \approx 7.44 \text{ lakhs} \]

For the second house (with a loss of 5%):
- Let the Cost Price (CP) of the second house be \( CP_2 \).
- Using the formula for selling price with loss:
\[ SP = CP_2 - \left( \frac{5}{100} \times CP_2 \right) \]
\[ 7.81 = CP_2 \left( 1 - \frac{5}{100} \right) \]
\[ 7.81 = CP_2 \times 0.95 \]
\[ CP_2 = \frac{7.81}{0.95} \approx 8.22 \text{ lakhs} \]

### Step 3: Calculate the Total Cost Price and Total Selling Price
- Total Cost Price (CP) = \( CP_1 + CP_2 \)
\[ CP = 7.44 + 8.22 = 15.66 \text{ lakhs} \]

- Total Selling Price (SP) = \( 7.81 + 7.81 = 15.62 \text{ lakhs} \)

### Step 4: Calculate the Overall Gain or Loss
- Overall Loss = Total CP - Total SP
\[ \text{Loss} = 15.66 - 15.62 = 0.04 \text{ lakhs} \]

### Step 5: Calculate the Percentage of Loss
- Percentage Loss = \( \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 \)
\[ \text{Percentage Loss} = \left( \frac{0.04}{15.66} \right) \times 100 \approx 0.255 \% \]

### Conclusion
The overall effect of the sale on the whole is approximately **0.25% loss**.

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