Profit and Loss – Equal selling price again with ±5%: A man sells two houses for Rs 7.81 lakhs each. On one he gains 5% and on the other he loses 5%. What is the overall percentage effect on the whole sale?

Introduction / Context:
This is the same structure as the classic equal selling price with opposite percentage changes. The result is a small net loss given by a^2 / 100.

Given Data / Assumptions:

• SP1 = SP2 = Rs 7.81 lakhs
• One item at +5%, the other at -5%

Concept / Approach:
For equal SP and opposite percentage of the same magnitude a, overall loss% = a^2 / 100.

Step-by-Step Solution:
a = 5Loss% = 5^2 / 100 = 25 / 100 = 0.25%

Verification / Alternative check:
Compute CP1 = SP / 1.05 and CP2 = SP / 0.95, then compare total CP with total SP; it will be a 0.25% loss.

Why Other Options Are Wrong:
0.25% gain and no profit contradict the identity. 2.5% and 1% are wrong magnitudes.

Common Pitfalls:
Assuming gains and losses cancel because they “average” to zero.

Final Answer:
0.25% loss